Consider an economy with no production. The economy is endowed with 50 bushels of alfalfa, a, and 50 bushels of barley, b. Two individuals, Mary and Larry, live in this economy and have the usual convex, negatively sloped indifference curves. Larry has an initial endowment with 50 bushels of alfalfa and no barley. Mary has no alfalfa and 50 bushels of barley. This initial endowment is not on the contract curve. At the initial endowment, Larry's utility function is U(a,b) = b + 2a and Mary's is U(a,b) = 2b +10a .
(a) If Mary offers a trade whereby she would give Larry three of her barley for one of his alfalfa, would Larry accept? Explain briefly. Illustrate your answer with an Edgeworth diagram. Show, on the same diagram, the set of efficient trades these individuals would rationally make.
(b) Now introduce prices. One of the points on the set of efficient trades you illustrated in your diagram will be a competitive equilibrium. Show such a point and illustrate the equilibrium price ratio pa / pb .