Problem 2Suppose that John's preferences over meat (M) and vegetables (V) are represented by thefollowing utility functionU(M,V) = a ln(M) + (1 − a) ln(V)where 0 < a < 1.¹No claim of realism is made for the numbers in this example.1(a) Write down the Lagrangian for John's optimization problem. (Recall that John max-imizes utility given an income, I, and prices pè and på for the goods.)(b) Solve for John's optimal consumption bundle (M*, V*) (as a function of income andprices) using the Lagrangian method.=(c) Suppose a = . Suppose also that John has income I=1 and pv2. What is the value of John's optimalhappens if John's income doubles to I = 400?200 and faces prices pconsumption bundle? What=

The utility function for John is given as follows. The value of * lies between 0 and 1. The income…

Problem 2 Suppose that John's preferences over meat (M) and vegetables (V) are represented by the following utility function U(M,V) = a ln(M) + (1 − a) ln(V) where 0 < a < 1. ¹No claim of realism is made for the numbers in this example. 1 (a) Write down the Lagrangian for John's optimization problem. (Recall that John max- imizes utility given an income, I, and prices pm and py for the goods.) (b) Solve for John's optimal consumption bundle (M*, V*) (as a function of income and prices) using the Lagrangian method. 200 and faces prices PM = 1 and pv = 2. What is the value of John's optimal consumption bundle? What happens if John's income doubles to I = 400? (c) Suppose a = . Suppose also that John has income I =

Problem 2 Suppose that John's preferences over meat (M) and vegetables (V) are represented by the following utility function U(M,V) = a ln(M) + (1 − a) ln(V) where 0 < a < 1. ¹No claim of realism is made for the numbers in this example. 1 (a) Write down the Lagrangian for John's optimization problem. (Recall that John max- imizes utility given an income, I, and prices pm and py for the goods.) (b) Solve for John's optimal consumption bundle (M, V) (as a function of income and prices) using the Lagrangian method. 200 and faces prices PM = 1 and pv = 2. What is the value of John's optimal consumption bundle? What happens if John's income doubles to I = 400? (c) Suppose a = . Suppose also that John has income I =

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Consumer Choice Theory

Section: Chapter Questions

Problem 3SQP

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Problem 2 Suppose that John's preferences over meat (M) and vegetables (V) are represented by the following utility function U(M,V) = a ln(M) + (1 − a) ln(V) where 0 < a < 1. ¹No claim of realism is made for the numbers in this example. 1 (a) Write down the Lagrangian for John's optimization problem. (Recall that John max- imizes utility given an income, I, and prices på and på for the goods.) (b) Solve for John's optimal consumption bundle (M*, V*) (as a function of income and prices) using the Lagrangian method. = (c) Suppose a = . Suppose also that John has income I = 1 and pv 2. What is the value of John's optimal happens if John's income doubles to I = 400? 200 and faces prices p consumption bundle? What =
3- Assuming that the equation F(U, x, X2 = f(x1, x2,, ... Xn): ******* **** ,xn) = 0 implicitly defines a utilityfunction U 073 a) Find the expressions for 60, 6U and 6x4 " 3 6x2 6xn 6x2 6xn b) Interpret their respective economic meanings. c) Now. assume the utility function is U(x, y) = y√x. Does the consumer believe that more is better for each good? Do the consumer's preferences exhibit a diminishing marginal utility of x? Is the marginal utility of y diminishing?
On a given evening, J. P. enjoys the consumption of cigars (c) and brandy (b) according tothe functionU(c, b) = 20c− c²+ 18b − 3b²a. How many cigars and glasses of brandy does he consume during an evening? (Cost isno object to J. P.)b. Lately, however, J. P. has been advised by his doctors that he should limit the sum ofglasses of brandy and cigars consumed to 5. How many glasses of brandy and cigarswill he consume under these circumstances?
Draw thes e utility functions a) u Cxiy) = 2. %3D
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1. Jie thinks a cup of coffee is just as good as five cups of orange juice. Let M stand for the number of cups of coffee and N stand for the number of cups of orange juice. Among the following utility functions, how many of them represent his preferences? (1) U(M,N) %3D тах(М,5N} (2) U(M, N) = M + 5N (3) U(M,N) = (3M + 15N)2 (4) U(M, N) = 5M2 + N A.0 B.1 С.2 D.3
This is a question about marginal analysis where one dependent variable is determined by two independent variables. If Utility =.5lnX+3Z+10+4√W then Marginal utility from X is....;. and the Mu of Z is ..... Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a10; 3 b 3, 4 c .5/X; 3 d 2/√W; 3
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1 Marginal utility and marginal rate of substitution Suppose an individual who derives utility u(x, y) from consuming a units of good X and y units of good Y. For each of the following utility functions, derive the marginal utility of good X, the marginal utility of good Y, and the marginal rate of substitution between X and Y. (A) u(x, y) = x+by¹/3 (B) u(x, y) = (xy) (C) u(x, y) = ax + xy + by² (D) u(x, y) = n(ax + y) 1 (E) u(x, y) = (x² + √y²) = 2