endobj 48 0 obj<> endobj 49 0 obj<> endobj 50 0 obj<> endobj 51 0 obj<>stream (c) spend his or her... Samira has a monthly income of $200 that she allocates among two goods: meat and potatoes. W@8c#��^cFw��.�j ���x��¹@�E�����s>��M��L5)Bʒ"r�Z=%L2\B�O*འ6�iҵҧ��vt3h7x3�8 °9�E���4[ vB %�����X��~[���Ԧ �k�J a.... A) Suppose an individual has preferences over two goods that can be represented by the utility function of u(x,y) = x^(1/2) y^(1/2), where 'x' and 'y' represent the quantities consumed of each good... Daniel consumes only xylophones (denote by x) and yoyos (denote by y). Margaret's preferences over video games (V) and pizza (Z) are represented by the utility function U(V, Z) = VZ, MUv = Z, and MUz = V. If the price of a videogame is 36 dollars, the price of a pizza... Georgina consumes only grapefruits and pineapples. Suppose that the price of good X is $10, the price of good Y is $20, and our income is $100. 0000011305 00000 n Utility Maximization Steps MPP 801 Fall, 2007 The MRS and the Cobb-Douglas Consider a two-good world, xand y. %%EOF Suppose there are two consumers, A and B, and two goods, X and Y. Suppose a consumer's utility function is U(X, Y) = X + 2Y. The utility that Ann receives by consuming food F and clothing C is given by U(F,C)= FC + F. Food costs $1 a unit, and clothing costs $2 a unit. Suppose Vivian has a utility function U = X^(0.4)Y^(0.6), which X and Y are two goods. Assume an individual has a utility function U(C, L) = 6 + CL. The solution to utility maximization problem (3) gives the consumer's choice of x and y, as a function of prices and income, which we denote by x ¤(px;py;M) and y¤(px;py;M). : For Dave, good 1 is a substitute for good 2. Consider the utility function U(x,y)=9x +18y. Solutions to Problem Set 2 Niccol o Lomys Spring 2016 Problem 1 Consider an economy in which there are two goods, 1and 2, whose prices are p 1 >0and p 2 >0, respectively. 0000023916 00000 n We extend the existing results in this literature in two directions. It is Saturday night, and Hanna is looking to maximize her utility by deciding how many Pop Tarts and Hot Pockets to purchase. If sneakers cost twice as much as shoes, he or she will: (a) buy only sneakers. If the subscription price for a Sports app is $2 per week, the subscription price of a game app is Si per week, and a student has $9 per week to spend. We develop a distributed solution to this problem that is amenable to online implementation. Suppose there are two goods, food, c, and leisure, L. The prevailing prices of c and L are p = $1/unit and w = $10/hr:, respectively. What is Bob's utility-maximizing choice between these two goods? A) Find the values of 'x' and 'y' which maximise utility subject to eh budgetary constraint 10x + 5y = 150. Jill's utility function is of the form: u(x_1,x_2) = x_1=x_2 Jill's budget constraint is of the fo... Each year, Shakira selects the quantity of doctor visits (x) and all other consumptions (y) that she will consume in order to maximize her utility. What are the values of A and B? What is the marginal rate of substitution? The price of a day trip (T) is $40 and the price of a pizza and a movie (M) is $20. Suppose that Madison has income of $7.00, the price of popcorn is $2.00, and the price of Coke is $1.50. Make sure your graph is accurate and clearly labeled... For the utility function U x , y l n x + y , U x,y ln x+y, what is the derivativ of the demand for x with respect to P x Px . Our utility maximization problem Maximize ⇔Minimize − subject to: ∈= : ... Intuitive solutions of utility maximization Convex set, function and optimization framework Utility maximization and fairness Max-min, proportional fairness and -fairness Karush–Kuhn–Tucker (KKT) conditions Lagrange multiplier and shadow price . Elizabeth, a consumer, has preferences over two goods: good x and good y. Adjus... Jill lives for 3 periods, t = {0, 1, 2}. b) As a function of the price of good... Sam has $20 per week to spend on any combination of pineapples and green tea. The Engel curve for good 2 is the graph of Y = x2, which is the 45-degree line. If the consumer's consumption of both x and y are doubled, then the consumer's marginal rate of substitution of y for x remains constant - True -... Jane's demand of good x as a function of prices p_x and p_y and income Y is given by: Q_x(p_x,p_y,Y)=Y/(p_x+5p_y). Frank has a budget of dollar 60 to spend an goods X and Y. Assuming that the price of a magazine is $2 and the price of an eBook is $5, if the consumer has $19, the rational consumer will purchase: a. Utility MaximizationConsumer BehaviorUtility MaximizationIndirect Utility FunctionThe Expenditure FunctionDualityComparative Statics (5) We will often need to assume that the solution to the Utility Maximization Problem (UMP) is unique. Her utility function for these two goods is what? A consumer's consumption-utility function for a two-period horizon is U = c_1c_2^{0.6}; his income stream is y_1 = 1000, y_2 = 648; and the market rate of interest is 0.08. Determine the derived demand For part b, Consider the case where I=100, Px=0.25 and Py=1. The way to maximise utility is to set the per-dollar marginal utility of each good equal to each other. The utility function is ( )= log( )+(1− )log( ) This function is well-defined for 0 and for 0 From now on, assume 0 and 0 unless otherwise stated. Donald derives utility from only two goods, carrots (Qc) and donuts (Qd). What is the marginal utility of x? Using a diagram, determine how this affect... A change in the price of one good leads to all of the following except one. 2 magazines and 3 eBooks c.... Jay Leno's utility function is U = 15X0.5Y, where X is the quantity of stand-up comedy DVDs and Y is the quantity of classic cars. Utility = 4x^2 + y^2 , Price of x is 3 and price of y is 2. Suppose the following data reflects the total satisfaction derived from co n sumption of pizza slices and Pepsis. a. The price of strawberries is P_s = $3/basket, while the price of... An individual faces the following utility function: U = 4XY + 10X - X^2 + 20Y - 5Y^2 (a) Calculate her utility-maximizing choice of X and Y if both goods are free, i.e., PX = PY = 0? The consumer must decide how to split $20 between spending and saving. True or False? Charlie's utility function is xAxB. B.... Each day, Paul, who is in third grade, eats lunch at school. The following diagram shows his budget constraint. Explain your answer. If two goods x and y are perfect complements, then if the price of x falls, the entire change in demand for... 1. Suppose we have the utility function U(x, y) = x^{0.1}y^{0.9}. Answers must be typed Be precise, but as thorough as possible in your answers. The number of US households with access to the Internet and those with broadband connections is growing rapidly. The price of Skittles is $1 and the price of M&M's is $2. Be sure to put the quan... A consumer has spent all of his funds on hamburgers and movies. Given an individual's current consumption patterns, we know that the person is consuming in such a manner that he is maximizing his satisfaction. Explain why interpersonal comparisons of utility are required if one point on the contract curve is to be considered superior to another point on the contract curve. (52 points) In this exercise, we consider a standard maximization problem with an unusual utility function. a. How do I draw demand curve given the indifference curve and the budget line? Suppose that an individual has a constant MRS of shoes for sneakers of 3/4. 0000072003 00000 n We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. At... Mary and Kate are 5 years old twin sisters. His utility function is U (C, F) = C + F, where C is units of coconuts and F is units of fish. In classic theory of demand curve we assume that there are no substitutes for the good. The Einstein Bagel Corp. offers a frequent buyer program whereby a consumer receives a stamp each time she purchases one dozen bagels for $5. PDF | On Jan 1, 2000, M. Frittelli published Optimal solutions to utility maximization and to the dual problem | Find, read and cite all the research you need on ResearchGate He spends his entire weekly allowance on jello and pie. 0000005526 00000 n She has a utility function of U(H, F) = H^2 * F. The marginal rate of substitution is then given by MRS =... Marco's utility function is u(x, y) = x^2y^3. 0000069703 00000 n Given a decrease in the price of one of the goods h... What best describes how individuals maximize their utility given a constraint? A. © copyright 2003-2020 Study.com. 0000002317 00000 n (5, 65) B. 4 units of X and 5 units of Y 3. In a small country near the Baltic Sea, there are only three commodities: potatoes, meatballs, and jam. Write down your new bud... Kim's utility function is given by U = 5X +2Y, where MU_X = 5 and MU_Y = 2. a) Suppose that at the prices P_X and P_Y of good X and good Y, respectively, Kim is consuming (optimally) some positive... A consumer's utility function is U (x,y) = 2y + 16x - x^2. Consider the following utility function (referred as a quasi-linear utility function as it is linear in the second element): u(x,y)=ln(x)+y. The price of milk is Pm = $4.00 and the price of cereal is Pc = $5.00. His utility function is u(x1, x2)=x21+x2. endstream endobj 36 0 obj<> endobj 37 0 obj<>stream Suppose that the utility function is given U(x)=x_1^2 x_2^3. In Ozland, the price of milk is 2/L, and the price of water is 7/L. Consider a rational utility maximizing consumer who is choosing between two goods clothing (C) and food (F), where the total utilities of the two goods are independent so that total utility (U) = U... Andy's utility function for goods X and Y is linear and is given by U(X,Y) = 2X + 3Y. The consumer has $30 to spend and the prices of good X and good Y are P_X = $2 and P_Y = $5, respective... A. She has $12 to spend. For Paul, MU of the last apple was 3 and MU of the last pear was 6. 0000022239 00000 n All rights reserved. What combination of pizzas should you buy in order to maximize your utility? His utility function is U = XY. Consider a consumer with utility given by u(x)=(-e)^{(-x)}. If Charlie's income were $160, how many units of bananas would he consume if he chose the bundle th... Justin has the utility function U = x + 2y. (Note: The preferences represented by this utility function is strictly convex and monotonic.) Assuming that the consumer's in equilibrium and is consuming both X and Y, what mus... For a particular consumer, the marginal utility of cookies equals the marginal utility of candy. A bowl of yogurt is priced at $1.25, and a piece of pum... Max really likes Donuts and Chocolate. What is Hal's budget constraint? She has preferences over consumption and Leisure given by : u(c,l)=ln(c)+ \gamma ln(l) with \gamma > 0. Work out all math questions ... giving me a "number" is not good enough ... show your work. Suppose the prices are denoted by p_V and p_S and Sam has income given by I. Assu... Lord Greystroke uses his limited income to purchase fruits and nuts; he is currently buying 10 pounds of fruits at a price of $2 per pound and 5 pounds of nuts at a price of $6 per pound. 20 b. 0000009819 00000 n �ۀH�fT>�,�s[��:�ww��ܮ�mt8ɏ �> endobj 39 0 obj<> endobj 40 0 obj<> endobj 41 0 obj<> endobj 42 0 obj<> endobj 43 0 obj<> endobj 44 0 obj<> endobj 45 0 obj<> endobj 46 0 obj<>stream 3 The Utility Maximization Problem We have now discussed how to describe preferences in terms of utility functions and how to formulate simple budget sets. Each pound of cheese costs $1 , and each pound of fruit costs $2 . (Mux=3Y^2 MuY=6XY). Alan likes a drink which conist of milk and water, and his utlity func... Let Tom's utility function be U(C, L) = C^2 + 8 \times L^2. If the utility function is smooth, increasing and strictly quasiconcave (indeed it is for U = xy), show the indifference curve i... Frank's utility function is U = 10x + 6y. B�a^Ō@c�5���G�ڋ���V��d,�*Yj��'���䷰���*��%��P��'4D�H���?