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g. h. Assume c = 1. Solve for the optimal w that U sets. Write down U - D1's profit when c = 1. Compare your answers in (e) and (1) when c = 1. Does U-DI's commitment power (i.e. commit not to sell to D2) benefit or harm U-D1?

g. h. Assume c = 1. Solve for the optimal w that U sets. Write down U - D1's profit when c = 1. Compare your answers in (e) and (1) when c = 1. Does U-DI's commitment power (i.e. commit not to sell to D2) benefit or harm U-D1?

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter11: Price And Output Determination: Monopoly And Dominant Firms
Section: Chapter Questions
Problem 6E
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Help me understand g-h

Q2. Vertical integration An upstream manufacturer U supplies to two downstream retailers, D1 and D2. One unit of input is transformed into one unit of output. For simplicity, there is no production cost for U. U sets a per unit wholesale price w. D1 and D2 set quantities 9₁ and 92. In addition to the wholesale payment made to U, each downstream firm also incurs a packaging cost when selling q units. The inverse market demand function of the retail market is P(Q) = 1-Q where Q is the total output. The game has two stages when all three firms are independent. In stage 1, U sets the per unit wholesale price w. In stage 2, D1 and D2 simulta- neously and independently set retail quantities q₁ and 92 respectively. Consider the case when all firms are independent. Solve for the equilibrium quantities q₁(w) and q2(w) for a given w in the downstream market. Derive the optimal w that U sets. Calculate U's equilibrium profit. Next, suppose U acquires D1 and thus there is a vertically integrated firm U - D1. Suppose U - D1 commits not to supply input to D2. What retail price p₁ will U - D1 set? a. b. C. d. e. Finally, suppose U-D1 can no longer commit not to sell inputs to D2. Suppose it sells input to D2 at a per unit wholesale price w. Calculate U D1's profit. Compare your answers in (c) and (e). Illustrate the impact of the vertical integration on U's profit. (U's profit is just U-D1's profit after the vertical integration) f. For a given w, solve the equilibrium quantities q₁ (w) and 92 (w) in the downstream market. Assume c = 1. Solve for the optimal that U sets. g. h. Write down U-D1's profit when c = 1. Compare your answers in (e) and (1) when c = 1. Does U-D1's commitment power (i.e. commit not to sell to D2) benefit or harm U-D1?
Transcribed Image Text:Q2. Vertical integration An upstream manufacturer U supplies to two downstream retailers, D1 and D2. One unit of input is transformed into one unit of output. For simplicity, there is no production cost for U. U sets a per unit wholesale price w. D1 and D2 set quantities 9₁ and 92. In addition to the wholesale payment made to U, each downstream firm also incurs a packaging cost when selling q units. The inverse market demand function of the retail market is P(Q) = 1-Q where Q is the total output. The game has two stages when all three firms are independent. In stage 1, U sets the per unit wholesale price w. In stage 2, D1 and D2 simulta- neously and independently set retail quantities q₁ and 92 respectively. Consider the case when all firms are independent. Solve for the equilibrium quantities q₁(w) and q2(w) for a given w in the downstream market. Derive the optimal w that U sets. Calculate U's equilibrium profit. Next, suppose U acquires D1 and thus there is a vertically integrated firm U - D1. Suppose U - D1 commits not to supply input to D2. What retail price p₁ will U - D1 set? a. b. C. d. e. Finally, suppose U-D1 can no longer commit not to sell inputs to D2. Suppose it sells input to D2 at a per unit wholesale price w. Calculate U D1's profit. Compare your answers in (c) and (e). Illustrate the impact of the vertical integration on U's profit. (U's profit is just U-D1's profit after the vertical integration) f. For a given w, solve the equilibrium quantities q₁ (w) and 92 (w) in the downstream market. Assume c = 1. Solve for the optimal that U sets. g. h. Write down U-D1's profit when c = 1. Compare your answers in (e) and (1) when c = 1. Does U-D1's commitment power (i.e. commit not to sell to D2) benefit or harm U-D1?
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