1 two individuals fred and helen in an economy

Question

1. Two individuals, Fred and Helen, in an economy with no production, each have the utility function U = 10XY. Prices of both X and Y are set at $1. Initial endowments for Fred are 10 units of X and 6 units of Y. Helen has 8 units of X and 12 units of Y. Show that this initial endowment is not on the contract curve.

2. Consider a society consisting of just a farmer and a tailor. The farmer has 10 units of food but no clothing. The tailor has 20 units of clothing but no food. Suppose

each has the utility function U = F·C. The price of clothing is always $1. If the price of food is $3, does a competitive equilibrium exist? If not, what will happen to the price of food?

3. Jack and Jill are the only two inhabitants on an island. Jack starts out with 10 lobsters and five coconuts. Jill starts out with 10 lobsters and 15 coconuts. After trading Jack ends up with 5 lobsters and 7 coconuts. Jack feels neither better nor worse off than when he started but cannot get Jill to agree to any more trades. Jill feels better off than when she started. Draw the Edgeworth box consistent with this story.

4. Anne and Spyros consume only pizza, Z, and cola, C. Anne's utility function is U_A = Z_AC_A, and Spyros' utility function is U_S = Z_S0.5CS0.5. Their endowments are Z_A = 10, C_A = 20, Z_S = 20, and C_S = 10.

a.What are the marginal rates of substitution for each person?

b.What is the formula for the contract curve?

c.Draw an Edgeworth box, labeling carefully, and indicate the contract curve.