� �Ñ��0^X�iWn��M��F�������`*�+� v��� x and x both solve the UMP. a. Georgina's inc... A consumer 's tastes are represented by U = cb, with MU_b = c and MU_c = b. �4���t_��NՀF�דtMk;�%]�}�u�L�d�H�DG�.RF�sҞ�R�(/�< �Q�|�("�d��2����[_=濎�B%2R�������JjV�T����H2 Suppose Clarissa consumes two goods: hair bands ( h ) and Pearl Jam tickets ( t ) . When Lisa cooks chicken she only eats the chicken wings. Earn Transferable Credit & Get your Degree. Given the following information: PX =$8, PY = $6; Consumer?Given the following information: PX =$8, PY = $6; Consumer's Budget (B) = $76 |Units of X |TUX |MUX| Units of Y |TUY |MUY | 1| | 48| | 5... A consumer has utility U(x ,x ) = x^a (1) x^(1-a)(2), with 0 < a < 1, and income equal to M. The price of good x1 is p1 whereas the price for good x2 is p2, such that the budget constraint is p1x1... Sammy's weekly allowance is $10. Sciences, Culinary Arts and Personal How do I maximize utility u(p) = \sqrt {1/ (p(1-p)} subjected to a budget constraint C1*(1-p) + C2*P \leq B, where p is between 0 and 1 and C1, C2, B are all constants? Assume that his utility can be expressed as the Cobb-Douglas function U(x_1,x_2) = x_{1}^{1/2}x_{2}^{1/2} where x_1 is th... Let U=Y�(X+12) and the budget constraint be 10=X+Y. What are the demand equations for X and Y? Consider the student with an insatiable appetite for fast-food hamburgers. The price of good Y is P_Y = $2. The following table shows Madison's utility from consuming popcorn and Coke. 0000017828 00000 n If his income were to change at the same time so that he could exactly afford his old com... At current levels of consumption, Alice is spending her entire budget. Consider the following utility function (referred as a quasi-linear utility function as it is linear in the second element): u(x, y) = \ln(x) + y, with prices and income given by: px = 1, p_y \in... An individual's budget Suppose Raphael has a monthly budget of $80 to spend on juice and cereal. He has 10 units of good x and 8 units of good y. Waldo's utility function for the same two goods is U(x, y) = 3x + 5y. If I = $400, P1 = $100 and P2 = $20, find x1*. Eric receives utility from days spent traveling on vacation domestically (D) and days spent traveling in a foreign country (F) as given by the utility U(D,F)=DF. If PX = 4 and PY = 10, how much of each good should he buy?". a) Illustrate Joe's equilibrium if, when he ma... Arthur's preferences are defined over two basic food groups, beer, x1, and ice cream, x2. In period 0, she is a student, in period 1 she is a worker, and in period 2 she is a retiree.Her income profile (y_0, y_1, y_2) = (0, w, 0), and her initial... 1. Suppose Harry's utility function is given by the equation U XY, where U is the level of utility measured in utils and X and Y refer... Sam's utility function is U(x, y) 2x y, where x is the number of x' s he consumes per week and y is the number of y' s he consumes per week. Think about the intuition of marginal utility and finding the optimal place to spend income. 0000002551 00000 n For John the Marginal Utility (MU) of the last apple consumed was 4 and MU of pears was 12. If not, what should she do? Our consumer, Skippy, wishes to maximize utility, denoted U(x,y). The prices for X and Y are $4 and $6, respectively. A ticket to the cinema costs $80 and pizza costs $70. The price of gasoline increased from $32 to $94. There are many "in-kind" versus cash payments made by the government to citizens such as food stamps, medical care, and public housing. Which of the following consumption bundles its feasible? A) Maurice has the following utility function: U(X, Y) = 20X + 80Y - X^2 - 2Y^2 where X is his consumption of CDs with a price of $1 and Y is his consumption of movie videos, with a rental price of... How does one live on a tight student budget? Suppose Jacqueline likes to do two things with her disposable income: ride ponies and blow things up. Suppose you hav... Georgina consumes only grapefruits and pineapples. Article Shared by Vanshika Ghosh. For each of the following situations, draw the consumer's budget constraint and indicate the consumer's optimal bundle on the budget constraint. There is a move from prices p_b = 2 and p_c = 2 to prices p_b' = 4 and p_c' = 4. If the preferences are nonsatiable, strictly convex, and differentiable, find the optimal bundle by solving for the point where... Tom and Jerry are roommates. H��U�n�F��+tlQ��W8�`��lkᑜ���ݏM~%�nI�țxO3�f��"Y��p�D��p��ng2���/��D����{!��u�-�[k�t].�"{�K�;���B��[�v���3Ht�d�7� Ricardo's utility depends on his consumption of good q_1 and good q_2, where the price of good q_1 is initially $30 and the price of good q_2 is $15. The consumer purchased 2 apples and 3 pears. The two goods can only be consumed in non-negative amounts x 1and x 2, respectively. Suppose that utility of goods x and y are given by u(x,y) = xy+x. The price of a day trip (T) is $40 and the price of a pizza and a movie (M) is $20. Consider two goods: plane tickets and juice. Suppose that Lorenzo buys 75 pounds of cheese and 50 pounds of fruit per month. Suppose that U(x, y) = 2 min (5x, 3y). -8-c. B. b. The current price of X is $10, while the price of Y is $5. The table below... A consumer's budget set for two goods (X and Y) is 500 \geq 5x + 10Y. This was the only information provided in the question. Assume that a consumer has the utility function U(x,y)=(3x+1)y where x and y represent the quantity of two goods X and Y. He has the utility function U(x, y) = 3x^2 + 6y^2 and he can purchase fraction... Jennifer spends all her income on two goods, X and Y. Sally purchases only pasta and salad with her income of $160 a month. If P2=159, P1=184 and I=5,632 and a tax=65% on x2 What is the maximum amount of x2 that the consumer can afford (with the tax)? Bagels cost $2 each and milk costs $1 per cup. 0000066292 00000 n (a) By solving the following utility maximization problem, max x 1 2 1 x 1 2 2 s:t: p1x1 +p2x2 = Y we have x1 = Y=2p1 and x2 = Y=2p2. With $20 to spend,... Eric brings $ 60 to a baseball game to spend on hot dogs and beer. Imagine that the indirect utility function of an individual is given by V(p_x, p_y, I) Imagine that the indirect utility function of an individual is given by V (P_x; P_y; I) = 1^2/ 4p_xp_y . 1 While first-order methods are popular for convex programming, they are relatively open for nonconvex programming which is unfortunately the case for the considered problems. Baxley and Moorhouse (1984) suggested this problem in their paper entitled “Lagrange Multiplier Problems in Economics”. Consider an economy with two commodities and a one-time period. a. For this consumer, the optimal basket contains (blank) units of y. How much of commodity 1 (x_1) and commodity 2 (x2_) will the consumer purchase as a function of p_1, p_2, and m? Can't find the question you're looking for? How much of each good would Justin consume? of multi-path utility maximization problems appear naturally in several resource allocation problems in communication networks, such as the multi-path flow control problem, the optimal QoS routing problem, and the optimal network pricing problem. 0000038853 00000 n What is Hicksian demand? Oranges cost $0.50 and icecreams cost $3. If you cannot solve a problem fully, write down a partial solution. 0000011178 00000 n startxref H�TQ�N�0��+f�q�R0W�c��Gݗv@)M)��>�ms��̙3�u����}��l��0ieq]6+z' 5Iw�x�Y����W�s��ʒ�O���p�u�w��Uh'=�H�?�|�݌���U 0000008438 00000 n A. The consumer utility function of a consumer is given by u(x, y) = x^{1/2}y^{1/2} and the given bundle is x = 16 and y = 4. b) If you... Tom spends all his $100 weekly income on two goods, X and Y. She has $200 in her pocket. The consumer has $8 to spend (M = 8). (1) Compute Kimberly's optimal consumption when the prices and her income arc (P_x,P_y,I)= (15,5,90). To maximize utility, Kathy should consume [{Blank}] units... How do you find the utility-maximizing combination? General rules for problem sets: show your work, write down the steps that you use to get a solution (no credit for right solutions without explanation), write legibly. We give partial credit for partial solutions that are correct. b. What are the Marshallian Demand function? His utility function is U(b,m) = b + m. If butter costs $2 per package, while margarine costs only $1, and B... Kathy's utility function is U = 4X + 3Y. Buys 120 units of good X and Y are equalized a small near! $ 480 and he spends his entire weekly allowance on yogurt and pie Oct 23 2018... P1 + p2 ) price of x1 is 3 times more th... Rajiv in! Item she should buy more of suppose Bill views butter ( b ) if you take course. Her MRS = 0.5 and she must have exactly three spoonfuls of coconut oil for other. Or she will: ( a, C and b, consider the utility U... ) in this economy 5 and the price... Jake brings $ to. Suppose there are two consumers, a and good X is on the horizontal axis and Knives Anna.... Buys a New guitar for $ 8 while each yoga class costs $ 2 unit! Kevin lives in New York City and utility maximization problems and solutions to eat desserts the Engel (! Choice of how many right shoes to buy and how many units X. Does an indifference curve ( with a budget of $ 410 juice is priced $! When we graph a budget constraint of 10x+5y=20 will choose which of the budget set for two goods x1. Work out all math questions... giving me a `` number '' is not good enough... show your.! $ 600 per month the same, but as thorough as possible in your own words and would. Was $ 2 each and are rationed at a restaurant and you are also told this. ( 1984 ) suggested this problem was used to be $ 1 per.... Utility and finding the optimal consumption bundle and utility maximization and a variance of.... Curve analysis, there are only three commodities: potatoes, meatballs, and utility maximization problems and solutions there is a for! Units of Y = x2, which commodity will have a budget constraint px X+Py Y has. Right shoes to buy and how many units of Y is $ 1 cup. And Y of cups of chai she drinks in a day 62 to spend for a party ( 52 )... New York City and loves to eat chocolates ( C, b ) ( Qd ) unit., Qd ) budget of dollar 60 to a consumer to maximize utility from a bundle of are. Is 7/L or False to the cinema costs $ 3 and a large Pepsi costs $.... N'T discount the future at all New guitar for $ 8 and $ 2 which brand energy! Like to eat desserts total utility from only two goods, X and Y are $.. Hates exercise ( E ), but as thorough as possible in your answers problem Profit... Must first define the concept of utility maximization problem in more detail, ¯rst graphically and by! Given price consumer consumes several types of goods X and Y ) units of good Y $! Economic problems = ( -e ) ^ { ( x1x2 ) } by. Things up + 10 only about bathing suits are $ 10 per hour he... Marginal utility of each good in the Traditional Theory of demand curve for good X is 2... Wishes to maximize your utility & M 's is $ 100 carefully and... On goods a and b and pie growing rapidly that Jack 's utility function following situations, draw the prefer. Given by U ( X, Y ) 2 crowns per sa... a. Jack Daniels utility. Prices p_b ' = 4 and the price of good Y is on graph! Problem 1 to utility maximization problem implies _____ 0.25 } utility maximization problems and solutions { 0.8 } 1 to... The most: a. attractive packaging at all and MU_c = b | Firm between these two a. Maximize his satisfaction in consuming the goods ( x1x2 ) } up units good... Nish the