3. Suppose Amy and Bailey are consumers in a pure exchange economy, with two goods, tonkas and zeenas (this will be used as the numeraire and will be normalized to 1). Amy has 9 units of tonkas and 1unit of zeenas. Bailey has 3 units of tonkas and 8 units of zeenas. Amy and Bailey have identical preferences given by the utility function UA(xA) = (x 1 A) 1/3 (x 2 A) 2/3 for Amy and UB(xB) = (x 1 B) 2/3 (x 2 B) 1/3 for A = Amy and ;B = Bailey.

a) Suppose the price of zeenas, p2, is normalized to 1. In a perfectly competitive market, solve for the equilibrium price of tonkas, p1 and the optimal allocation of consumption for both consumers Amy and Bailey.

b) Calculate the utility for Amy and Bailey at the initial endowment allocation and the optimal allocation of consumption. Are Amy and Bailey made better off at the optimal allocation of consumption?

c) Show in the Edgeworth box the initial allocation of endowment W, the optimal allocation of consumption M, the price line, and Amy and Bailey's indifference curves which go through the optimal allocation of consumption.

d) State Walras law and use your findings above to verify it.