Question

6. Suppose a firm engaged in the illegal copying of DVD’s has a daily short run total cost function given by:

STC=(q^2)+25

A. If pirated DVD’s sell for $20, how many will the firm copy each day? What will its profits be?

B. What is the firm’s short run producer surplus at P=20?

C. Develop a general expression for this firm’s producer surplus as a function of the price of pirated DVD’s.

Answer 1

a)

STC=q^2+25

Short run marginal cost=SMC=dSTC/dQ=2q

In perfect competition, firms set output level such that Marginal Cost is equal to market price.

So,

SMC=Market price

2q=20

q=10

Firm would copy 10 DVDs each day.

Total Revenue=P*q=20*10=$200

Total Cost=q^2+25=10^2+25=$125

Profit=Total Revenue-Total Cost=200-125=$75

b)

Firm's supply curve is given by

P=SMC=2q

We know that q=10 when P=$20

and P=0 at q=0

So, producer surplus at P=$20=1/2*(20-0)*(10-0)=$100

C)

We know that P=2q or q=P/2

So, Producer surplus at P is given by

PS=1/2*(P-0)*(q-0)=1/2*(P)*(P/2)=(1/4)P²