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utility function

utility function

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Questions d) to f)

QUESTION 4 Linguini and Colette consume only éclair (x,) and profiterole (x,). Linguini has utility function UA = xfxf and Colette has utility function U® = 2xf x%. Linguini is endowed with 10 éclair (r,) and 3 profiterole (x,), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x,). (a) Draw an Edgeworth boz with x, on the horizontal azis and x2 on the vertical azis. Position Linguini on the bottom left corner and Colette on the top right corner. Indicate the total number of units of x, and x2. Label the endowment allocation. (b) Derive the equation of the contract eurve, ie., find x (xt). In your graph in (a), draw the contract curve. Suppose the price of éclair (x,) is $1 and the price of profiterole (x,) is $2. (c) Find each consumer's utilitymaximising basket. (d) How much of each good does each consumer want buy or sell? Are the markets in equilibrium at the given prices? (e) Verify that Walras' law holds at these prices. Now we will solve for the competitive equilibrium. () Use your solution to (b) to find the equilibrium price ratio, P1/P2- () Set x2 as the numeraire, i.e., assume pi = p and p2 = 1. Write each consumer's budget line equation given the equilibrium price ratio. (h) Find the equilibrium allocation, ((xf,x±), (xf, xf)).
Transcribed Image Text:QUESTION 4 Linguini and Colette consume only éclair (x,) and profiterole (x,). Linguini has utility function UA = xfxf and Colette has utility function U® = 2xf x%. Linguini is endowed with 10 éclair (r,) and 3 profiterole (x,), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x,). (a) Draw an Edgeworth boz with x, on the horizontal azis and x2 on the vertical azis. Position Linguini on the bottom left corner and Colette on the top right corner. Indicate the total number of units of x, and x2. Label the endowment allocation. (b) Derive the equation of the contract eurve, ie., find x (xt). In your graph in (a), draw the contract curve. Suppose the price of éclair (x,) is $1 and the price of profiterole (x,) is $2. (c) Find each consumer's utilitymaximising basket. (d) How much of each good does each consumer want buy or sell? Are the markets in equilibrium at the given prices? (e) Verify that Walras' law holds at these prices. Now we will solve for the competitive equilibrium. () Use your solution to (b) to find the equilibrium price ratio, P1/P2- () Set x2 as the numeraire, i.e., assume pi = p and p2 = 1. Write each consumer's budget line equation given the equilibrium price ratio. (h) Find the equilibrium allocation, ((xf,x±), (xf, xf)).
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