Lec_04_profit_max

# 200 m 100 m 200 m 2gal 200 m average cost total cost

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\$200 M 100 M . \$200 M \$2/gal \$200 M 0 Average cost Total cost Marginal cost Fixed cost Quantity (gals/yr) \$2.67/gl \$800 M \$2/gal \$200 M 300 M \$2.50/gl \$1000 M \$2/gal \$200 M 400 M \$3/gal \$600 M \$2/gal \$200 M 200 M \$4/gal \$400 M \$2/gal \$200 M 100 M . \$200 M \$2/gal \$200 M 0 Average cost Total cost Marginal cost Fixed cost Quantity (gals/yr) Marginal and average cost 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 100 200 300 400 500 Millions of gallons \$/gallon MC AC

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5 Marginal and average cost 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 100 200 300 400 500 Millions of gallons \$/gallon MC AC AC = TC/Q TC = AC x Q Marginal and average cost 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 100 200 300 400 500 Millions of gallons \$/gallon MC AC Total cost of producing 200M gal/yr is \$3/gal x 200 M gal = \$600 M AC = TC/Q TC = AC x Q Chapter 9: Monopoly, Oligopoly, and Monopolistic Competition A. Total revenue and marginal revenue B. Total cost, marginal cost and fixed cost C. Profit maximization Proposition: any firm maximizes profit by setting marginal revenue equal to marginal cost First method of proof: calculus TR ± total revenue TC ± total cost TR " TC ± profit Firm maximizes profit by finding derivative of profit with respect to Q and setting it to zero d TR " TC   dQ ± 0 requires d TR   dQ ± d TC   dQ or marginal revenue ± marginal cost
6 Second method of proof: intuition Suppose the firm wasn’t following our advice, and operated at a level where MR > MC Then if it produced one more unit: its revenues would go up by MR its costs would go up by MC if MR > MC, its revenues would go up by more than its costs if it produced one more unit Conclusion: if MR > MC, firm can increase profits by producing one more unit Or, suppose instead the firm wasn’t following our advice, and operated at a level where MR < MC

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• Spring '08
• Kim

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