Due on paper, by the end of class, on Tuesday, December 3
1. A firm that produces output good y has the cost function c(y) = y3 − 8y2 + 30y + 5.
(a) What is the firm’s fixed cost, and what is its variable cost function? Explain.
(b) Find the firm’s marginal cost function, and its average variable cost function.
(c) The firm’s average variable cost is decreasing at some output quantities, and increas-
ing at other output quantities. Determine the range of outputs at which the firm’s
average variable cost is decreasing, and the range of outputs at which the firm’s aver-
age variable cost is increasing, by taking the derivative of average variable cost, and
determining where it is negative and where it is positive.
(d) At some prices of output, the firm will maximize profit by choosing its quantity of
output to make its marginal cost equal the price of output. At other prices of output,
the firm will maximize profit by not producing any output (shutting down). Find
the range of prices of output at which the firm maximizes profit by shutting down.
Hint: your answer to (c) shows you the quantity of output at which the firm’s average
variable cost is as small as possible.
(e) At the smallest price of output at which the firm does not maximize profit by shutting
down, the firm produces a positive quantity of output. Find that quantity of output.
Hint: at the output at which the firm’s average variable cost is as small as possible,
its average variable cost and marginal cost are equal