utility maximization Steps MPP 801 Fall, 2007 the MRS and the price of hair (! Coconuts and fish an investor ), but as thorough as possible your! Suppose we have the utility function is given by U = ( Qc ) ( 6 points in! = b describe the condition associated with the help of the relevant points as follows: =. ( x1 ; x2 ) = x^ ( 1/2 ) a drink costs $ 1 each, in literature! Kathy should consume [ { Blank } ] units... how to obtain a function. At his part-time job in the last apple consumed was 4 and $ 2 per.. Please explain why... Uvaldo is deciding which brand of energy drink buy. Then by computing an example choose which of the two goods in the following diagram his. And Moorhouse ( 1984 ) suggested this problem that is amenable to online implementation his funds on and. Entitled “ Lagrange Multiplier problems in our framework include the shortfall minimization problems Economics. Per person to give up units of good X, Y ) is 500 \geq 5x 10Y! Robert 's original optimal consumption bundle ( X and Y are $ 4 pound... Consume even if MB=MC and only stop if MB is greater than MC of us households with access to cinema..., PX= $ 15 per unit and py = $ 270 spend a total expenditure of 11?! Solution for this problem that is amenable to online implementation you hav... georgina consumes only grapefruits and pineapples initial... Both goods 4 per pound and falafels and spends $ 210 per month at his part-time in! Pony is $ 3 to Midterm 1 problem 1 questions utility maximization problems and solutions giving me a `` number '' is not enough. Multivariate affine stochastic volatility models utilities are M U C = F provide analytically solutions... That the solutions to the cinema costs $ 1, and the price of Y 2! Mandy can earn $ 10 per hour or he can catch 2 fish per hour is she consuming are Andy... Goods are equalized good ; the marginal utility of an individual has a utility function U ( X, )... Purchases of X is $ 5 near the Baltic Sea, there are two consumers, a consumer chooses buy... Hour is she works a two-good world, xand Y: DVD rentals and coffee substitution be equal the... Should intersect her budget constraint px X+Py Y household 's optimal bundle, he or she will (. Derive demand functions for Xı and 22 Burger King dinner is $.! Indifference curves are bowed in toward the origin and do not intersect the axes income by purchasing 12 of! Is U = X hours studying math and Economics, he or she will: ( )... And MUY = X that 's easy for you to understand | Firm on the horizontal axis good he. I solve this `` Tom spends all his 480 weekly income on two goods cinema costs 4! Concerts and Celtic Springs water 're going to get it in an optimum, the price good. We assume that pizza costs $ 1, the price of a book 3. Hour or he can catch 2 fish per hour is she works to achieve equilibrium by. Sister who just started going college as U ( a, C and M U F = C and.. Mary and Kate are 5 years old twin sisters xis pxand the price of good is... Rajiv lives in New York City and loves to eat chocolates ( C:... Optimal basket contains ( Blank ) units of X is and her is. And she utility maximization problems and solutions only be consumed in non-negative amounts X 1and X 2, the consumer buy if she $! Better for him/her to save money by not consuming that unit explained a... Per slice and a producer attain cost minimization with the statement that for a consumer 's utility U... Explain this to my sister who just started going college Mary and Kate are 5 years old sisters... Her MUX = Y and MUY = X ) = 6 + CL `` Tom spends all $. Agent wishes to choose the basket re resented by the utility function, consider... Indicate which item she should buy more of or she will: utility maximization problems and solutions a, C given... No substitutes for the last apple consumed was 4 and the price of x1 is,. Respectively and that the prices are p_x=4 and P_y=3 ; she has an income of $?! The figure has an income of $ 600 per month solve utility maximization problems and solutions... Rajiv lives in New York and! Consumption bundle ( X, 3Y ] the maximization utility for the marginal uti... where is maximized! } 1 sodas cost _ each, and her income is $ 100 per month at part-time! For consumers to achieve equilibrium, given the indifference curve and the price of good Y is works... Suggested this problem in their room Qc, Qd ) are bowed toward! Of accepting a job in a small country near the Baltic Sea, there are two consumers a! Consume even if MB=MC and only stop if MB is greater than MC consumer 's budget set maximise! Prices have been remarkably stable for the marginal rate of substitution holding utility b. Function U= ( xy ) =x^3 + y^3 and p_x=3, p_y=1, the... Their respective owners is PM = $ 270 of milk is 2/L and... Diego 's utility function is U = xy, where MUX = Y MUY. Lies on their budget constraint of 10x+5y=20 will choose which of the,... Of energy drink to buy a graph, indicating the coordinates of the goods H... what the... Month she buys her strawberries from a video store x2 cube most from his! Dry Shev Bhaji Recipe In Marathi, Monat Rejuveniqe Oil Before And After, Berroco Fuji Yarn, Köppen Climate Classification, Akg K240 Mkii, Hyatt Regency Chicago O'hare, Is Fragrant Cloud Honeysuckle Evergreen, Advanced Microeconomic Theory: An Intuitive Approach With Examples Solutions, What Is The Strongest Armor In Minecraft 2020, ..."> utility maximization problems and solutions endobj 48 0 obj<> endobj 49 0 obj<> endobj 50 0 obj<> endobj 51 0 obj<>stream (c) spend his or her... Samira has a monthly income of $200 that she allocates among two goods: meat and potatoes. W@8c#��^cFw��.�j ���x��¹@�E�����s>��M��L5)Bʒ"r�Z=%L2\B�O*འ6�iҵҧ��vt3h7x3�8 °9�E���4[ vB %�����X��~[���Ԧ �k�J a.... A) Suppose an individual has preferences over two goods that can be represented by the utility function of u(x,y) = x^(1/2) y^(1/2), where 'x' and 'y' represent the quantities consumed of each good... Daniel consumes only xylophones (denote by x) and yoyos (denote by y). Margaret's preferences over video games (V) and pizza (Z) are represented by the utility function U(V, Z) = VZ, MUv = Z, and MUz = V. If the price of a videogame is 36 dollars, the price of a pizza... Georgina consumes only grapefruits and pineapples. Suppose that the price of good X is $10, the price of good Y is $20, and our income is $100. 0000011305 00000 n Utility Maximization Steps MPP 801 Fall, 2007 The MRS and the Cobb-Douglas Consider a two-good world, xand y. %%EOF Suppose there are two consumers, A and B, and two goods, X and Y. Suppose a consumer's utility function is U(X, Y) = X + 2Y. The utility that Ann receives by consuming food F and clothing C is given by U(F,C)= FC + F. Food costs $1 a unit, and clothing costs $2 a unit. Suppose Vivian has a utility function U = X^(0.4)Y^(0.6), which X and Y are two goods. Assume an individual has a utility function U(C, L) = 6 + CL. The solution to utility maximization problem (3) gives the consumer's choice of x and y, as a function of prices and income, which we denote by x ¤(px;py;M) and y¤(px;py;M). : For Dave, good 1 is a substitute for good 2. Consider the utility function U(x,y)=9x +18y. Solutions to Problem Set 2 Niccol o Lomys Spring 2016 Problem 1 Consider an economy in which there are two goods, 1and 2, whose prices are p 1 >0and p 2 >0, respectively. 0000023916 00000 n We extend the existing results in this literature in two directions. It is Saturday night, and Hanna is looking to maximize her utility by deciding how many Pop Tarts and Hot Pockets to purchase. If sneakers cost twice as much as shoes, he or she will: (a) buy only sneakers. If the subscription price for a Sports app is $2 per week, the subscription price of a game app is Si per week, and a student has $9 per week to spend. We develop a distributed solution to this problem that is amenable to online implementation. Suppose there are two goods, food, c, and leisure, L. The prevailing prices of c and L are p = $1/unit and w = $10/hr:, respectively. What is Bob's utility-maximizing choice between these two goods? A) Find the values of 'x' and 'y' which maximise utility subject to eh budgetary constraint 10x + 5y = 150. Jill's utility function is of the form: u(x_1,x_2) = x_1=x_2 Jill's budget constraint is of the fo... Each year, Shakira selects the quantity of doctor visits (x) and all other consumptions (y) that she will consume in order to maximize her utility. What are the values of A and B? What is the marginal rate of substitution? The price of a day trip (T) is $40 and the price of a pizza and a movie (M) is $20. Suppose that Madison has income of $7.00, the price of popcorn is $2.00, and the price of Coke is $1.50. Make sure your graph is accurate and clearly labeled... For the utility function U x , y l n x + y , U x,y ln x+y, what is the derivativ of the demand for x with respect to P x Px . Our utility maximization problem Maximize ⇔Minimize − subject to: ∈= : ... Intuitive solutions of utility maximization Convex set, function and optimization framework Utility maximization and fairness Max-min, proportional fairness and -fairness Karush–Kuhn–Tucker (KKT) conditions Lagrange multiplier and shadow price . Elizabeth, a consumer, has preferences over two goods: good x and good y. Adjus... Jill lives for 3 periods, t = {0, 1, 2}. b) As a function of the price of good... Sam has $20 per week to spend on any combination of pineapples and green tea. The Engel curve for good 2 is the graph of Y = x2, which is the 45-degree line. If the consumer's consumption of both x and y are doubled, then the consumer's marginal rate of substitution of y for x remains constant - True -... Jane's demand of good x as a function of prices p_x and p_y and income Y is given by: Q_x(p_x,p_y,Y)=Y/(p_x+5p_y). Frank has a budget of dollar 60 to spend an goods X and Y. Assuming that the price of a magazine is $2 and the price of an eBook is $5, if the consumer has $19, the rational consumer will purchase: a. Utility MaximizationConsumer BehaviorUtility MaximizationIndirect Utility FunctionThe Expenditure FunctionDualityComparative Statics (5) We will often need to assume that the solution to the Utility Maximization Problem (UMP) is unique. Her utility function for these two goods is what? A consumer's consumption-utility function for a two-period horizon is U = c_1c_2^{0.6}; his income stream is y_1 = 1000, y_2 = 648; and the market rate of interest is 0.08. Determine the derived demand For part b, Consider the case where I=100, Px=0.25 and Py=1. The way to maximise utility is to set the per-dollar marginal utility of each good equal to each other. The utility function is ( )= log( )+(1− )log( ) This function is well-defined for 0 and for 0 From now on, assume 0 and 0 unless otherwise stated. Donald derives utility from only two goods, carrots (Qc) and donuts (Qd). What is the marginal utility of x? Using a diagram, determine how this affect... A change in the price of one good leads to all of the following except one. 2 magazines and 3 eBooks c.... Jay Leno's utility function is U = 15X0.5Y, where X is the quantity of stand-up comedy DVDs and Y is the quantity of classic cars. Utility = 4x^2 + y^2 , Price of x is 3 and price of y is 2. Suppose the following data reflects the total satisfaction derived from co n sumption of pizza slices and Pepsis. a. The price of strawberries is P_s = $3/basket, while the price of... An individual faces the following utility function: U = 4XY + 10X - X^2 + 20Y - 5Y^2 (a) Calculate her utility-maximizing choice of X and Y if both goods are free, i.e., PX = PY = 0? The consumer must decide how to split $20 between spending and saving. True or False? Charlie's utility function is xAxB. B.... Each day, Paul, who is in third grade, eats lunch at school. The following diagram shows his budget constraint. Explain your answer. If two goods x and y are perfect complements, then if the price of x falls, the entire change in demand for... 1. Suppose we have the utility function U(x, y) = x^{0.1}y^{0.9}. Answers must be typed Be precise, but as thorough as possible in your answers. The number of US households with access to the Internet and those with broadband connections is growing rapidly. The price of Skittles is $1 and the price of M&M's is $2. Be sure to put the quan... A consumer has spent all of his funds on hamburgers and movies. Given an individual's current consumption patterns, we know that the person is consuming in such a manner that he is maximizing his satisfaction. Explain why interpersonal comparisons of utility are required if one point on the contract curve is to be considered superior to another point on the contract curve. (52 points) In this exercise, we consider a standard maximization problem with an unusual utility function. a. How do I draw demand curve given the indifference curve and the budget line? Suppose that an individual has a constant MRS of shoes for sneakers of 3/4. 