Question

A single firm monopolizes the entire market for shoelaces and can produce at constant average and marginal costs of $10. The firm faces a market demand curve given by

Q_D = 60 - P

A) Calculate the firm’s profits

Answer 1

Firm maximises it's profit where MR equals MC.

MR can be find by taking derivative of total revenue.

Total revenue =Price *quantity

First we have to find inverse demand function.

Qd=60-P

P=60-Q.

So now total revenue =Price *quantity

=60-Q*(Q)

=60Q-Q^2.

MR =dTR/dQ

=60-2Q.

MC=10

Now firm maximizes its profit where MR equals MC.

MR =MC

60-2Q=10

60-10=2Q

50=2Q

50/2=Q

25=Q.

Now price can be find by putting Q in inverse demand function.

P=60-Q

=60-25

=35.

Total revenue =Price *quantity

=35*25

=875

Total cost =ATC *quantity

=10*25

=250.

Profit =total revenue - total cost

   =875-250

=625