QUESTION 4 Linguini and Colette consume only éclair (x₁) and profiterole (x₂). Linguini has utility function U^ = x₁¹x₁ and Colette has utility function U = 2x1x². Linguini is endowed with 10 éclair (x₂) and 3 profiterole (x₂), while Colette is endowed with 20 éclair (x₁) and 9 profiterole (x₂). (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, ie., find x(xf). In your graph in (a), draw the contract curve. Suppose the price of éclair (x₂) is $1 and the price of profiterole (x₂) is $2. (c) 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 () 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, ((x,x), (x,x)).
QUESTION 4 Linguini and Colette consume only éclair (x₁) and profiterole (x₂). Linguini has utility function U^ = x₁¹x₁ and Colette has utility function U = 2x1x². Linguini is endowed with 10 éclair (x₂) and 3 profiterole (x₂), while Colette is endowed with 20 éclair (x₁) and 9 profiterole (x₂). (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, ie., find x(xf). In your graph in (a), draw the contract curve. Suppose the price of éclair (x₂) is $1 and the price of profiterole (x₂) is $2. (c) 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 () 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, ((x,x), (x,x)).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Questions g) and h)
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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