Answer to Question #250250 in Macroeconomics for Mehwash Sk

Question

4. Suppose that a typical firm in a perfectly competitive industry has the following total cost curve:

TC = 240 Q "?o 6 Q² + .08 Q³

a. Is this a short-run cost curve, or a long-run cost curve? How do you know?

b. What will the price of the product be in the long-run?

Answer 1

Solution:

a.). This is a long-run total cost curve. This is because there are no fixed costs or factors in the long-run total cost curve. In the short run, some inputs are fixed while the others are variable. On the other hand, in the long run, the company can vary all of its inputs. Long-run cost is the minimal cost of producing any given level of output when all individual factors are variable.

 

b.). The long-run price is equal to both the long-run average total cost and the marginal cost.

First derive the long-run average total cost:

Long-run average total cost = $\frac{TC}{Q} = \frac{240Q - 6Q^{2} + 0.08Q^{3} }{Q} = 240 - 6Q + 0.08Q^{2}$

Long-run average total cost = 240 – 6Q + 0.08Q²

Calculate the level of output when the average cost reaches a minimum:

When the average cost is minimized, its derivative is equal to zero. Therefore:

$\frac{ \triangle ATC}{ \triangle Q} = 0$

-6 + 0.16Q = 0

0.16Q = 6

Q = 37.5 Units

Substitute in the ATC function to derive the long-run price:

240 – 6Q + 0.08Q² = 240 – 6(37.5) + 0.08(37.5)² = 127.5

The long-run price = 127.5