(Please Help with D-G)

8. Suppose demand is: ()=1002

and the total cost function is: ()=20

a. Find the perfectly competitive P* and Q*.

P=100-2Q

MC=20

P*= $20

100-2Q=20

2Q=100-20

2Q=80

Q*= 40 units

b. Find the P and Q chosen by a profit-maximizing monopolist.

Monopolist maximize profit at MR=MC

P=100-2Q

MR=100-4Q

MC=20

100-4Q=20

4Q=100-20

4Q=80

Q= 20 units

P=100-2*20

P=$60

c. What is producer surplus under perfect competition?

Producer surplus under perfect competition= (1/2)(20-0)(40-0) = $400

d. What is producer surplus under monopoly? Suppose a firm discovers a way to lower marginal cost to $10 per unit.

e. If the pre-existing market was perfectly competitive, how large is the benefit to the innovating firm (in terms of the change in producer surplus)?

f. If the pre-existing market was a monopoly, how large is the benefit to the innovating firm (in terms of the change in producer surplus)?

g. Will the change in deadweight loss be larger if the pre-existing market was perfectly competitive or if it is a monopoly?