Need help for questions d),e),f) Linguini and Colette consume only éclair (x1) and profiterole (x2). Linguini has utility functionU4 = xfx$ and Colette has utility function UB = 2xfx?. Linguini is endowed with 10 éclair (x1)and 3 profiterole (x2), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x,).(a) Draw an Edgeworth box with x1 on the horizontal axis and x2 on the vertical axis. PositionLinguini on the bottom left corner and Colette on the top right corner. Indicate the total numberof units of x1 and x2. Label the endowment allocation.(b) Derive the equation of the contract curve, i.e., find x (xf). In your graph in (a), draw thecontract curve.Suppose the price of éclair (x,) is $1 and the price of profiterole (x,) is $2.(e) Find each consumer's utility-maximizing basket.(d) How much of each good does each consumer want to buy 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.(f) Use your solution to (b) to find the equilibrium price ratio, P1/P2.e) Set x2 as the numeraire, i.e., assume P1 = p and p2 = 1. Write each consumer's budget lineequation given the equilibrium price ratio.(h) Find the equilibrium allocation, (xf,x±), (xf,x£)).

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Linguini and Colette consume only éclair (x1) and profiterole (x2). Linguini has utility function UA = xfx£ and Colette has utility function UB = 2xfx?. Linguini is endowed with 10 éclair (x) and 3 profiterole (x2), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x,).

Linguini and Colette consume only éclair (x1) and profiterole (x2). Linguini has utility function UA = xfx£ and Colette has utility function UB = 2xfx?. Linguini is endowed with 10 éclair (x) and 3 profiterole (x2), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x,).

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.11P

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Question

Need help for questions d),e),f)

Linguini and Colette consume only éclair (x1) and profiterole (x2). Linguini has utility function
U4 = xfx$ and Colette has utility function UB = 2xfx?. Linguini is endowed with 10 éclair (x1)
and 3 profiterole (x2), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x,).
(a) Draw an Edgeworth box with x1 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 x1 and x2. Label the endowment allocation.
(b) Derive the equation of the contract curve, i.e., 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 utility-maximizing basket.
(d) How much of each good does each consumer want to 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.
(f) Use your solution to (b) to find the equilibrium price ratio, P1/P2.
e) Set x2 as the numeraire, i.e., assume P1 = p and p2 = 1. Write each consumer's budget line
equation given the equilibrium price ratio.
(h) Find the equilibrium allocation, (xf,x±), (xf,x£)).

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