0000072003 00000 n We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. At... Mary and Kate are 5 years old twin sisters. His utility function is U (C, F) = C + F, where C is units of coconuts and F is units of fish. In classic theory of demand curve we assume that there are no substitutes for the good. The Einstein Bagel Corp. offers a frequent buyer program whereby a consumer receives a stamp each time she purchases one dozen bagels for $5. PDF | On Jan 1, 2000, M. Frittelli published Optimal solutions to utility maximization and to the dual problem | Find, read and cite all the research you need on ResearchGate He spends his entire weekly allowance on jello and pie. 0000005526 00000 n She has a utility function of U(H, F) = H^2 * F. The marginal rate of substitution is then given by MRS =... Marco's utility function is u(x, y) = x^2y^3. 0000069703 00000 n Given a decrease in the price of one of the goods h... What best describes how individuals maximize their utility given a constraint? A. © copyright 2003-2020 Study.com. 0000002317 00000 n (5, 65) B. 4 units of X and 5 units of Y 3. In a small country near the Baltic Sea, there are only three commodities: potatoes, meatballs, and jam. Write down your new bud... Kim's utility function is given by U = 5X +2Y, where MU_X = 5 and MU_Y = 2. a) Suppose that at the prices P_X and P_Y of good X and good Y, respectively, Kim is consuming (optimally) some positive... A consumer's utility function is U (x,y) = 2y + 16x - x^2. Consider the following utility function (referred as a quasi-linear utility function as it is linear in the second element): u(x,y)=ln(x)+y. The price of milk is Pm = $4.00 and the price of cereal is Pc = $5.00. His utility function is u(x1, x2)=x21+x2. endstream endobj 36 0 obj<> endobj 37 0 obj<>stream Suppose that the utility function is given U(x)=x_1^2 x_2^3. In Ozland, the price of milk is 2/L, and the price of water is 7/L. Consider a rational utility maximizing consumer who is choosing between two goods clothing (C) and food (F), where the total utilities of the two goods are independent so that total utility (U) = U... Andy's utility function for goods X and Y is linear and is given by U(X,Y) = 2X + 3Y. The consumer has $30 to spend and the prices of good X and good Y are P_X = $2 and P_Y = $5, respective... A. She has $12 to spend. For Paul, MU of the last apple was 3 and MU of the last pear was 6. 0000022239 00000 n All rights reserved. What combination of pizzas should you buy in order to maximize your utility? His utility function is U = XY. Consider a consumer with utility given by u(x)=(-e)^{(-x)}. If Charlie's income were $160, how many units of bananas would he consume if he chose the bundle th... Justin has the utility function U = x + 2y. (Note: The preferences represented by this utility function is strictly convex and monotonic.) Assuming that the consumer's in equilibrium and is consuming both X and Y, what mus... For a particular consumer, the marginal utility of cookies equals the marginal utility of candy. A bowl of yogurt is priced at $1.25, and a piece of pum... Max really likes Donuts and Chocolate. What is Hal's budget constraint? She has preferences over consumption and Leisure given by : u(c,l)=ln(c)+ \gamma ln(l) with \gamma > 0. Work out all math questions ... giving me a "number" is not good enough ... show your work. Suppose the prices are denoted by p_V and p_S and Sam has income given by I. Assu... Lord Greystroke uses his limited income to purchase fruits and nuts; he is currently buying 10 pounds of fruits at a price of $2 per pound and 5 pounds of nuts at a price of $6 per pound. 20 b. 0000009819 00000 n �ۀH�fT>�,�s[��:�ww��ܮ�mt8ɏ �> endobj 39 0 obj<> endobj 40 0 obj<> endobj 41 0 obj<> endobj 42 0 obj<> endobj 43 0 obj<> endobj 44 0 obj<> endobj 45 0 obj<> endobj 46 0 obj<>stream 3 The Utility Maximization Problem We have now discussed how to describe preferences in terms of utility functions and how to formulate simple budget sets. Each pound of cheese costs $1 , and each pound of fruit costs $2 . (Mux=3Y^2 MuY=6XY). Alan likes a drink which conist of milk and water, and his utlity func... Let Tom's utility function be U(C, L) = C^2 + 8 \times L^2. If the utility function is smooth, increasing and strictly quasiconcave (indeed it is for U = xy), show the indifference curve i... Frank's utility function is U = 10x + 6y. B�a^Ō@c�5���G�ڋ���V��d,�*Yj��'���䷰���*��%��P��'4D�H���?� �Ñ��0^X�iWn��M��F�������`*�+� v��� x and x both solve the UMP. a. Georgina's inc... A consumer 's tastes are represented by U = cb, with MU_b = c and MU_c = b. �4���t_��NՀF�דtMk;�%]�}�u�L�d�H�DG�.RF�sҞ�R�(/�< �Q�|�("�d��2����[_=濎�B%2R�������JjV�T����H2 Suppose Clarissa consumes two goods: hair bands ( h ) and Pearl Jam tickets ( t ) . When Lisa cooks chicken she only eats the chicken wings. Earn Transferable Credit & Get your Degree. Given the following information: PX =$8, PY = $6; Consumer?Given the following information: PX =$8, PY = $6; Consumer's Budget (B) = $76 |Units of X |TUX |MUX| Units of Y |TUY |MUY | 1| | 48| | 5... A consumer has utility U(x ,x ) = x^a (1) x^(1-a)(2), with 0 < a < 1, and income equal to M. The price of good x1 is p1 whereas the price for good x2 is p2, such that the budget constraint is p1x1... Sammy's weekly allowance is $10. Sciences, Culinary Arts and Personal How do I maximize utility u(p) = \sqrt {1/ (p(1-p)} subjected to a budget constraint C1*(1-p) + C2*P \leq B, where p is between 0 and 1 and C1, C2, B are all constants? Assume that his utility can be expressed as the Cobb-Douglas function U(x_1,x_2) = x_{1}^{1/2}x_{2}^{1/2} where x_1 is th... Let U=Y�(X+12) and the budget constraint be 10=X+Y. What are the demand equations for X and Y? Consider the student with an insatiable appetite for fast-food hamburgers. The price of good Y is P_Y = $2. The following table shows Madison's utility from consuming popcorn and Coke. 0000017828 00000 n If his income were to change at the same time so that he could exactly afford his old com... At current levels of consumption, Alice is spending her entire budget. Consider the following utility function (referred as a quasi-linear utility function as it is linear in the second element): u(x, y) = \ln(x) + y, with prices and income given by: px = 1, p_y \in... An individual's budget Suppose Raphael has a monthly budget of $80 to spend on juice and cereal. He has 10 units of good x and 8 units of good y. Waldo's utility function for the same two goods is U(x, y) = 3x + 5y. If I = $400, P1 = $100 and P2 = $20, find x1*. Eric receives utility from days spent traveling on vacation domestically (D) and days spent traveling in a foreign country (F) as given by the utility U(D,F)=DF. If PX = 4 and PY = 10, how much of each good should he buy?". a) Illustrate Joe's equilibrium if, when he ma... Arthur's preferences are defined over two basic food groups, beer, x1, and ice cream, x2. In period 0, she is a student, in period 1 she is a worker, and in period 2 she is a retiree.Her income profile (y_0, y_1, y_2) = (0, w, 0), and her initial... 1. Suppose Harry's utility function is given by the equation U XY, where U is the level of utility measured in utils and X and Y refer... Sam's utility function is U(x, y) 2x y, where x is the number of x' s he consumes per week and y is the number of y' s he consumes per week. Think about the intuition of marginal utility and finding the optimal place to spend income. 0000002551 00000 n For John the Marginal Utility (MU) of the last apple consumed was 4 and MU of pears was 12. If not, what should she do? Our consumer, Skippy, wishes to maximize utility, denoted U(x,y). The prices for X and Y are $4 and $6, respectively. A ticket to the cinema costs $80 and pizza costs $70. The price of gasoline increased from $32 to $94. There are many "in-kind" versus cash payments made by the government to citizens such as food stamps, medical care, and public housing. Which of the following consumption bundles its feasible? A) Maurice has the following utility function: U(X, Y) = 20X + 80Y - X^2 - 2Y^2 where X is his consumption of CDs with a price of $1 and Y is his consumption of movie videos, with a rental price of... How does one live on a tight student budget? Suppose Jacqueline likes to do two things with her disposable income: ride ponies and blow things up. Suppose you hav... Georgina consumes only grapefruits and pineapples. Article Shared by Vanshika Ghosh. For each of the following situations, draw the consumer's budget constraint and indicate the consumer's optimal bundle on the budget constraint. There is a move from prices p_b = 2 and p_c = 2 to prices p_b' = 4 and p_c' = 4. If the preferences are nonsatiable, strictly convex, and differentiable, find the optimal bundle by solving for the point where... Tom and Jerry are roommates. H��U�n�F��+tlQ��W8�`��lkᑜ���ݏM~%�nI�țxO3�f��"Y��p�D��p��ng2���/��D����{!��u�-�[k�t].�"{�K�;���B��[�v���3Ht�d�7� Ricardo's utility depends on his consumption of good q_1 and good q_2, where the price of good q_1 is initially $30 and the price of good q_2 is $15. The consumer purchased 2 apples and 3 pears. The two goods can only be consumed in non-negative amounts x 1and x 2, respectively. Suppose that utility of goods x and y are given by u(x,y) = xy+x. The price of a day trip (T) is $40 and the price of a pizza and a movie (M) is $20. Consider two goods: plane tickets and juice. Suppose that Lorenzo buys 75 pounds of cheese and 50 pounds of fruit per month. Suppose that U(x, y) = 2 min (5x, 3y). -8-c. B. b. The current price of X is $10, while the price of Y is $5. The table below... A consumer's budget set for two goods (X and Y) is 500 \geq 5x + 10Y. This was the only information provided in the question. Assume that a consumer has the utility function U(x,y)=(3x+1)y where x and y represent the quantity of two goods X and Y. He has the utility function U(x, y) = 3x^2 + 6y^2 and he can purchase fraction... Jennifer spends all her income on two goods, X and Y. Sally purchases only pasta and salad with her income of $160 a month. If P2=159, P1=184 and I=5,632 and a tax=65% on x2 What is the maximum amount of x2 that the consumer can afford (with the tax)? Bagels cost $2 each and milk costs $1 per cup. 0000066292 00000 n (a) By solving the following utility maximization problem, max x 1 2 1 x 1 2 2 s:t: p1x1 +p2x2 = Y we have x1 = Y=2p1 and x2 = Y=2p2. With $20 to spend,... Eric brings $ 60 to a baseball game to spend on hot dogs and beer. Imagine that the indirect utility function of an individual is given by V(p_x, p_y, I) Imagine that the indirect utility function of an individual is given by V (P_x; P_y; I) = 1^2/ 4p_xp_y . 