Question

4. Consider an economy with 24 firms in the short run. The market demand function is given by p= 50 – 2Q. A firm's cost function is C(q) = 3+q?. (a) [10 pts) Derive the equilibrium price in the short run. ts] Firms face a cost of 6 to enter this industry. Calculate the equilibrium price and number of firms in the long run.

Answer 1

a) Here n = 24. Market demand P = 50 - 2Q or Q = 25 - 0.5P and marginal cost is MC = 2q

Supply function by 1 firm is P = MC or 2q = P.

This gives q = P/2.

Market supply function is 24q or Q = 24P/2 which gives Qs = 12P

At equilibrium Qd = Qs

25 - 0.5P = 12P

P = 25/12.5 = $2 per unit and Q = 24 units

Also each firm produces 2/2 = 1 unit

Price is $2 in short run

b) Note that firm is earning losses in the short run since profit = revenue - cost = 2*1 - 3 - 1 = -2.

This implies that there is no entry in the long run, in fact there will be exist

In long run P = AC = MC

P = 3/q + q = 2q

q^2 = 3

q = 1.732

P = $3.464

Market quantity = 25 - 0.5*3.464 = 23.268

Number of firms = 13 (approx).