Suppose a monopoly supplier of some good faces an inverse demand of P = 5250 20Q

Question

Suppose a monopoly supplier of some good faces an inverse demand of P = 5250 20Q and a constant marginal cost of 170.

(A) If the firm charges one price to all of its customers, what is the equilibrium price?

(B) If the firm charges one price to all of its customers, what is the equilibrium profit of the firm?

(C) Suppose, instead, that the firm can perfectly discriminate between its customers and charges each customer the profit maximizing price. What will its profits be in equilibrium?

(D) What is the resulting deadweight loss (the decrease in total surplus from the level achieved in a perfectly competitive market) when the firm can perfectly discriminate between its customers?

Explanation / Answer

a. P = 5250 20Q , MC = 170

TR = P*Q = (5250 - 20Q)*Q

MR = dTR/dQ = 5250 - 40Q

Profit of monopoly is maximized where MR = MC

hence

5250 - 40Q = 170

40Q = 5080

Q = 127

B. P = 5250 - 20Q = 5250 - 20*127 = 2710

Profit = TR - TC = P*Q - MC*Q = (P - MC)*Q = (2710 - 170)*127 = 322580

C. IN case if firm perfctly price discriminate then

Profit = Integral(P - MC)Q = Integral(P - 170)127 with P going from 170 to 5250

= [P^2/2 - 170P]127  with P going from 170 to 5250

=   1636871250 - (-1835150)

= 1638706400

D. Deadweight Loss will be Zero.

Since the entire consumer surplus is being converted into the producer surplus under perfect discrimination, so there will be no DWL.

If you don't understand anything then comment, I'ill revert back onthe same. :)

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