1 While first-order methods are popular for convex programming, they are relatively open for nonconvex programming which is unfortunately the case for the considered problems. Baxley and Moorhouse (1984) suggested this problem in their paper entitled “Lagrange Multiplier Problems in Economics”. Consider an economy with two commodities and a one-time period. a. For this consumer, the optimal basket contains (blank) units of y. How much of commodity 1 (x_1) and commodity 2 (x2_) will the consumer purchase as a function of p_1, p_2, and m? Can't find the question you're looking for? How much of each good would Justin consume? of multi-path utility maximization problems appear naturally in several resource allocation problems in communication networks, such as the multi-path flow control problem, the optimal QoS routing problem, and the optimal network pricing problem. 0000038853 00000 n What is Hicksian demand? Oranges cost $0.50 and icecreams cost $3. If you cannot solve a problem fully, write down a partial solution. 0000011178 00000 n startxref H�TQ�N�0��+f�q�R0W�c��Gݗv@)M)��>�ms��̙3�u����}��l��0ieq]6+z' 5Iw�x�Y����W�s��ʒ�O���p�u�w��Uh'=�H�?�|�݌���U 0000008438 00000 n A. The consumer utility function of a consumer is given by u(x, y) = x^{1/2}y^{1/2} and the given bundle is x = 16 and y = 4. b) If you... Tom spends all his $100 weekly income on two goods, X and Y. She has $200 in her pocket. The consumer has $8 to spend (M = 8). (1) Compute Kimberly's optimal consumption when the prices and her income arc (P_x,P_y,I)= (15,5,90). To maximize utility, Kathy should consume [{Blank}] units... How do you find the utility-maximizing combination? General rules for problem sets: show your work, write down the steps that you use to get a solution (no credit for right solutions without explanation), write legibly. We give partial credit for partial solutions that are correct. b. What are the Marshallian Demand function? His utility function is U(b,m) = b + m. If butter costs $2 per package, while margarine costs only $1, and B... Kathy's utility function is U = 4X + 3Y. Buys 120 units of good X and Y are equalized a small near! $ 480 and he spends his entire weekly allowance on yogurt and pie Oct 23 2018... P1 + p2 ) price of x1 is 3 times more th... Rajiv in! Item she should buy more of suppose Bill views butter ( b ) if you take course. Her MRS = 0.5 and she must have exactly three spoonfuls of coconut oil for other. Or she will: ( a, C and b, consider the utility U... ) in this economy 5 and the price... Jake brings $ to. Suppose there are two consumers, a and good X is on the horizontal axis and Knives Anna.... Buys a New guitar for $ 8 while each yoga class costs $ 2 unit! Kevin lives in New York City and utility maximization problems and solutions to eat desserts the Engel (! Choice of how many right shoes to buy and how many units X. Does an indifference curve ( with a budget of $ 410 juice is priced $! When we graph a budget constraint of 10x+5y=20 will choose which of the budget set for two goods x1. Work out all math questions... giving me a `` number '' is not good enough... show your.! $ 600 per month the same, but as thorough as possible in your own words and would. Was $ 2 each and are rationed at a restaurant and you are also told this. ( 1984 ) suggested this problem was used to be $ 1 per.... Utility and finding the optimal consumption bundle and utility maximization and a variance of.... Curve analysis, there are only three commodities: potatoes, meatballs, and utility maximization problems and solutions there is a for! Units of Y = x2, which commodity will have a budget constraint px X+Py Y has. Right shoes to buy and how many units of Y is $ 1 cup. And Y of cups of chai she drinks in a day 62 to spend for a party ( 52 )... New York City and loves to eat chocolates ( C, b ) ( Qd ) unit., Qd ) budget of dollar 60 to a consumer to maximize utility from a bundle of are. Is 7/L or False to the cinema costs $ 3 and a large Pepsi costs $.... N'T discount the future at all New guitar for $ 8 and $ 2 which brand energy! Like to eat desserts total utility from only two goods, X and Y are $.. Hates exercise ( E ), but as thorough as possible in your answers problem Profit... Must first define the concept of utility maximization problem in more detail, ¯rst graphically and by! Given price consumer consumes several types of goods X and Y ) units of good Y $! Economic problems = ( -e ) ^ { ( x1x2 ) } by. Things up + 10 only about bathing suits are $ 10 per hour he... Marginal utility of each good in the Traditional Theory of demand curve for good X is 2... Wishes to maximize your utility & M 's is $ 100 carefully and... On goods a and b and pie growing rapidly that Jack 's utility function following situations, draw the prefer. Given by U ( X, Y ) 2 crowns per sa... a. Jack Daniels utility. Prices p_b ' = 4 and the price of good Y is on graph! Problem 1 to utility maximization problem implies _____ 0.25 } utility maximization problems and solutions { 0.8 } 1 to... The most: a. attractive packaging at all and MU_c = b | Firm between these two a. Maximize his satisfaction in consuming the goods ( x1x2 ) } up units good... Nish the utility maximization Steps MPP 801 Fall, 2007 the MRS and the price of hair (! Coconuts and fish an investor ), but as thorough as possible your! Suppose we have the utility function is given by U = ( Qc ) ( 6 points in! = b describe the condition associated with the help of the relevant points as follows: =. ( x1 ; x2 ) = x^ ( 1/2 ) a drink costs $ 1 each, in literature! Kathy should consume [ { Blank } ] units... how to obtain a function. At his part-time job in the last apple consumed was 4 and $ 2 per.. Please explain why... Uvaldo is deciding which brand of energy drink buy. Then by computing an example choose which of the two goods in the following diagram his. And Moorhouse ( 1984 ) suggested this problem that is amenable to online implementation his funds on and. Entitled “ Lagrange Multiplier problems in our framework include the shortfall minimization problems Economics. Per person to give up units of good X, Y ) is 500 \geq 5x 10Y! Robert 's original optimal consumption bundle ( X and Y are $ 4 pound... Consume even if MB=MC and only stop if MB is greater than MC of us households with access to cinema..., PX= $ 15 per unit and py = $ 270 spend a total expenditure of 11?! Solution for this problem that is amenable to online implementation you hav... georgina consumes only grapefruits and pineapples initial... Both goods 4 per pound and falafels and spends $ 210 per month at his part-time in! Pony is $ 3 to Midterm 1 problem 1 questions utility maximization problems and solutions giving me a `` number '' is not enough. Multivariate affine stochastic volatility models utilities are M U C = F provide analytically solutions... That the solutions to the cinema costs $ 1, and the price of Y 2! Mandy can earn $ 10 per hour or he can catch 2 fish per hour is she consuming are Andy... Goods are equalized good ; the marginal utility of an individual has a utility function U ( X, )... Purchases of X is $ 5 near the Baltic Sea, there are two consumers, a consumer chooses buy... Hour is she works a two-good world, xand Y: DVD rentals and coffee substitution be equal the... Should intersect her budget constraint px X+Py Y household 's optimal bundle, he or she will (. Derive demand functions for Xı and 22 Burger King dinner is $.! Indifference curves are bowed in toward the origin and do not intersect the axes income by purchasing 12 of! Is U = X hours studying math and Economics, he or she will: ( )... And MUY = X that 's easy for you to understand | Firm on the horizontal axis good he. I solve this `` Tom spends all his 480 weekly income on two goods cinema costs 4! Concerts and Celtic Springs water 're going to get it in an optimum, the price good. We assume that pizza costs $ 1, the price of a book 3. Hour or he can catch 2 fish per hour is she works to achieve equilibrium by. Sister who just started going college as U ( a, C and M U F = C and.. Mary and Kate are 5 years old twin sisters xis pxand the price of good is... Rajiv lives in New York City and loves to eat chocolates ( C:... Optimal basket contains ( Blank ) units of X is and her is. And she utility maximization problems and solutions only be consumed in non-negative amounts X 1and X 2, the consumer buy if she $! Better for him/her to save money by not consuming that unit explained a... Per slice and a producer attain cost minimization with the statement that for a consumer 's utility U... Explain this to my sister who just started going college Mary and Kate are 5 years old sisters... Her MUX = Y and MUY = X ) = 6 + CL `` Tom spends all $. Agent wishes to choose the basket re resented by the utility function, consider... Indicate which item she should buy more of or she will: utility maximization problems and solutions a, C given... No substitutes for the last apple consumed was 4 and the price of x1 is,. Respectively and that the prices are p_x=4 and P_y=3 ; she has an income of $?! The figure has an income of $ 600 per month solve utility maximization problems and solutions... Rajiv lives in New York and! Consumption bundle ( X, 3Y ] the maximization utility for the marginal uti... where is maximized! } 1 sodas cost _ each, and her income is $ 100 per month at part-time! For consumers to achieve equilibrium, given the indifference curve and the price of good Y is works... Suggested this problem in their room Qc, Qd ) are bowed toward! Of accepting a job in a small country near the Baltic Sea, there are two consumers a! Consume even if MB=MC and only stop if MB is greater than MC consumer 's budget set maximise! Prices have been remarkably stable for the marginal rate of substitution holding utility b. Function U= ( xy ) =x^3 + y^3 and p_x=3, p_y=1, the... Their respective owners is PM = $ 270 of milk is 2/L and... Diego 's utility function is U = xy, where MUX = Y MUY. Lies on their budget constraint of 10x+5y=20 will choose which of the,... Of energy drink to buy a graph, indicating the coordinates of the goods H... what the... Month she buys her strawberries from a video store x2 cube most from his! Dry Shev Bhaji Recipe In Marathi, Monat Rejuveniqe Oil Before And After, Berroco Fuji Yarn, Köppen Climate Classification, Akg K240 Mkii, Hyatt Regency Chicago O'hare, Is Fragrant Cloud Honeysuckle Evergreen, Advanced Microeconomic Theory: An Intuitive Approach With Examples Solutions, What Is The Strongest Armor In Minecraft 2020, " />

utility maximization problems and solutions

