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Strategic Pricing: Theory, Practice and Policy

Strategic Pricing: Theory, Practice and Policy. Professor John W. Mayo mayoj@georgetown.edu. This Lecture: Supply-side (Costs) and prices. Basics: supply, demand and prices Costs and prices Relevant and irrelevant costs Cost changes and Price changes (Pass-through).

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Strategic Pricing: Theory, Practice and Policy

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  1. Strategic Pricing: Theory, Practice and Policy Professor John W. Mayo mayoj@georgetown.edu

  2. This Lecture: Supply-side (Costs) and prices • Basics: supply, demand and prices • Costs and prices • Relevant and irrelevant costs • Cost changes and Price changes (Pass-through)

  3. Prices, Industry Supply & Demand, and the Role of Industrial Organization $ $ S mc ac D q Q

  4. Demand Growth and Prices $/Q $/q S mc ac P2 P1 D2 D1 q Q With Demand growth, upward pressure exists for prices

  5. Supply Changes and Prices $/Q $/q S1 mc S2 ac P2 P1 D2 D1 q Q Increases in Supply create downward pressure on prices

  6. Monopoly and Competition cs= consumer surplus $ mc ac cs D mr Prices are higher under Monopoly than competition Next lecture will deal with industrial structure and prices

  7. Costs and Prices • What are the relevant costs to the determination of price? • Incremental Costs • Avoidable cost • Opportunity Costs • What are costs that are NOT relevant to the determination of price? • Fixed costs • Sunk costs Note: read Nagel and Holden for examples

  8. Maximizing profits: The economic approach π = p*Q(p) –c[Q(p)] dπ/dp = Q + p*dQ/dp – (dc/dQ)dQ/dp = 0. Rearranging, p*dQ/dp – (dc/dQ)(dQ/dp) = - Q, or [p - (dc/dQ)](dQ/dp) = - Q [p - (dc/dQ)]= - Q /(dQ/dp) Dividing through by p [p - (dc/dQ)]/p= - [(Q/p) /(dQ/dp)] = -1/ε The profit maximizing markup is inversely related to the firm’s price elasticity of demand

  9. Maximizing profits: Multiple Markets Suppose the firm produces in multiple markets with interdependent demands: π = p1*Q1(p1,p2) + p2*Q2(p1,p2) –c[Q1(p1, p2)] - c[Q2(p1, p2) ] ∂dπ/ ∂ pi = 0 Solving… (Pi - ∂C/ ∂qi)/Pi = -1/ εii - [(pj- ∂C/ ∂qj)Qj εij] / Ri εii. where εii is the own-price elasticity, [∂Q1/ ∂p1]/(p1/q1) εij is the cross-price elasticity, [∂Q2/ ∂p1]/(p1/q2) ∂C/ ∂qi is the marginal cost wrt i, and Ri is the revenue of the ith product

  10. Pricing with Substitutes (Pi - ∂C/ ∂qi)/Pi = -1/ εii - [(pj- ∂C/ ∂qj)Qj εij] / Ri εii. Implications: Suppose that the firm produces substitute products so εij > 0. Then the optimal mark-up is larger than if the firm optimized mark-ups on each product independent of the other. Example: Say, e.g., the εii = 2, pj=10, ∂C/ ∂qj) = 5, Qj =100 and εij = -.5. How does this change the value of the Lerner Index?

  11. Pricing with Complements (Pi - ∂C/ ∂qi)/Pi = -1/ εii - [(pj- ∂C/ ∂qj)Qj εij] / Ri εii. Implications: Suppose that the firm produces complementary products so εij < 0. Then the optimal mark-up is smaller than if the firm optimized mark-ups on each product independent of the other. Example: Say, e.g., the εii = 2, pj=10, ∂C/ ∂qj) = 5, Qj =100 and εij = -.5. How does this change the value of the Lerner Index?

  12. Cost changes and Price changes(Constant Elasticity) Can we understand optimal price changes in the face of cost changes? Profit maximization requires MR=MC = p[1 + (1/ε)] Suppose demand is given by p = q 1/ε Thus, for constant ε, we have a simple rule of thumb to optimal pricing: TR = q 1/ε+ 1 = q (ε + 1)/ ε , MR = [(ε + 1)/ ε]q1/ε = [(ε + 1)/ ε]p Thus we have [(ε + 1)/ ε]p =MC or p = [ε/(ε + 1)]MC dp/dMC = [ε/(1+ ε)] Suppose that we knew that MC=10 and ε = -5. What is the optimal price? Assuming ε is a constant, what is your recommendation regarding price if costs increase to 20?

  13. Cost changes and Price changes(Linear Demand) Suppose demand is given by p = α - βq Thus, TR = (α – βq)q = αq – βq2, MR = α – 2βq Setting MR=MC, we have α – 2βq =MC, or q = (α/2β) – (1/2β)MC Substituting q back into the inverse demand function, p = α - βq = α – β[(α/2β) – (1/2β)MC ] Or p = α - α/2 +(1/2)MC, so Dp/dMC = ½. The optimal cost flow-through is always ½ the change in the cost

  14. When might it make sense to fully pass through cost changes? Consider a demand function facing the firm equal to P= α –β ln Q. In this case, MR = p – β, Setting MR=MC and solving, we get Dp/dMC = 1. In this instance cost changes are flowed through dollar for dollar.

  15. Notes: assumes ε=5; α = 5; Β= 2, respectively

  16. A Pint-Sized Problem • How have retailers addressed cost increases?

  17. Next Lecture: The role of Industrial Organization on Pricing • Competition v. Monopoly • Oligopoly • Bertrand • Cournot • Dominant firm price leadership

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