Consider a pure exchange economy with two consumers, 1 and 2. There are two goods, x and y. Each consumer starts with half a unit of each good. The utility functions are:

u1 = x₁²y₁, u2 = x₂y₂

a. Show this economy's preferences and initial endowments in an Edgeworth box diagram. b. Find the equation for the contract curve and draw it on your Edgeworth box. Is the initial allocation Pareto efficient? Why or why not?

c. Find the competitive equilibrium in this economy. That is, solve for the equilibrium relative price p and the bundles (x1 *, y1 *) and (x2 *, y2 *).