QUESTION 4Linguini and Colette consume only éclair (x,) and profiterole (x,). Linguini has utility functionUA = 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. PositionLinguini on the bottom left corner and Colette on the top right corner. Indicate the total numberof 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 thecontract 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 wantbuy or sell? Are the markets in equilibriumat 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 lineequation given the equilibrium price ratio.(h) Find the equilibrium allocation, ((xf,x±), (xf, xf)).

"Since you have posted multiple sub-part questions, I can only answer the first 3 parts, the rest…

QUESTION 4 Linguini and Colette consume only éclair (x,) and profiterole (x,). Linguini has utility function UA = xfx£ and Colette has utility function U" = 2xf x£. Linguini is endowed with 10 éclair (x,) and 3 profiterole (x,), while Colette is endowed with 20 éclair (x,) and 9 profiterole (r,). (w) Draw an Edgeworth box with x, on the horizontal axis and x2 on the vertical axis. 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 curve, ie., find x†(xf). 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. (e) Find each consumer's utilitymaximizing basket.

QUESTION 4 Linguini and Colette consume only éclair (x,) and profiterole (x,). Linguini has utility function UA = xfx£ and Colette has utility function U" = 2xf x£. Linguini is endowed with 10 éclair (x,) and 3 profiterole (x,), while Colette is endowed with 20 éclair (x,) and 9 profiterole (r,). (w) Draw an Edgeworth box with x, on the horizontal axis and x2 on the vertical axis. 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 curve, ie., find x†(xf). 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. (e) Find each consumer's utilitymaximizing basket.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.14P

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