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Multiple Plants, Markets & Products

Multiple Plants, Markets & Products. Multiple Plants Equalize marginal cost across plants Multiple Markets, Same Product Price Discrimination Multiple Products Substitutes or Complements in Production or Consumption A Prisoner’s Dilemma?. Multi-plant Example.

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Multiple Plants, Markets & Products

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  1. Multiple Plants, Markets & Products • Multiple Plants • Equalize marginal cost across plants • Multiple Markets, Same Product • Price Discrimination • Multiple Products • Substitutes or Complements in Production or Consumption • A Prisoner’s Dilemma?

  2. Multi-plant Example • Two plants with different costs • MCA = 28 + 0.04QA • MCB = 16 + 0.02QB • Find the inverse MC functions • QA = -700 + 25MCA • QB = -800 + 50MCB • Add these together • QA +QB = QT = -1500 +75MCT • Invert the QT equation to get MCT • MCT = 20 + 0.0133QT

  3. Multi-plant Example, cont’d • Demand, Inverse Demand, & MR • QT = 5,000 – 100P • P = 50 – 0.01QT • MR = 50 – 0.02QT • Set MR = MCT, solve for QT* and P* • MR = 50 – 0.02QT = 20 + 0.0133QT = MCT • 30 = 0.0333QT => QT* = 900 • P* = 50 – 0.01QT = 50 – 0.01(900) = $41

  4. Multi-plant Example, cont’d • Find value of MR = MCT at QT* • MR = 50 – 0.02QT = 50 – 0.02(900) = 32 • Set MCA = 32 = MCB, solve for QA*, QB* • MCA = 28 + 0.04QA = 32 • QA* = (32-28)/0.04 = 100 • MCB = 16 + 0.02QB = 32 • QB* = (32-16)/0.02 = 800 • P* = $41, QT* = 900, QA* = 100, QB* = 800

  5. Multiple Markets: Price Discrimination • A firm charges different consumers different prices for the same good • Necessary conditions • The firm has some market power • Demand differs for groups of consumers • The firm can identify and separate these groups • Purchasers must be unable to resell the product (No Arbitrage) • Examples?

  6. Maximize Profits with Price Discrimination • Separate consumers into groups • Profit max requires MR=MC for each group • The good is the same so costs are the same (MC) • Demand differs across groups • MR differs across groups • Add MR’s together to find MRT = MC • If MC is constant, set MR = MC in each market

  7. Price Discrimination Example • Demand and Marginal Revenue • Q1 = 600 – 10P1; Q2 = 800 – 10P2 • P1 = 60 – 0.1Q1; P2 = 80 – 0.1Q2 • MR1 = 60 - 0.2Q1; MR2 = 80 – 0.2Q2 • MC = 20 • Set MR1 = MC = MR2, find Q1 and Q2 • 60 – 0.2Q1 = 20; Q1 = 200 • 80 – 0.2Q2 = 20; Q2 = 300 • Calculate P1 and P2 • P1 = 60 – 0.1(200) = $40 • P2 = 80 – 0.1(300) = $50

  8. Elasticity and Discrimination • Recall MR = P[1 + (1/E)], E < 0 • MR1 = MR2 = MRT = MC • So P1[1+(1/E1)] = P2[1+(1/E2)] • Suppose P1 < P2 • Then 1 + 1/E1 > 1 + 1/E2 • Or, 1/E1 > 1/E2 • E1 < E2 • Price is lower in the market with more elastic demand

  9. Multiple Products • Production • Substitutes-more of one, less of the other • Complements-more of both; scope economies • Consumption • Substitutes-one instead of the other • Complements-consumed together • When do multi-product firms produce more than single product firms? Less?

  10. Why Multiple Products? • Substitutes • Create barrier to entry by “crowding” • Price discriminate • Strategic interaction in oligopoly • Complements • Brand recognition • Reduce cost and increase convenience (one-stop shopping) • Maintain quality control

  11. Is Product Variety a Prisoner’s Dilemma?

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