Suppose that there are 20 identical firms in the bolt-making market, a perfectly

Question

Suppose that there are 20 identical firms in the bolt-making market, a perfectly competitive market. Each firm has short-run total cost function TC(q) = 16 + q2, where q is the annual output of the firm. The corresponding short-run marginal cost function is MC(q) = 2q. The market demand for bolts is QD = 110 – P, where P is the market price.

(a) Find the short-run competitive supply curve.

(b) Find the short-run competitive equilibrium price and quantity for this market.

(c) How much does each individual firm produce in equilibrium? What is each firm’s profit?

(d) Find total market producer surplus.

(e) Find total market surplus.        

Explanation / Answer

a) The rising portion of the marginal cost curve (MC) just as soon as it cuts the average variable cost AC from below is the firm’s short run supply curve. For this firm, TVC = q2. Find the individual firm’s supply curve by finding the minimum of AVC which is TVC/q or q2/q = q.

Minimum of AVC = AVC'(q) = 1. So MC cuts AVC when AVC = 1. This gives MC = AVC or 2q = 1. So from q= 1/2, the supply curve of firm is represented as: P = 2q, q>1/2

Industrial Supply curve: Q = 10P, q>1/2, Q = 20q

b) Short-run competitive equilibrium price and quantity for this market are derived when Qd = Qs.

110 - P = 10P

110 = 11P

P = 10, Q = 100

So the short-run competitive equilibrium price is $10 and quantity for this market is 100

c) Each individual firm produce 100/20 = 5 units in equilibrium. Each firm’s profit is the difference between TR and TC so:

=p*q - TC

=5*10 - 16 - 25 = $9

So each firm’s profit is $9.

d) Producer surplus is the area between the price line and supply curve. This is given by 1/2*(10)*100 = $500.

e) Market surplus adds consumer and producer surplus, Consumer surplus is 1/2*(110 - 10)*100 = $5000. Market surplus is therefore, $5,500.

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