Consider the following exchange economy with two consumers and two goods. Consumer 1 has utility function u(x,y) = x1/2 y1/2 and initial endowments (ex,ey)=(1,0). Consumer 2 has utility function u(x,y) = x2 y and initial endowments (ex,ey)=(0,1). Assume the price of good x is equal to 1.
a. Compute the set of Pareto optimal allocations (also known as contract curve). Hint: this is a function relating x and y. What portion of the contract curve yield trades that improve consumers' welfare relative to their initial endowments?
b. Derive Consumer 1 demand for goods x and y (these are the x and y that maximize her utility given her budget constraint), do the same for Consumer 2.
c. Compute the competitive equilibrium for this exchange economy (these are the prices at which demand equals supply for both goods). What are the trades that the consumers make in equilibrium?
d. Draw the Edgeworth box describing this economy, the equilibrium, and the Pareto optimal allocation.