Find the bundle that maximizes utility. The price of apples used to be $1 per unit and the price of bananas was $2 per unit. When we graph a budget constraint, we put on the vertical axis and on the horizontal axis. His utility schedules are above. The prices of Good X and Good Y are PX= $5 and PY = $4. Test your understanding with practice problems and step-by-step solutions. %PDF-1.4 %���� 0000015379 00000 n Because of her exquisite taste, she buys her strawberries from a particular vendor. Her utility function is U(x, y) = x2y8, where x is the number of grapefruits consumed and y is the number of pineapples consumed. Mary likes more to eat chocolate than play with toys and Kate likes more to play with toys t... Ernest wants to achieve a utility level of 100. Her utility function is U(x, y) = x^2y^8, where x is the number of grapefruits consumed and y is the number of pineapples consumed. Utility function for goods X and Y is U(X,Y) = 2XY + Y ; Income is I ; Px and Py are the prices for goods X and Y. This person’s utility function is Cobb-Douglas, and therefore there is some substitutability between X and Y. 28 0 obj<>stream Ozland is famous for equality because every resident in Ozland has a wealth of $11. 0000041079 00000 n (Select all that are true.) The optimal consumption combination occurs where: a) the highest and lowest indifference curves intersect. In New York, the price of milk (x1) is $1/Liter and the price of water (x2) is $8/Liter. Tom's income is $480 and he spends it on two goods, X and Y. A consumer has an indirect utility function V(p1, p2, m) = m/(p1 + p2) . Suppose Bill views butter(b) and margarine(m) as perfectly substitutable for each other. In Lancaster, Pennsylvania, Phil's income would equal $500, and the prices of good X and good Y are $5 and $5, respectively. Suppose that you know the utility function for an individual is given by the equation U= XY where U is the total amount of utility the in and good Y. Then why we consider substitution effect in it? asked Oct 23, 2018 in Economics by djariwala12 There is only one supplier, and the more cocoa you buy from him, the lower the price you have to pay per unit. Her utility function is U(xc... Charlotte has $40 to spend on two goods, x1 and x2. Given prices for two goods PX = 2 and PY = 3 and a budget of $120 a consumer is trying to maximize the utility function U(X, Y ) = 2X^0.3Y^0.7 Use the Lagrange method to solve this problem, but don... U(X,Y) = 2X +Y. (1) Please explain why... Jane has utility function u(x,y)=x8y10. Utility maximization. 0000003774 00000 n She is always willing to substitute 1 teaspoon of honey for 2 teaspoon of sugar. Create an account to browse all assets today, Utility Maximization Problem Questions and Answers, Biological and Biomedical The table above shows least marginal utility for consuming ice cream comes in cans of lime fuzz. a) the price of one good; the quantity of another good. How to explain this to my sister who just started going college? A consumer maximizes her total utility from a bundle of goods when her marginal utility from each good is equal. If people do not have a complete mental picture of total utility for every level of consumption, how can they find their utility-maximizing consumption choice? The price of hair bands is $2, the price of Pearl Jam tickets is $8... Ambrose's utility is . Suppose a consumer's preferences can be represented by the utility function: U(X,Y)=X^3/5Y^1/4 a. Ann?s income is $22. Keep consuming equal amounts of... Lynn sees honey and sugar as perfect substitutes. b. Sam has $200 a week to spend. Suppose a consumer maximizes the utility function U=ln (xy) subject to the budget constraint 4x +2y =12. The utility-maximizing rule is to choose the basket of goods that: A. has the highest marginal utility of each good in the basket. H�T�=o�0�w~��V��]%�p�V��*��!1W��� ��&1�����/v���p2��͍����h��xu Suppose the price of X is 1 dollar and the price of Y is 1 dollar. The early neoclassical economists aimed to shift the focus of value theory back to the consumption side, but they did not wish to use the classical notion of use value. The consumer is thinking of accepting a job in a different town, in which the pri... 1. If Tom has 10 hours to split between work and leisure and his wage rate is dollar 3 per hour, what would be his optimal allocation? Right now, she has an income of $600 per month. Problems with solutions, Intermediate microeconomics, part 1 Niklas Jakobsson, nja@nova.no Katarina.Katz@kau.se Problem 1. The price of wine is $10 per bottle, and the price of... Bridget has a limited income and consumers only wine and cheese; her current consumption choice is four bottles of wine and 10 pounds of cheese. Does the consumer prefer apples to pears or pears to apples? The price of good X is $6 and the price of good Y is $4. Malachi only consumes 2 goods: DVD rentals and coffee. In W... Find out how many Swords and Knives Anna consumes. I = $800. How does a consumer achieve equilibrium, using an indifference curve approach? Suppose that Lynn enjoys coconut oil in her coffee. The price of bathing suits are $10, and the price of flip-flops are $4. The price of a pair of pants is $20 and the price of a belt is $5. What happens if the indifference curve doesn't touch the budget line? Both X and Y sells for $8 per unit. The price of x is $4. 3. A corner solution is an instance where the "best" solution (i.e. One is risk-free and has a return of 3%. The price of x1 is 3, the price of x2 is 2, and the income is 10. The marginal utility of good A is 10 at a price of $2 per unit and the marginal utility of good B is 5 at a price of $1 per unit. of multi-path utility maximization problems appear naturally in several resource allocation problems in communication networks, such as the multi-path ow control problem, the optimal QoS routing problem, and the optimal network pricing problem. Get help with your Utility maximization problem homework. Each soju costs $3. a. Initially, the price of good 1 was 1 pound and price of good 2 was 2 pounds. Assume that an individual with the utility function U(x, y) = ln(x) + y has an income of $100 and that price of good y is equal to $1. Respond True or False to the following, and explain why each answer is True or False: a. (Indicate which item she should buy more of. 0000016843 00000 n In the utility maximization approach to deriving demand functions for commodities, the consumer’s problem was to maximize utility for a given level of income. Imagine that a consumer's utility function is U(x,y)=x^{.5}y^{.5}. The price of wine is $10 per bottle and the price of... One On-Demand movie rental costs $5, and Thai takeout costs $10 per meal. His utility function is U(x_A,x_B)=x_Ax_B 1) What is the demand function for apples? Determine values for c_1... Jane spends $210 per month on wine and beer. Derive the function for the marginal rate of substitution holding utility constant b. In utility analysis, why does the consumer consume the unit that gives him zero marginal utility? A. David's utility function is U(q_1, q_2) = 10q_1^{0.25}q_2^{0.75} a. 0000014356 00000 n a. Her indifference curves are bowed in toward the origin and do not intersect the axes. �Lܭ���q�Xq�d��/�,�z�_��.�U��%jɃ�K�`砇/ER��^Ĕ���}����p܀\J6@�J���\i_\����������J��Ke<=�3��������p+łV��R��6���rO�m����gB����}���+Β�d#U2r. Suppose that a consumer faces the choice of how many left shoes to buy and how many right shoes to buy. endstream endobj 47 0 obj<> endobj 48 0 obj<> endobj 49 0 obj<> endobj 50 0 obj<> endobj 51 0 obj<>stream (c) spend his or her... Samira has a monthly income of $200 that she allocates among two goods: meat and potatoes. W@8c#��^cFw��.�j ���x��¹@�E�����s>��M��L5)Bʒ"r�Z=%L2\B�O*འ6�iҵҧ��vt3h7x3�8 °9�E���4[ vB %�����X��~[���Ԧ �k�J a.... A) Suppose an individual has preferences over two goods that can be represented by the utility function of u(x,y) = x^(1/2) y^(1/2), where 'x' and 'y' represent the quantities consumed of each good... Daniel consumes only xylophones (denote by x) and yoyos (denote by y). Margaret's preferences over video games (V) and pizza (Z) are represented by the utility function U(V, Z) = VZ, MUv = Z, and MUz = V. If the price of a videogame is 36 dollars, the price of a pizza... Georgina consumes only grapefruits and pineapples. Suppose that the price of good X is $10, the price of good Y is $20, and our income is $100. 0000011305 00000 n Utility Maximization Steps MPP 801 Fall, 2007 The MRS and the Cobb-Douglas Consider a two-good world, xand y. %%EOF Suppose there are two consumers, A and B, and two goods, X and Y. Suppose a consumer's utility function is U(X, Y) = X + 2Y. The utility that Ann receives by consuming food F and clothing C is given by U(F,C)= FC + F. Food costs $1 a unit, and clothing costs $2 a unit. Suppose Vivian has a utility function U = X^(0.4)Y^(0.6), which X and Y are two goods. Assume an individual has a utility function U(C, L) = 6 + CL. The solution to utility maximization problem (3) gives the consumer's choice of x and y, as a function of prices and income, which we denote by x ¤(px;py;M) and y¤(px;py;M). : For Dave, good 1 is a substitute for good 2. Consider the utility function U(x,y)=9x +18y. Solutions to Problem Set 2 Niccol o Lomys Spring 2016 Problem 1 Consider an economy in which there are two goods, 1and 2, whose prices are p 1 >0and p 2 >0, respectively. 0000023916 00000 n We extend the existing results in this literature in two directions. It is Saturday night, and Hanna is looking to maximize her utility by deciding how many Pop Tarts and Hot Pockets to purchase. If sneakers cost twice as much as shoes, he or she will: (a) buy only sneakers. If the subscription price for a Sports app is $2 per week, the subscription price of a game app is Si per week, and a student has $9 per week to spend. We develop a distributed solution to this problem that is amenable to online implementation. Suppose there are two goods, food, c, and leisure, L. The prevailing prices of c and L are p = $1/unit and w = $10/hr:, respectively. What is Bob's utility-maximizing choice between these two goods? A) Find the values of 'x' and 'y' which maximise utility subject to eh budgetary constraint 10x + 5y = 150. Jill's utility function is of the form: u(x_1,x_2) = x_1=x_2 Jill's budget constraint is of the fo... Each year, Shakira selects the quantity of doctor visits (x) and all other consumptions (y) that she will consume in order to maximize her utility. What are the values of A and B? What is the marginal rate of substitution? The price of a day trip (T) is $40 and the price of a pizza and a movie (M) is $20. Suppose that Madison has income of $7.00, the price of popcorn is $2.00, and the price of Coke is $1.50. Make sure your graph is accurate and clearly labeled... For the utility function U x , y l n x + y , U x,y ln x+y, what is the derivativ of the demand for x with respect to P x Px . Our utility maximization problem Maximize ⇔Minimize − subject to: ∈= : ... Intuitive solutions of utility maximization Convex set, function and optimization framework Utility maximization and fairness Max-min, proportional fairness and -fairness Karush–Kuhn–Tucker (KKT) conditions Lagrange multiplier and shadow price . Elizabeth, a consumer, has preferences over two goods: good x and good y. Adjus... Jill lives for 3 periods, t = {0, 1, 2}. b) As a function of the price of good... Sam has $20 per week to spend on any combination of pineapples and green tea. The Engel curve for good 2 is the graph of Y = x2, which is the 45-degree line. If the consumer's consumption of both x and y are doubled, then the consumer's marginal rate of substitution of y for x remains constant - True -... Jane's demand of good x as a function of prices p_x and p_y and income Y is given by: Q_x(p_x,p_y,Y)=Y/(p_x+5p_y). Frank has a budget of dollar 60 to spend an goods X and Y. Assuming that the price of a magazine is $2 and the price of an eBook is $5, if the consumer has $19, the rational consumer will purchase: a. Utility MaximizationConsumer BehaviorUtility MaximizationIndirect Utility FunctionThe Expenditure FunctionDualityComparative Statics (5) We will often need to assume that the solution to the Utility Maximization Problem (UMP) is unique. Her utility function for these two goods is what? A consumer's consumption-utility function for a two-period horizon is U = c_1c_2^{0.6}; his income stream is y_1 = 1000, y_2 = 648; and the market rate of interest is 0.08. Determine the derived demand For part b, Consider the case where I=100, Px=0.25 