Consider an exchange economy with two consumers 1 and 2, and two goods x and y. Consumer 1's initial endowment is: x₁⁰= 4, and y₁⁰= 7.

Consumer 2's initial endowment is x₂⁰= 6 and y₂⁰= 3. Their preferences are given by the

utility functions U₁(x₁ , y₁)= x₁ +log(y₁) , and U₂(x₂ , y₂)= y₂+log(x₂)

Remember that the derivative of log(x) is given by 1/x.

(a) Draw an Edgeworth box for this economy with the initial endowment, the indifference curves of the two consumers at their initial endowment, and the set of allocations that Pareto dominate the initial allocation.

(b) Compute the marginal rates of substitution for both consumers.

(c) Characterize the efficient allocations in this economy. On the Edgeworth box from question (a), draw the set of efficient allocations that dominate the initial allocation

(this is called the contract curve).

(d) Denoting by p the price of good x and normalizing the price of good y to 1, compute the demands of the two consumers for both goods as a function of p.

(e) Characterize the competitive equilibrium for this economy. Find the equilibrium price p, and the equilibrium allocation?

(f) Show that the market equilibrium is efficient.