Question

a. Monopolist faces the following demand curve: P = 510 - 0.7Q; its total cost is given by: TC = 800 + 0.15Q Find marginal cost and marginal revenue

b. Monopolist faces the following demand curve: P = 520 - 0.7Q; its total cost is given by: TC = 800 + 0.3Q Find marginal cost and marginal revenue

Answer 1

a. Given,

Inverse demand function: P = 510 - 0.7Q

Total revenue, TR = Price x Output = P x Q = (510 - 0.7Q) x Q = 510Q - 0.7Q²

Marginal Revenue, MR =d/dQ (TR) = d/dQ (510Q-0.7Q²) = 510 d/dQ (Q) - 0.7 d/dQ (Q²) = 510 - 0.7 x (2Q) = 510-1.4Q

Total Cost, TC = 800 + 0.15Q

Marginal Cost, MC = d/dQ (TC) = d/dQ (800 +0.15Q) = d/dQ(800) + 0.15d/dQ(Q) = 0 + 0.15 = 0.15

b.

Inverse demand function: P = 520 - 0.7Q

Total revenue, TR = Price x Output = P x Q = (520 - 0.7Q) x Q = 520Q - 0.7Q²

Marginal Revenue, MR =d/dQ (TR) = d/dQ (520Q-0.7Q²) = 520 d/dQ (Q) - 0.7 d/dQ (Q²) = 520 - 0.7 x (2Q) = 520-1.4Q

Total Cost, TC = 800 + 0.3Q

Marginal Cost, MC = d/dQ (TC) = d/dQ (800 +0.3Q) = d/dQ(800) + 0.3 d/dQ(Q) = 0 + 0.3 = 0.3