Question

A monopoly firm have marginal cost MC=2. The demand is P=20-Q

(a) If price discrimination is not allowed, how large is the PS?

(b) If firm engages in first-degree price discrimination, how large is PS?

Answer 1

(a) Profit maximizing output of monopolist is determined where MR = MC
Total Revenue, TR = P*Q = (20 - Q)*Q = 20Q - Q²
So, Marginal Revenue, MR = d(TR)/dQ = 20 - 2Q
Now, MR = MC gives,
20 - 2Q = 2
So, 2Q = 20 - 2 = 18
So, Q = 18/2
So, Q = 9
P = 20 - Q = 20 - 9 = 11

PS = Area of rectangle = (P - MC)*Q = (11 - 2)*9 = 9*9 = 81
Thus, PS = 81

(b) Under first degree price discrimination, output is produced where P = MC.
So, 20 - Q = 2
So, Q = 20 - 2 = 18
Thus, Q = 18

Under first degree price discrimination, entire area is producer surplus.
Maximum price possible (when Q = 0) is P = 20 - 0 = 20
So, PS = area of triangle = (1/2)*base*height = (1/2)*Q*(Maximum Price - MC) = (1/2)*(18)*(20 - 2) = (1/2)*18*18 = 162
So, PS = 162