Answer to Question #263029 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.

(c) Assuming that the firm is a price-taker operating in a competitive market, derive an expression for the firm’s supply curve, (the profit maximizing output for the firm as a function of the market price, i.e., qS = f(p). Assuming the firm is one of 100 identical firms in the industry, what is the short-run supply curve for the industry, i.e., QS = f(p)? If demand is given by QD = 1000 – 100p, what are the short-run equilibrium price, market quantity, and firm quantity? Is this a long-run equilibrium? [Hint: Calculate firm profit in the equilibrium.]

(d) 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 + 0.5Q^1/2

^{MC = Q}

Demand function = 1000 - 100P

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) Since 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..