(4) Consider a Cobb-Douglas utility function U(1,2) = ria, where U is the utilitylevel, x, and 2 are the amounts of two commodities, respectively, and a > 0, b> 0, a+b=1.Suppose that the commodity prices for 1 and 2 are p andP2, respectively.(a) Set up the utility maximization problem subject to the budget constraint such thatPix+P2x2 = I, where I is the income level.(b) Suppose that P1, P2, and I are given exogenously. Solve the utility-maximizing levelsof r and r2. [Hint: Derive the demands for 1 and 2, respectively, as a function of pi. P2,and I.(c) Compute the indirect utility function V (P1, P2, I). [Hint: Write the utility as a func-tion of P1, P2, and I.](d) Verify the Roy's identity such thatav (pi PJ)дрOV (p1.p2.1)arfor i = 1,2.

The utility maximization problem is to choose the amounts of commodities x1 and x2 to maximize the…

Answered: (4) Consider a Cobb-Douglas utility…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Jasper utility function for beer and pizza can be expressed as: U(B,P) = BXP Suppose beer costs $5 per glass, pizzas cost $10 each, and Jasper has a total of $30 to spend. Assume Jaspeer is allowed to purchase fractional amounts of each good. Part A) Based on the above information, what is Jaspeer's optimal amount of beer? Enter the number below. glasses Beer = 3 Part B) Now suppose the price of beer falls from $5 down to $3. Calculate the following and fill in the blanks below. When necessary, round answers to two places after the decimal. (Hint: find the decomposition basket to calculate the substitution and income effects). Jasper's total effect on beer is to increase total consumption by glasses of beer. Jasper's substitution effect is to increase beer consumption by 0.28 Jasper's income effect is to increase beer by 1.12 glasses of beer. glasses of beer.
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