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Profit Maximization

Profit Maximization. Perfect Competition and Firms with Market Power. General Condition. Profit: π = R(Q) – C(Q) At a maximum: ∆ π /∆Q = (∆R/∆Q) – (∆C/∆Q) = 0 ∆R/∆Q = Marginal Revenue = MR ∆C/∆Q = Marginal Cost = MC Implies MR – MC = 0 or MR = MC To maximize profit

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Profit Maximization

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  1. Profit Maximization Perfect Competition and Firms with Market Power

  2. General Condition • Profit: π = R(Q) – C(Q) • At a maximum: ∆π/∆Q = (∆R/∆Q) – (∆C/∆Q) = 0 • ∆R/∆Q = Marginal Revenue = MR • ∆C/∆Q = Marginal Cost = MC • Implies MR – MC = 0 or MR = MC • To maximize profit • Choose quantity for which MR = MC

  3. Marginal Revenue • MR = ∆R/∆Q = ∆(PQ)/∆Q = P + (∆P/∆Q)Q • This expression can be related to the price elasticity of demand • P + (∆P/∆Q)Q = P + (∆P/∆Q)Q(P/P) • = P + [(∆P/∆Q)(Q/P)]P = P + P(1/EP) • EP = (∆Q/∆P)(P/Q) • MR = P(1 + 1/EP) • Suppose QD = 500 - 10P • P = 50 – 0.1Q and R = PQ = 50Q – 0.1Q2 • MR = ∆R/∆Q = 50 – 2(0.1)Q = 50 – 0.2Q • MR has twice the slope of the inverse demand equation • Graph

  4. Implications of MR = MC • MR = P(1 + 1/EP) = P + P/EP = MC • (P – MC) + P/EP = 0 • P – MC = -P/EP • (P – MC)/P = -1/EP • In Perfect Competition, firms are price-takers • EP → -∞ => (P – MC)/P → 0 or P = MC • Graph • For firms with market power • MR = MC = P(1 + 1/EP) • (P – MC)/P = -1/EP • Graph

  5. Compare Perfect Competition with Market Power • Suppose P = 50 - 0.1Q and MC = 5 + 0.5Q • Perfect Competition: P = MC • 50 - 0.1Q = 5 + 0.5Q • 45Q = 0.6Q or Q = 75 • P = 50 – 0.1(75) = 50 – 7.5 = $42.50 • Market Power: MR = MC • MR = 50 – 0.2Q = 5 + 0.5Q = MC • 45 = 0.7Q or Q ≈ 64 • P = 50 – 0.1(64) = 50 – 6.4 = $43.60 • MC = 5 + 0.5(64) = 5 + 32 = $37.00 • DWL = 0.5(75 – 64)(43.6 – 37) = $36.30 • Graph

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