Consider a competitive, constant-cost industry. Firms operating in this market face an identical cost of production. The total cost is given by TC = 180 + 33q + 5q2. What is the price in the long-run market equilibrium?
Question
Consider a competitive, constant-cost industry. Firms operating in this market face an identical cost of production. The total cost is given by TC = 180 + 33q + 5q2. What is the price in the long-run market equilibrium?
Solution
In a competitive, constant-cost industry, firms will produce at the minimum point of their average total cost (ATC) curve in the long run. The ATC can be calculated by dividing the total cost (TC) by the quantity (q):
ATC = TC / q = (180 + 33q + 5q^2) / q = 180/q + 33 + 5q
To find the minimum point of the ATC curve, we need to find where the derivative of ATC with respect to q equals zero:
d(ATC)/dq = -180/q^2 + 5 = 0
Solving for q, we get:
180/q^2 = 5 q^2 = 180/5 q = sqrt(36) q = 6
So, each firm produces 6 units of output in the long run.
Substituting q = 6 back into the ATC equation, we can find the price in the long-run market equilibrium:
ATC = 180/q + 33 + 5q ATC = 180/6 + 33 + 5*6 ATC = 30 + 33 + 30 ATC = 93
Therefore, the price in the long-run market equilibrium is $93.
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