Answer to Question #264277 in Microeconomics for mujtaba syed

Question

Suppose a firm operating in a perfectly competitive industry has costs in the short run given by:

SRTC = 8 + 1/2Q^2 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?

Answer 1

Short-run total cost = $8+1/2Q^2$

^{MC = Q}

Let's say Demand function = 1000 - 100P for instance, then

1) The short-run supply curve for the firm is the portion of the marginal cost curve that is above the average variable cost curve.

Short-run supply curve of a competitive firm is given by

P = MC

P = Q ...( Short-run supply equation)

2) Let us assume there are 100 identical firms ,

the supply curve of the market is given by , Q_s = nQ= 100*P = 100P

3) At equilibrium Q_s= Q_d

100P = 1000 -100P

200P = 1000

P = 5

put this value in either demand or supply function

Q_d = 1000 - 5*100

= 1000 - 500

= 500

Equilibrium quantity of the market is 500

Firm Quantity = Market quantity / 100

$=\frac{ 500}{100}$

= 5

4) Profits are ZERO in the competitive market in the long-run ..

With the available prices and quantity the profit is not zero in this case.

so it is not the long-run equilibrium.