Consider the following economy with production. There is a firm which can turn one unit of oranges into two apples, or two units of oranges into three apples. There is a consumer who is endowed with two oranges. The consumer sees apples and oranges as perfect complements,

i.e. her utility function for consuming apples a and oranges o is,

u = min(o, a)

Restrict your attention to allocations that have only integer values - i.e. it is not possible to demand or supply fractional units of either good.

1.What is the set of Pareto Optimal allocations?

2.Consider the price system wherep_o/p_a = 2. What are the firm's profit-maximizing production plans? What are the firm's profits?

3.Is p_o/p_a = 2 an equilibrium price ratio? Explain