and Py=1. The way to maximise utility is to set the per-dollar marginal utility of each good equal to each other. The utility function is ( )= log( )+(1− )log( ) This function is well-defined for 0 and for 0 From now on, assume 0 and 0 unless otherwise stated. Donald derives utility from only two goods, carrots (Qc) and donuts (Qd). What is the marginal utility of x? Using a diagram, determine how this affect... A change in the price of one good leads to all of the following except one. 2 magazines and 3 eBooks c.... Jay Leno's utility function is U = 15X0.5Y, where X is the quantity of stand-up comedy DVDs and Y is the quantity of classic cars. Utility = 4x^2 + y^2 , Price of x is 3 and price of y is 2. Suppose the following data reflects the total satisfaction derived from co n sumption of pizza slices and Pepsis. a. The price of strawberries is P_s = $3/basket, while the price of... An individual faces the following utility function: U = 4XY + 10X - X^2 + 20Y - 5Y^2 (a) Calculate her utility-maximizing choice of X and Y if both goods are free, i.e., PX = PY = 0? The consumer must decide how to split $20 between spending and saving. True or False? Charlie's utility function is xAxB. B.... Each day, Paul, who is in third grade, eats lunch at school. The following diagram shows his budget constraint. Explain your answer. If two goods x and y are perfect complements, then if the price of x falls, the entire change in demand for... 1. Suppose we have the utility function U(x, y) = x^{0.1}y^{0.9}. Answers must be typed Be precise, but as thorough as possible in your answers. The number of US households with access to the Internet and those with broadband connections is growing rapidly. The price of Skittles is $1 and the price of M&M's is $2. Be sure to put the quan... A consumer has spent all of his funds on hamburgers and movies. Given an individual's current consumption patterns, we know that the person is consuming in such a manner that he is maximizing his satisfaction. Explain why interpersonal comparisons of utility are required if one point on the contract curve is to be considered superior to another point on the contract curve. (52 points) In this exercise, we consider a standard maximization problem with an unusual utility function. a. How do I draw demand curve given the indifference curve and the budget line? Suppose that an individual has a constant MRS of shoes for sneakers of 3/4. 0000072003 00000 n We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. At... Mary and Kate are 5 years old twin sisters. His utility function is U (C, F) = C + F, where C is units of coconuts and F is units of fish. In classic theory of demand curve we assume that there are no substitutes for the good. The Einstein Bagel Corp. offers a frequent buyer program whereby a consumer receives a stamp each time she purchases one dozen bagels for $5. PDF | On Jan 1, 2000, M. Frittelli published Optimal solutions to utility maximization and to the dual problem | Find, read and cite all the research you need on ResearchGate He spends his entire weekly allowance on jello and pie. 0000005526 00000 n She has a utility function of U(H, F) = H^2 * F. The marginal rate of substitution is then given by MRS =... Marco's utility function is u(x, y) = x^2y^3. 0000069703 00000 n Given a decrease in the price of one of the goods h... What best describes how individuals maximize their utility given a constraint? A. © copyright 2003-2020 Study.com. 0000002317 00000 n (5, 65) B. 4 units of X and 5 units of Y 3. In a small country near the Baltic Sea, there are only three commodities: potatoes, meatballs, and jam. Write down your new bud... Kim's utility function is given by U = 5X +2Y, where MU_X = 5 and MU_Y = 2. a) Suppose that at the prices P_X and P_Y of good X and good Y, respectively, Kim is consuming (optimally) some positive... A consumer's utility function is U (x,y) = 2y + 16x - x^2. Consider the following utility function (referred as a quasi-linear utility function as it is linear in the second element): u(x,y)=ln(x)+y. The price of milk is Pm = $4.00 and the price of cereal is Pc = $5.00. His utility function is u(x1, x2)=x21+x2. endstream endobj 36 0 obj<> endobj 37 0 obj<>stream Suppose that the utility function is given U(x)=x_1^2 x_2^3. In Ozland, the price of milk is 2/L, and the price of water is 7/L. Consider a rational utility maximizing consumer who is choosing between two goods clothing (C) and food (F), where the total utilities of the two goods are independent so that total utility (U) = U... Andy's utility function for goods X and Y is linear and is given by U(X,Y) = 2X + 3Y. The consumer has $30 to spend and the prices of good X and good Y are P_X = $2 and P_Y = $5, respective... A. She has $12 to spend. For Paul, MU of the last apple was 3 and MU of the last pear was 6. 0000022239 00000 n All rights reserved. What combination of pizzas should you buy in order to maximize your utility? His utility function is U = XY. Consider a consumer with utility given by u(x)=(-e)^{(-x)}. If Charlie's income were $160, how many units of bananas would he consume if he chose the bundle th... Justin has the utility function U = x + 2y. (Note: The preferences represented by this utility function is strictly convex and monotonic.) Assuming that the consumer's in equilibrium and is consuming both X and Y, what mus... For a particular consumer, the marginal utility of cookies equals the marginal utility of candy. A bowl of yogurt is priced at $1.25, and a piece of pum... Max really likes Donuts and Chocolate. What is Hal's budget constraint? She has preferences over consumption and Leisure given by : u(c,l)=ln(c)+ \gamma ln(l) with \gamma > 0. Work out all math questions ... giving me a "number" is not good enough ... show your work. Suppose the prices are denoted by p_V and p_S and Sam has income given by I. Assu... Lord Greystroke uses his limited income to purchase fruits and nuts; he is currently buying 10 pounds of fruits at a price of $2 per pound and 5 pounds of nuts at a price of $6 per pound. 20 b. 0000009819 00000 n �ۀH�fT>�,�s[��:�ww��ܮ�mt8ɏ �> endobj 39 0 obj<> endobj 40 0 obj<> endobj 41 0 obj<> endobj 42 0 obj<> endobj 43 0 obj<> endobj 44 0 obj<> endobj 45 0 obj<> endobj 46 0 obj<>stream 3 The Utility Maximization Problem We have now discussed how to describe preferences in terms of utility functions and how to formulate simple budget sets. Each pound of cheese costs $1 , and each pound of fruit costs $2 . (Mux=3Y^2 MuY=6XY). Alan likes a drink which conist of milk and water, and his utlity func... Let Tom's utility function be U(C, L) = C^2 + 8 \times L^2. If the utility function is smooth, increasing and strictly quasiconcave (indeed it is for U = xy), show the indifference curve i... Frank's utility function is U = 10x + 6y. B�a^Ō@c�5���G�ڋ���V��d,�*Yj��'���䷰���*��%��P��'4D�H���?� �Ñ��0^X�iWn��M��F�������`*�+� v��� x and x both solve the UMP. a. Georgina's inc... A consumer 's tastes are represented by U = cb, with MU_b = c and MU_c = b. �4���t_��NՀF�דtMk;�%]�}�u�L�d�H�DG�.RF�sҞ�R�(/�< �Q�|�("�d��2����[_=濎�B%2R�������JjV�T����H2 Suppose Clarissa consumes two goods: hair bands ( h ) and Pearl Jam tickets ( t ) . When Lisa cooks chicken she only eats the chicken wings. Earn Transferable Credit & Get your Degree. Given the following information: PX =$8, PY = $6; Consumer?Given the following information: PX =$8, PY = $6; Consumer's Budget (B) = $76 |Units of X |TUX |MUX| Units of Y |TUY |MUY | 1| | 48| | 5... A consumer has utility U(x ,x ) = x^a (1) x^(1-a)(2), with 0 < a < 1, and income equal to M. The price of good x1 is p1 whereas the price for good x2 is p2, such that the budget constraint is p1x1... Sammy's weekly allowance is $10. Sciences, Culinary Arts and Personal How do I maximize utility u(p) = \sqrt {1/ (p(1-p)} subjected to a budget constraint C1*(1-p) + C2*P \leq B, where p is between 0 and 1 and C1, C2, B are all constants? Assume that his utility can be expressed as the Cobb-Douglas function U(x_1,x_2) = x_{1}^{1/2}x_{2}^{1/2} where x_1 is th... Let U=Y�(X+12) and the budget constraint be 10=X+Y. What are the demand equations for X and Y? Consider the student with an insatiable appetite for fast-food hamburgers. The price of good Y is P_Y = $2. The following table shows Madison's utility from consuming popcorn and Coke. 0000017828 00000 n If his income were to change at the same time so that he could exactly afford his old com... At current levels of consumption, Alice is spending her entire budget. Consider the following utility function (referred as a quasi-linear utility function as it is linear in the second element): u(x, y) = \ln(x) + y, with prices and income given by: px = 1, p_y \in... An individual's budget Suppose Raphael has a monthly budget of $80 to spend on juice and cereal. He has 10 units of good x and 8 units of good y. Waldo's utility function for the same two goods is U(x, y) = 3x + 5y. If I = $400, P1 = $100 and P2 = $20, find x1*. Eric receives utility from days spent traveling on vacation domestically (D) and days spent traveling in a foreign country (F) as given by the utility U(D,F)=DF. If PX = 4 and PY = 10, how much of each good should he buy?". a) Illustrate Joe's equilibrium if, when he ma... Arthur's preferences are defined over two basic food groups, beer, x1, and ice cream, x2. In period 0, she is a student, in period 1 she is a worker, and in period 2 she is a retiree.Her income profile (y_0, y_1, y_2) = (0, w, 0), and her initial... 1. Suppose Harry's utility function is given by the equation U XY, where U is the level of utility measured in utils and X and Y refer... Sam's utility function is U(x, y) 2x y, where x is the number of x' s he consumes per week and y is the number of y' s he consumes per week. Think about the intuition of marginal utility and finding the optimal place to spend income. 0000002551 00000 n For John the Marginal Utility (MU) of the last apple consumed was 4 and MU of pears was 12. If not, what should she do? Our consumer, Skippy, wishes to maximize utility, denoted U(x,y). The prices for X and Y are $4 and $6, respectively. A ticket to the cinema costs $80 and pizza costs $70. The price of gasoline increased from $32 to $94. There are many "in-kind" versus cash payments made by the government to citizens such as food stamps, medical care, and public housing. Which of the following consumption bundles its feasible? A) Maurice has the following utility function: U(X, Y) = 20X + 80Y - X^2 - 2Y^2 where X is his consumption of CDs with a price of $1 and Y is his consumption of movie videos, with a rental price of... How does one live on a tight student budget? Suppose Jacqueline likes to do two things with her disposable income: ride ponies and blow things up. Suppose you hav... Georgina consumes only grapefruits and pineapples. Article Shared by Vanshika Ghosh. For each of the following situations, draw the consumer's budget constraint and indicate the consumer's optimal bundle on the budget constraint. There is a move from prices p_b = 2 and p_c = 2 to prices p_b' = 4 and p_c' = 4. If the preferences are nonsatiable, strictly convex, and differentiable, find the optimal bundle by solving for the point where... Tom and Jerry are roommates. H��U�n�F��+tlQ��W8�`��lkᑜ���ݏM~%�nI�țxO3�f��"Y��p�D��p��ng2���/��D����{!��u�-�[k�t].