2- Suppose a consumer who consumes two goods, good 1 and good 2. We denote his consumption of good 1 by q1, and his consumption of good 2 by q2. Its preferences for good 1 and good 2 can be represented by the following utility function: U (Q1/ Q2) = 3 (Q1) 1/3 * (Q2) 2/3 The marginal utility of good 1 is um1 = (Q2/Q1) 2/3 and the marginal utility of good 2 is um2 = 2 (Q1/Q2) 1/3 Determine the quantity of good 2 q2 'in the shopping basket (q1 '; q2) = (32; q2 ) so as to find on the same indifference curve as the consumption basket (q1; q2) = (8; 64). %3D

2- Suppose a consumer who consumes two goods, good 1 and good 2. We denote his consumption of good 1 by q1, and his consumption of good 2 by q2. Its preferences for good 1 and good 2 can be represented by the following utility function: U (Q1/ Q2) = 3 (Q1) 1/3 * (Q2) 2/3 The marginal utility of good 1 is um1 = (Q2/Q1) 2/3 and the marginal utility of good 2 is um2 = 2 (Q1/Q2) 1/3 Determine the quantity of good 2 q2 'in the shopping basket (q1 '; q2) = (32; q2 ) so as to find on the same indifference curve as the consumption basket (q1; q2) = (8; 64). %3D

Microeconomics: Principles & Policy

14th Edition

ISBN:9781337794992

Author:William J. Baumol, Alan S. Blinder, John L. Solow

Publisher:William J. Baumol, Alan S. Blinder, John L. Solow

Chapter5: Consumer Choice: Individual And Market Demand

Section: Chapter Questions

Problem 3DQ

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A consumer has GH¢600 to spend on two commodities, A and B. Commodity A costs GH¢20 per unit and Commodity B costs GH¢30 per unit. Suppose that the utility derived by the consumer from x units of Commodity A, and y Commodity B is given by the Cobb-Douglas utility functionU (x, y) = 10x0.6y0.4a. How many units of each commodity should the consumer buy tomaximize utility?b. Is the budget constraint binding?
True or false with reasoning: 1) _______When we claim that utility can be ordinally measured, we assume that the consumer is able to measure the total and marginal utility received when one extra unit of a commodity is consumed. 2)_______If MRS between two goods is constant, then having more of one good without having more of the other does not increase utility. 3)_______Marginal Utility increases until total utility is at a maximum and then marginal utility decreases.
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A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility which their consumption will yield is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend. Product X Product Y Product Z Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ 1 42 NA 1 14 NA 1 32 ___NA__ 2 82 4 2 26 6 2 60 __3.5_ 3 118 3.6 3 36 5 3 84 __3___ 4 148 3 4 44 4 4 100 __2___ 5 170 2.2 5 50 3 5 110 _1.25___ 6 182 1.2 6 54 2 6 116 _0.75__ 7 182 0 7 56.4 1.2 7 120 _0.5_ How many units of X, Y, and Z will the consumer buy when maximizing utility and spending all…
1. An individual is confronted with three commodities x, y and z. Suppose the consumer’s money income is Birr 39 and the marginal utility of each good is independent of the amount consumed of other goods. Using the hypothetical data given below, find the optimum quantities of a consumer. Unit of each good 1 2 3 4 5 6 7 8 9 10 Mux 12 11 10 9 8 7 3 0 -2 -6 MUy 60 55 48 40 27 21 19 18 9 0 MUz 70 60 50 45 30 25 18 10 0 -5 a) If the three goods were “free” or no budget constraint. b) If respective prices are Px= 1 Birr, Py=3 Birr and Pz=5 Birr
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Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…
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