Reference no: EM133082487

Consider an economy with two consumers and two goods. The total amount of good 1 is x1 = 50 and the total amount of good 2 is x2 = 75. Alice has the utility function uA(x A 1 , xA 2 ) = (x A 1 ) 1 4 (x A 2 ) 3 4 and Bob's utility function is uB(x B 1 , xB 2 ) = (x B 1 ) 0.5 (x B 2 ) 0.5

a) Find the demand functions for Alice and Bob.

b) Use your answer in part a) to write out the conditions that a Walrasian equilibrium pair of prices (p ∗ 1 , p∗ 2 ) must satisfy.

c) Assuming that Alice has 20 units of good 1 and 10 units of good 2. Bob has 30 units of good 1 and 65 units of good 2. Sketch the endowment point and the indifference curves for both consumers in a clearly labelled Edgeworth box.

d) Under the endowments given in c), use Walras' law to find a Walrasian equilibrium involving p ∗ 1 = 1.

e) Verify that demand equals supply in both markets by calculating the excess demand functions for both consumers in both markets. Write down the allocation after trading at the prices you have found.

f) Is the allocation Pareto efficient? Is it equitable?