Your firm is one of 100 identical firms operating in the short run in a perfectl

Question

Your firm is one of 100 identical firms operating in the short run in a perfectly competitive market. Your total cost function (short run and long run) is C = 500 + 20 q + q2, and your marginal cost function is MC = 20 + 2q. The (short run and long run) market demand curve is given by Q = 4,500 – 5P.

a. Find the supply curve for your firm. Then, find the short-run market supply curve. Show work.

b. Find equilibrium price, P*, and quantity, Q*, in the market in the short run. Show work.

c. Find your firm’s total revenue, total cost, and profit in the short run. Show work.

d. Find the minimum efficient scale (MES) for your firm. Show work. Find the long-run equilibrium price in the market after entry or exit has occurred. Show work.

Explanation / Answer

a)

The supply curve of the firm in competitive market is the portion of marginal cost curve above the minimum of AVC.

AVC for this firm is TC/q = 20 + q

Minimum of AVC is achieved when q = 1. When q = 1, MC = $22. Hence, the supply curve for the firm is the altered equation of the MC with the condition that MC>22:

P= 20 + 2q

q = 0.5P - 10

This is the supply curve for the firm. For the supply curve of the market, multiply the individual supply equation with 100.

Industrial supply curve =

100q = 50P - 1000.

b)

Equilibrium occers where Qd = Qs

50P - 1000 = 4500 - 5P

55P= 5500

P = $100, Q = 4000, q = 40

Each firm takes the market price P* = $100 per unit as given, producing 40 units each, cumulatively 4000 units by 100 firms.

c)

Total revenue for a firm is P*q = $100*40 = $4000. Total cost = 500 + 20(40) + (1600) =$2900. Hence short run profits are $1100.

d)

The minimum efficient scale of production is the level of production at which there lies the lowest level of LRATC which is arrived when ATC = 500/q + 20 + q is minimized. This gives q = 22. At this level, economic profits are eliminated, since long run equilibrium requires LRATC = P = LRMC. At q = 22, ATC = 65.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.