Question

Assume that in a perfect competitive market there are 8 firms, each firm has the following total cost function TC (q_i) = 4q_i² + 8q_i +2. The market demand function is Q = 48 – P.

Find the consumer surplus (CS) in the short run.

Answer 1

Supply curve is given by P = MC.
MC = d(TC)/dq = 2*4q + 8 = 8q + 8
So, P = MC = 8q + 8
So, 8q = P - 8
So, q = (P/8) - (8/8) = (P/8) - 1

Total supply, Q = 8q = 8*[(P/8) - 1] = (8P/8) - 8
So, Q = P - 8

Equilibrium price is determined where demand = supply.
So, 48 - P = P - 8
So, P + P = 48+8
So, 2P = 56
So, P = 56/2
So, P = 28

Q = P - 8 = 28 - 8 = 20

Maximum price (at Q = 0) is Q = 0 = 48 - P
So, Pmax = 48

Consumer surplus = area of triangle = (1/2)*base*height = (1/2)*Q*(Pmax-P) = (1/2)*(20)*(48-28) = 10*20 = 200

Thus, CS = 200