Question

#4. Please show all work :)

It is 1908 and you are the CEO of Ford Motor Company. General Motors started producing cars this year and has quickly become your chief rival. Their recent entrance, as well as your assembly line methods, allows you the advantage of producing cars faster and choosing your output levels first. Assume the 1908 inverse demand function for cars is P = 3900 - Q (customers view cars as identical products at this point in time) and production costs are C(qi) = 100qi.

a. What is Ford’s profit-maximizing output level? GM's?

b. Fill in the following table assuming the Ford vs. GM duopoly from question 4.a:

Model	Output	Price	Profits
Bertrand
Cournot
Collusion

Answer 1

a) Collusion:

P = 3900 - Q

TR = PQ = (3900 - Q)Q

TR = 3900Q - Q²

MR = 3900 - 2Q

MC = 100

Equilibrium condition: MR = MC

3900 - 2Q = 100

2Q = 3800

Q = 1900 units

P = 3900 - 1900

P = $ 2000