Question

Assume a monopolist with total cost C(y) = 500 + 20y. Market demand is Q = 100 − P.

i. If price is set equal to marginal cost, what will the firm’s profits be?

ii. If price is set equal to average cost, what will the loss be in terms of output and total surplus from the first part? Please answer as a number.

iii. Suppose all consumers are identical. What will be two-tariff schedule (membership fee + marginal price) that maximizes total surplus while assuming zero profits?

Please explain as thoroughly as possible, thank you!

Answer 1

i) P = MC = 20

Then at eqm, Q= 100-20= 80

π = (P-MC)*Q - 500

= -500

total Surplus = CS + PS

= .5*(100-20)*80 -500

= 2700

ii) P=AC= 500/y + 20

At eqm, Q= 100-P

Q= 100-20-500/Q

Q= 80- 500/Q

Q*= 73.166, P*= 26.834

loss of Output = 80-73.166

= 6.834

loss of Surplus = 23.368

CS'= .5(100-26.834)*73.166

= 2676.63

PS = 0, as P = AC

Total loss of Surplus = 2700-2676.83

= 23.368

iii)

Two part Tariff

Marginal price = MC= 20

Membership fee f = Consumer Surplus value when Q= 80

CS = f = .5*(100-20)*80

= 3200

No Deadweight loss occurs, Hence total Surplus is maximized