Question

A ice cream parlous in a monopolistically competitive market faces a demand curve given by P = 12 – 0.5Q. Marginal revenue of MR = 12 – Q. The variable costs of producing ice cream are VC = 2Q and so the marginal costs are constant at $2. If the ice cream parlor is in a long-run equilibrium, what must its fixed costs be?

Answer 1

Monopolistically competitive in the long run condition:

MR = MC and P = ATC

Set MR = MC

=> 12-Q = 2

=> Q = 12 - 2

=> Q = 10.

Long run equilibrium output is 10 units.

and, P = 12 - 0.5Q

put Q = 10

=> P = 12 - 0.5(10)

=> P = 12 - 5

=> P = 7

Long run equilibrium price is $7.

----------------------------

TC = VC + FC

=> TC = 2Q + FC

ATC = (TC/Q)

=> ATC = (2Q+FC) / Q

=> ATC = 2 + (FC /Q)

Put, P = ATC

=> 7 = 2 + (FC/Q)

=> 7 = 2 + (FC /10)

=> 7 - 2 = (FC/10)

=> 5 = (FC/10)

=> FC = 5 * 10

=> FC = 50.

Fixed cost would be 50.