Question

1. Suppose the market of ice-cream is competitive. A typical firm producing ice- cream has the following total cost function:

   C = 60 + 3q + 6q2

   where C is total cost and q is the output level.

   Assume the market price of ice-cream is $39.

   1. i) Find the marginal cost function of a typical ice-cream firm. Show your steps.

   2. ii) Find the profit maximizing output level of a typical ice-cream firm. Show your steps.

   3. iii) Find the amount of loss of a typical ice-cream firm. Show your steps.

   4. iv) Explain whether a typical ice-cream firm should shut down in the short run.

Answer 1

C = 60 + 3q + 6q2, Fixed Cost = 60 and Variable Cost = 3q + 6q2 (the part of cost dependent on output)

Average Variable Cost AVC = VC/q = 3+6q

AC = C/q = 60/q + 3 + 6q

MC = dC/dq = 3+12q (the first order derivative of the cost function)

The profit max condition is P=MC, so

39=3+12q

12q = 36 or q = 3 units (output level of a firm is competitive industry at a price of $39)

ATC or average total cost at q =3 will be = 60/q + 3 + 6q = 60/3+3+6*3 = $41

AVC or average variable cost at q =3 will be = 3 + 6q = 3+6*(3)= $21

Profits = (P-ATC)*Q = (39-41)*3 = -6, negative sign means the firm is suffering loss

The firm will NOT shut down as price P=$39 is greater than the average variable cost AVC =$21. The firm will NOT shut down in short run as it is able to cover its variable cost from the revenues.