PART 1: Consider an economy with two consumers, Arnold and Bryan, and two consumption goods, 1 and 2. The initial endowment of Arnold is A = (6, 0), while the one of Bryan is B = (0, 6). Their utility function is given by u (x1, x2) = x1x2.

1. Compute the marginal rate of substitution for both agents and nd their values in the allocation ((3, 3) , (3, 3)) and the allocation ((4, 2) , (2, 4)).

2. Are these allocations Pareto efficient?

3. Derive the contract curve of this economy. 4. Find an initial pair of endowments and the relative price that make the allocation ((3, 3) , (3, 3)) a competitive equilibrium.

PART 2: Consider an economy with two consumers, Arnold and Bryan, and two consumption goods, 1 and 2. The initial endowment of Arnold is A = (6, 0), while the one of Bryan is B = (0, 6). Their utility function is given by u (x1, x2) = x1x2.

1. Write down their budget constraint given a price vector (p1,p2).

2. Find the optimal demand functions.

3. What are the ordinary demands when p1 = 1 and p2 = 2?

4. Is this the equilibrium price vector?

5. Find the price ratioP2P1 that brings the equilibrium in market 1.

6. Repeat the previous question for good 2.

7. Draw the competitive equilibrium in an Edgeworth box.