Answer to Question #264780 in Microeconomics for mujtaba syed

Question

SRTC = 8 + 1⁄2q2 and therefore MC = q.

If the minimum point of the short-run ATC curve for all firms(existing and potential)is also the minimum point of the long-run average cost curve (LRAC), calculate the long-run equilibrium price, market quantity, and firm quantity. What is the long-run equilibrium number of firms in the industry? [4]

Answer 1

SRTC = 8 + 1/2q² (This is a function for each firm)

The equation can also be written as

TC = 16 + q²

In perfect competition, the long-run price equals average cost at the minimum of the average cost curve

Average cost = (16 + q²)/q = 16/q + q

Differentiate the equation to get the minimum average cost

dAC/dQ = -(16/q²) + 1 = 0

16/q² = 1

q² = 16

q = 4 units

Therefore, each firm produces 4 units of output in the long run.

p (price) = AC (At q = 4) = (16/q + q) = (16/4 + 4) = 8

Therefore the long-run equalibrium price is $8.

Demand function  = 1000 - 100P

q_d= 1000 - (100*8) = 200

Therefore market quantity = 200 units

Number of firms = Total market quantity/ single firm quantity

= 200/4 = 50 firms

SOLUTIONS

Long-run equilibrium price = $8

Market quantity = 200 units

Firm quantity = 4 units

Number of firms = 50 firms