Suppose a monopolist faces consumer demand given by P-400-TQ with a constant mar

Question

Suppose a monopolist faces consumer demand given by P-400-TQ with a constant marginal cost of $100 per unit (where marginal cost equals average total cost. assume the firm has no fixed costs) If the monopoly can only charge a single price, then it will earn profits of $L (Enter your response rounded as a whole number Correspondingly, consumer surplus is $ However, if the firm were to practice price discrimination such that consumer surplus becomes profit, then, holding output constant at 150, the monopoly would have profits of s

Explanation / Answer

P = 400 - Q

MC = $100

(a) Monopolist will equate Marginal revenue (MR) with MC.

Total revenue (TR) = P x Q = 400Q - Q2

MR = dTR / dQ = 400 - 2Q

400 - 2Q = 100

2Q = 300

Q = 150

P = 400 - 150 = $250

Profit = Q x (P - MC) = 150 x $(250 - 100) = 150 x $150 = $22,500

(b) From demand function, when Q = 0, P = 400 (Reservation price)

Consumer surplus (CS) = Area between demand curve and market price = (1/2) x $(400 - 250) x 150

= (1/2) x $150 x 150 = $11,250

(c) When Q = 150,

P = 400 - 150 = $250

Profit = 150 x $(250 - 100) = 150 x $150 = $22,500

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