The garment producer faces the inverse demand function PG = 300 - 2G, where PG is the price of garment and G is the quantity of garment. For simplicity, assume that the garment producer has no other cost of production, other than the price per unit of electricity it pays to the electricity producer. 2 Suppose that the electricity producer and the garment producer interact as fol- lows. First, the electricity producer sets a price PE that the garment producer must pay for each unit of electricity. Then the garment producer decides how much elec- tricity to purchase from the electricity manufacturer and how much garment G to produce and sell. (i) Suppose that the marginal cost of a unit of electricity is $10 per unit and every unit of garment requires two units of electricity. Find the profit maximizing prices and quantities of electricity and garment, PE, PG, E and G. What is the profit of each firm? What is the total profit? (ii) Now suppose that the two firms merge together, i.e., the cost of producing a unit of electricity is $10, it requires two units of electricity to produce a unit of garment and the inverse demand for garment is PG = 300-2G, where PG is the price of garment and G is the quantity of garment. Find the profit maximizing price and quantity of garment and the corresponding profit. (iii) Compare the results in parts (i) and (ii). In which case is the total profit higher? In which case is the price to the consumers lower? Intuitively, try to explain why these happen. If you were to recommend to someone about the merger of two firms (where the output of one firm is the input of the other firm) what will be your recommendation based upon the insights gained from this exercise? [Hint: For part (i), solve the problem backwards. (The solution to this problem is sim- ilar to a Stackelberg leadership problem.) Start with any price PE that the electricity manufacturer sets per unit of electricity. Using the production function, figure out the marginal cost of the garment producer. Solve for the profit maximizing quantity of garment, this will depend upon PE. Go back to the electricity manufacturer. Figure out its inverse demand function and solve its profit maximization problem. This will give PE and E. Now solve the garment producer's problem which was dependent on the unknown PE. In part (ii) there is no P. From the marginal cost of electricity and the production function figure out the marginal cost of garment and proceed.]