Question

Consider an economy with two consumers A and B. Consumers A and B have utility functions u(x+x)= Inx;" + Inx, and (x,x) - Inx' +-Inx, respectively. They face prices P, and P, for good 1 and good 2, respectively, and they have incomes “and I°, respectively a) Write formally the economic problem faced by consumer A and derive the demand functions xi (P1, P2,7") and x(P,P2,7^) [6] b) What are consumer B's demand functions for the two goods 1 and 2. Explain your answer [2] c) Calculate the optimal value of the Lagrange multiplier X for consumer A and explain its meaning [2] d) Explain Walras' Law. Why is this law important for the general equilibrium theory [2] e) If the consumers have initial endowments e' - (4,3) and e" - (10,7), what will be the Walrasian equilibrium for this economy, i. the equilibrium prices (PP) [4] ii. the equilibrium allocations (x;"(.p),x(p.p)) and (x"( PP),x(P.p.)) [2]

Answer 1

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