Question

1. Suppose that a competitive firm’s marginal cost function is given by MC(q) = 4 + aq, where a > 0 and the market price is 16.

a) What is the firm’s profit-maximizing level of output when a = 4?

b) Suppose the firm’s fixed costs increase and the value of a decreases. How will this affect the firm’s profit-maximizing level of output?

c) Suppose the firm’s producer surplus at its profit-maximizing level of output is 36. What is the value of a in the firm’s marginal cost function?

d) Suppose now that the average variable cost of the firm is given by AVC(q) = 4 + q and that the firm’s fixed costs are known to be $8. Write down an expression for the firm’s total cost function. That is C(q) =?

e) If the firm decides not to produce in the short with the cost functions described in part d), what must be true about the prevailing market price?

Answer 1

Market price = $16

a) A competitive firm produces an output level where MC = P.
4 + 4q = 16
4q = 12
q = 3

b) An increase in fixed cost won't affect the profit maximizing output level since it won't change the marginal cost as derivative of a constant is zero.
To see the effect of a decrease in value of a, let us solve for profit maximizing output level in terms of a:

MC = P
4 + aq = 16
aq = 12
q = 12/a
Thus, if the value of a decreases then profit maximizing output level will also increase.

c)

d)
Total variable cost, TVC = AVC(q)*q
= (4 + q)*q
= 4q + q²

Fixed Cost, FC = $8

Total Cost, C(q) = FC + TVC
= 8 + 4q + q²

e) If the firm decides not to produce any output in short run, then it must be true that P < AVC. That is firm is unable to recover its Average Variable cost in this market. Similarly, if the firm decides not to produce any output in long run then it must be the case that its not recovering its costs (i.e. P< ATC).