Question 2

GM is an automobile manufacturer. Assume that GM is a monopolist. Delphi is a firm that manufactures electrical systems for automobiles. One electrical system is required as an input to make one automobile. Electrical systems cost 1 each to manufacture. Automobiles cost 10 each to manufacture, PLUS the cost of the electrical system. Consumer demand for automobiles at price p is p = 20 - Q. (Note: these numbers approximate US market conditions if prices and costs are denominated in thousands of dollars and quantity is denominated in millions of cars per year.)

Assume that Delphi is a monopolist, and it sells electrical systems to GM at price r. We want to find the equilibrium in this market.

a. What is GM's marginal cost, as a function of r?

b. What is GM's profit function, as a function of r and p?

c. What price per automobile does GM charge, as a function of r?

d. How many autos are sold in equilibrium, as a function of r?

e. What demand function does Delphi face?

f. What price does Delphi charge per electrical system?

The next three answers you should write numbers, not as functions of r or any other variables.

g. What are Delphi's profits?

h. What are GM's profits?

i.What is consumer surplus?

Now assume that Delphi and GM merge into one Company. We want to find the new equilibrium.

j.What is the Company's marginal cost?

k. What price does the company charge?

l. What are profits?

m. What is consumer surplus?