Firm A = monopolist Market demand: y = 150 - p Total cost: C(y) = 30y y = quanti

Question

Firm A = monopolist

Market demand: y = 150 - p
Total cost: C(y) = 30y

y = quantity of machines
p = price per machine

a) After being the monopolist for awhile, there's a new firm entering the market. Both firms will be choosing output simultaneously (new firm has the same cost function)

How many machines would you recommend firm A to produce? How many machines would you anticipate firm B will produce?

b) There's a mole in the company -> firm B will make output decision after seeing firm A's output. Give your new output decisions.

Explanation / Answer

When I say, 1 and 2, I mean A and B.

a) Cournot strategy:
y=150-p => p=150-y=150-y1-y2, where y1 is firm 1's output, y2 is firm 2's output
Firm 1's profit condition:1=y1*p - y1c= y1 (150-y1-y2) - 30y1= 120y1-y1^2-y1y2

Take the derivative of 1 with respect to y1: 120-2y1-y2=0 => y2=120-2y1 (1)

By symmetry, 120-2y2-y1=0 (2) or y2=60-.5y1

Plug (1) into (2): 120-2(120-2y1)-y1=0

  -120+3y1=0 => y1=40, y2=40

So firm 1 and 2 both produce 40 machines.

b) Stalkerberg strategy: Firm 1 is the leader, Firm 2 is the follower

From a), 1=120y1-y1^2-y1y2 but y2=60-.5y1

=>1=120y1-y1^2-y1(60-.5y1)=120y1-y1^2-60y1+.5y1^2=60y1-.5y1^2

Take derivative, 60-y1=0 =>y1=60

y2=60-.5(60)=30

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