Consider the perfectly competitive market with the demand fu

Consider the perfectly competitive market with the demand function 0(p) = 12-p. There are 6 firms in the market. Each firm has the total cost function C (q) = 1 + q2, and all fixed costs are sunk. a) Determine the shut-down price ps of each firm (Hint: min (AVC)) b) Find the short-run supply curve of a single firm. That is, determine the formula 4. that shows how much output q (p) is produced by a single firm for each price p. (Hint: use the equilibrium condition in perfect competition) Find the short-run industry supply curve Q (p), that is, the total output for each price p. c) d) What are the short-run equilibrium price, output of a single firm, and the industry output?

Solution

(a)

C(q) = 1 + q²

Total varable cost (TVC) = q²

AVC = TVC / q = q

AVC is minimized when q = 0. Therefore,

Shut-down price = Minimum AVC = 0

(b) Firm\'s short run supply function is its Marginal cost (MC) function.

MC = dC(q)/dq = 2q

Therefore, firm\'s short run supply function: p = 2q

(c) Since there are 6 firms,

Market supply (Qs) = 6q

q = Qs / 6

p = 2 x (Qs/6)

p = Qs / 3

Qs = 3p [Industry supply function]

(d) In equilibrium, market quantity demanded equals market quantity supplied.

12 - p = 3p

4p = 12

p = 3

Q = 3 x 9 = 9

q = Q / 6 = 1.5