Question

Suppose that the market for wheat is perfectly competitive. Market

demand for wheat is given by the expression.
= 80 − 5P,
where P is the market price per bag of wheat. The short run market supply for wheat is
given by the expression.
= −20 + 20P.
Further, suppose that all firms are identical, and each firm has variable costs given by the
expression.
= + 0.52.
a) What is the short-run market price facing each firm? P = 4
b) What is the short-run profit-maximizing level of output for each firm?
c) Now suppose we are now in the long run. Suppose that the firm’s long-run total cost
function is given as:
T = 2 + + 0.52

What is the long-run level of output that a representative firm would produce at? 32.5 firms
d) Recall the market’s demand curve is = 80 − 5P. How many firms are in this market
in the long run

Answer 1

In a perfectly competitive market for wheat, the short-run market price facing each firm is $4. The short-run profit-maximizing level of output is determined when P = MR = MC. In the long run, a representative firm would produce at the level of output where AC is minimized.

Step-by-step explanation:

In a perfectly competitive market for wheat, the short-run market price facing each firm is equal to the market price per bag of wheat (P) which is given as P = $4. The short-run profit-maximizing level of output for each firm is determined by setting marginal cost equal to marginal revenue, which is also equal to market price. Therefore, the short-run profit-maximizing level of output for each firm is the quantity at which P = MR = MC. In the long run, a representative firm would produce at a level of output where the long-run total cost (AC) is minimized. This occurs when the firm produces at the minimum point of the long-run average cost curve. Given the long-run total cost function T = 2 + Q + 0.52Q^2, the level of output that minimizes cost is Q = 32.5 bags of wheat. In the long run, the number of firms in the market is determined by the market's demand curve. To find the number of firms in the long run, we need to find the output level at which the market price is equal to the minimum point on the long-run average cost curve. Using the demand curve P = 80 - 5Q, where Q is the total output of all firms in the market, we can solve for Q to find the number of firms.