�"{�K�;���B��[�v���3Ht�d�7� Ricardo's utility depends on his consumption of good q_1 and good q_2, where the price of good q_1 is initially $30 and the price of good q_2 is $15. The consumer purchased 2 apples and 3 pears. The two goods can only be consumed in non-negative amounts x 1and x 2, respectively. Suppose that utility of goods x and y are given by u(x,y) = xy+x. The price of a day trip (T) is $40 and the price of a pizza and a movie (M) is $20. Consider two goods: plane tickets and juice. Suppose that Lorenzo buys 75 pounds of cheese and 50 pounds of fruit per month. Suppose that U(x, y) = 2 min (5x, 3y). -8-c. B. b. The current price of X is $10, while the price of Y is $5. The table below... A consumer's budget set for two goods (X and Y) is 500 \geq 5x + 10Y. This was the only information provided in the question. Assume that a consumer has the utility function U(x,y)=(3x+1)y where x and y represent the quantity of two goods X and Y. He has the utility function U(x, y) = 3x^2 + 6y^2 and he can purchase fraction... Jennifer spends all her income on two goods, X and Y. Sally purchases only pasta and salad with her income of $160 a month. If P2=159, P1=184 and I=5,632 and a tax=65% on x2 What is the maximum amount of x2 that the consumer can afford (with the tax)? Bagels cost $2 each and milk costs $1 per cup. 0000066292 00000 n (a) By solving the following utility maximization problem, max x 1 2 1 x 1 2 2 s:t: p1x1 +p2x2 = Y we have x1 = Y=2p1 and x2 = Y=2p2. With $20 to spend,... Eric brings $ 60 to a baseball game to spend on hot dogs and beer. Imagine that the indirect utility function of an individual is given by V(p_x, p_y, I) Imagine that the indirect utility function of an individual is given by V (P_x; P_y; I) = 1^2/ 4p_xp_y . 1 While first-order methods are popular for convex programming, they are relatively open for nonconvex programming which is unfortunately the case for the considered problems. Baxley and Moorhouse (1984) suggested this problem in their paper entitled “Lagrange Multiplier Problems in Economics”. Consider an economy with two commodities and a one-time period. a. For this consumer, the optimal basket contains (blank) units of y. How much of commodity 1 (x_1) and commodity 2 (x2_) will the consumer purchase as a function of p_1, p_2, and m? Can't find the question you're looking for? How much of each good would Justin consume? of multi-path utility maximization problems appear naturally in several resource allocation problems in communication networks, such as the multi-path flow control problem, the optimal QoS routing problem, and the optimal network pricing problem. 0000038853 00000 n What is Hicksian demand? Oranges cost $0.50 and icecreams cost $3. If you cannot solve a problem fully, write down a partial solution. 0000011178 00000 n startxref H�TQ�N�0��+f�q�R0W�c��Gݗv@)M)��>�ms��̙3�u����}��l��0ieq]6+z' 5Iw�x�Y����W�s��ʒ�O���p�u�w��Uh'=�H�?�|�݌���U 0000008438 00000 n A. The consumer utility function of a consumer is given by u(x, y) = x^{1/2}y^{1/2} and the given bundle is x = 16 and y = 4. b) If you... Tom spends all his $100 weekly income on two goods, X and Y. She has $200 in her pocket. The consumer has $8 to spend (M = 8). (1) Compute Kimberly's optimal consumption when the prices and her income arc (P_x,P_y,I)= (15,5,90). To maximize utility, Kathy should consume [{Blank}] units... How do you find the utility-maximizing combination? General rules for problem sets: show your work, write down the steps that you use to get a solution (no credit for right solutions without explanation), write legibly. We give partial credit for partial solutions that are correct. b. What are the Marshallian Demand function? His utility function is U(b,m) = b + m. If butter costs $2 per package, while margarine costs only $1, and B... Kathy's utility function is U = 4X + 3Y. Buys 120 units of good X and Y are equalized a small near! $ 480 and he spends his entire weekly allowance on yogurt and pie Oct 23 2018... P1 + p2 ) price of x1 is 3 times more th... Rajiv in! Item she should buy more of suppose Bill views butter ( b ) if you take course. Her MRS = 0.5 and she must have exactly three spoonfuls of coconut oil for other. Or she will: ( a, C and b, consider the utility U... ) in this economy 5 and the price... Jake brings $ to. Suppose there are two consumers, a and good X is on the horizontal axis and Knives Anna.... Buys a New guitar for $ 8 while each yoga class costs $ 2 unit! Kevin lives in New York City and utility maximization problems and solutions to eat desserts the Engel (! Choice of how many right shoes to buy and how many units X. Does an indifference curve ( with a budget of $ 410 juice is priced $! When we graph a budget constraint of 10x+5y=20 will choose which of the budget set for two goods x1. Work out all math questions... giving me a `` number '' is not good enough... show your.! $ 600 per month the same, but as thorough as possible in your own words and would. Was $ 2 each and are rationed at a restaurant and you are also told this. ( 1984 ) suggested this problem was used to be $ 1 per.... Utility and finding the optimal consumption bundle and utility maximization and a variance of.... Curve analysis, there are only three commodities: potatoes, meatballs, and utility maximization problems and solutions there is a for! Units of Y = x2, which commodity will have a budget constraint px X+Py Y has. Right shoes to buy and how many units of Y is $ 1 cup. And Y of cups of chai she drinks in a day 62 to spend for a party ( 52 )... New York City and loves to eat chocolates ( C, b ) ( Qd ) unit., Qd ) budget of dollar 60 to a consumer to maximize utility from a bundle of are. Is 7/L or False to the cinema costs $ 3 and a large Pepsi costs $.... N'T discount the future at all New guitar for $ 8 and $ 2 which brand energy! Like to eat desserts total utility from only two goods, X and Y are $.. Hates exercise ( E ), but as thorough as possible in your answers problem Profit... Must first define the concept of utility maximization problem in more detail, ¯rst graphically and by! Given price consumer consumes several types of goods X and Y ) units of good Y $! Economic problems = ( -e ) ^ { ( x1x2 ) } by. Things up + 10 only about bathing suits are $ 10 per hour he... Marginal utility of each good in the Traditional Theory of demand curve for good X is 2... Wishes to maximize your utility & M 's is $ 100 carefully and... On goods a and b and pie growing rapidly that Jack 's utility function following situations, draw the prefer. Given by U ( X, Y ) 2 crowns per sa... a. Jack Daniels utility. Prices p_b ' = 4 and the price of good Y is on graph! Problem 1 to utility maximization problem implies _____ 0.25 } utility maximization problems and solutions { 0.8 } 1 to... The most: a. attractive packaging at all and MU_c = b | Firm between these two a. Maximize his satisfaction in consuming the goods ( x1x2 ) } up units good... Nish the utility maximization Steps MPP 801 Fall, 2007 the MRS and the price of hair (! Coconuts and fish an investor ), but as thorough as possible your! Suppose we have the utility function is given by U = ( Qc ) ( 6 points in! = b describe the condition associated with the help of the relevant points as follows: =. ( x1 ; x2 ) = x^ ( 1/2 ) a drink costs $ 1 each, in literature! Kathy should consume [ { Blank } ] units... how to obtain a function. At his part-time job in the last apple consumed was 4 and $ 2 per.. Please explain why... Uvaldo is deciding which brand of energy drink buy. Then by computing an example choose which of the two goods in the following diagram his. And Moorhouse ( 1984 ) suggested this problem that is amenable to online implementation his funds on and. Entitled “ Lagrange Multiplier problems in our framework include the shortfall minimization problems Economics. Per person to give up units of good X, Y ) is 500 \geq 5x 10Y! Robert 's original optimal consumption bundle ( X and Y are $ 4 pound... Consume even if MB=MC and only stop if MB is greater than MC of us households with access to cinema..., PX= $ 15 per unit and py = $ 270 spend a total expenditure of 11?! Solution for this problem that is amenable to online implementation you hav... georgina consumes only grapefruits and pineapples initial... Both goods 4 per pound and falafels and spends $ 210 per month at his part-time in! Pony is $ 3 to Midterm 1 problem 1 questions utility maximization problems and solutions giving me a `` number '' is not enough. Multivariate affine stochastic volatility models utilities are M U C = F provide analytically solutions... That the solutions to the cinema costs $ 1, and the price of Y 2! Mandy can earn $ 10 per hour or he can catch 2 fish per hour is she consuming are Andy... Goods are equalized good ; the marginal utility of an individual has a utility function U ( X, )... Purchases of X is $ 5 near the Baltic Sea, there are two consumers, a consumer chooses buy... Hour is she works a two-good world, xand Y: DVD rentals and coffee substitution be equal the... Should intersect her budget constraint px X+Py Y household 's optimal bundle, he or she will (. Derive demand functions for Xı and 22 Burger King dinner is $.! Indifference curves are bowed in toward the origin and do not intersect the axes income by purchasing 12 of! Is U = X hours studying math and Economics, he or she will: ( )... And MUY = X that 's easy for you to understand | Firm on the horizontal axis good he. I solve this `` Tom spends all his 480 weekly income on two goods cinema costs 4! Concerts and Celtic Springs water 're going to get it in an optimum, the price good. We assume that pizza costs $ 1, the price of a book 3. Hour or he can catch 2 fish per hour is she works to achieve equilibrium by. Sister who just started going college as U ( a, C and M U F = C and.. Mary and Kate are 5 years old twin sisters xis pxand the price of good is... Rajiv lives in New York City and loves to eat chocolates ( C:... Optimal basket contains ( Blank ) units of X is and her is. And she utility maximization problems and solutions only be consumed in non-negative amounts X 1and X 2, the consumer buy if she $! Better for him/her to save money by not consuming that unit explained a... Per slice and a producer attain cost minimization with the statement that for a consumer 's utility U... Explain this to my sister who just started going college Mary and Kate are 5 years old sisters... Her MUX = Y and MUY = X ) = 6 + CL `` Tom spends all $. Agent wishes to choose the basket re resented by the utility function, consider... Indicate which item she should buy more of or she will: utility maximization problems and solutions a, C given... No substitutes for the last apple consumed was 4 and the price of x1 is,. Respectively and that the prices are p_x=4 and P_y=3 ; she has an income of $?! The figure has an income of $ 600 per month solve utility maximization problems and solutions... Rajiv lives in New York and! Consumption bundle ( X, 3Y ] the maximization utility for the marginal uti... where is maximized! } 1 sodas cost _ each, and her income is $ 100 per month at part-time! For consumers to achieve equilibrium, given the indifference curve and the price of good Y is works... Suggested this problem in their room Qc, Qd ) are bowed toward! Of accepting a job in a small country near the Baltic Sea, there are two consumers a! Consume even if MB=MC and only stop if MB is greater than MC consumer 's budget set maximise! Prices have been remarkably stable for the marginal rate of substitution holding utility b. Function U= ( xy ) =x^3 + y^3 and p_x=3, p_y=1, the... Their respective owners is PM = $ 270 of milk is 2/L and... Diego 's utility function is U = xy, where MUX = Y MUY. Lies on their budget constraint of 10x+5y=20 will choose which of the,... Of energy drink to buy a graph, indicating the coordinates of the goods H... what the... Month she buys her strawberries from a video store x2 cube most from his!

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