Consider an Economy with Two Consumers, Consumer 1 and Consumer

Essay

Consider an economy with two consumers, consumer 1 and consumer 2 and two goods, good 1 and good 2. Suppose that consumer 1's utility function is given by U₁(x₁₁, x₂₁)= x₁₁x₂₁ and consumer 2's by U₂(x₁₂, x₂₂)= x₁₂ + x₂₂. Suppose the initial endowments are X₁₁ = 1, X₂₁ = 2, X₁₂ = 3, and X₂₂ = 2.
a)Graph carefully and accurately the Edgeworth box for this economy, showing the contract curve and the indifference curves of the two consumers through the initial endowment.
b)Find also the optimal level of x₁₂ as a function of p₁.
c)Find the equilibrium allocations when p₁=p₂=1.