Linguini and Colette consume only éclair (x1) and profiterole (x2). Linguini has utility function U^ = xfx£ and Colette has utility function U® = 2xfx? . Linguini is endowed with 10 éclair (x1) and 3 profiterole (x,), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x,). (a) 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 x1 and X2. Label the endownment 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 (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. () Use your solution to (b) to find the equilibrium price ratio, P,/p2. (g) 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£)).
Linguini and Colette consume only éclair (x1) and profiterole (x2). Linguini has utility function U^ = xfx£ and Colette has utility function U® = 2xfx? . Linguini is endowed with 10 éclair (x1) and 3 profiterole (x,), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x,). (a) 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 x1 and X2. Label the endownment 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 (x2) is $2. (c) Find each consumer's utility-maximizing basket. (d) How much of each good does each consumer want to buy or sell? Are the markets in equilibrium at the given prices? (e) Verify that Walras' law holds at these prices. Now we will solve for the competitive equilibrium. () Use your solution to (b) to find the equilibrium price ratio, P,/p2. (g) Set x2 as the numeraire, i.e., assume P1 = p and p2 = 1. Write each consumer's budget line equation given the equilibrium price ratio. (h) Find the equilibrium allocation, ((xf, x±), (xf, x£)).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Need help for g) and h). This is university intermediate
Transcribed Image Text:Linguini and Colette consume only éclair (x1) and profiterole (x2). Linguini has utility function
U4 = xfx$ 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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