= 1. Consider a vertically related market. Demand for the final product is given by P abQ. A manufacturer sells an input to a retailer. The retailer uses 1 unit of input to make 1 unit of output and then sells the final good to the consumer. Both the manufacturer and the retailer have zero production costs. The timing of the game is that at the wholesale stage, the manufacturer sets a contract. After observing the contract, at the retail stage, the retailer sets a final product price. (a) What are the joint-profit maximising final good quantity and price? (b) Suppose both parties act as independent profit maximisers. In the first stage, the manufacturer sets a wholesale price w. After observing w, in the second stage, the retailer sets a retail price P. In the retail stage, what is the profit maximising retail price as a function of w? (c) In the wholesale stage, what is the profit maximising wholesale price, w? Hence, what is the retail price in equilibrium? Compare your answers with those in part (a) and comment. (d) What would the outcome be if the two suppliers are vertically integrated? (e) If the manufacturer could charge the retailer a two-part tariff {w, F}, where w is a per-unit charge and F is a fixed fee, discuss how the optimal tariff should be set. (f) Explain how the manufacturer could use a maximum retail price to maximise profit. That is, in the wholesale stage, the manufacturer specifies a wholesale price w together with a maximum retail price. (g) Now, suppose there exist n > 1 retailers downstream, who compete in quantities. The timing is that in the wholesale stage, the manufacturer sets the wholesale price w. In the retail stage, all n retailers observe w and compete by choosing quantities simultaneously. Let b = 1. Show that the double marginalisation problem still exists. (h) Show that the double marginalisation problem in part (g) disappears as n∞. Interpret your result.
= 1. Consider a vertically related market. Demand for the final product is given by P abQ. A manufacturer sells an input to a retailer. The retailer uses 1 unit of input to make 1 unit of output and then sells the final good to the consumer. Both the manufacturer and the retailer have zero production costs. The timing of the game is that at the wholesale stage, the manufacturer sets a contract. After observing the contract, at the retail stage, the retailer sets a final product price. (a) What are the joint-profit maximising final good quantity and price? (b) Suppose both parties act as independent profit maximisers. In the first stage, the manufacturer sets a wholesale price w. After observing w, in the second stage, the retailer sets a retail price P. In the retail stage, what is the profit maximising retail price as a function of w? (c) In the wholesale stage, what is the profit maximising wholesale price, w? Hence, what is the retail price in equilibrium? Compare your answers with those in part (a) and comment. (d) What would the outcome be if the two suppliers are vertically integrated? (e) If the manufacturer could charge the retailer a two-part tariff {w, F}, where w is a per-unit charge and F is a fixed fee, discuss how the optimal tariff should be set. (f) Explain how the manufacturer could use a maximum retail price to maximise profit. That is, in the wholesale stage, the manufacturer specifies a wholesale price w together with a maximum retail price. (g) Now, suppose there exist n > 1 retailers downstream, who compete in quantities. The timing is that in the wholesale stage, the manufacturer sets the wholesale price w. In the retail stage, all n retailers observe w and compete by choosing quantities simultaneously. Let b = 1. Show that the double marginalisation problem still exists. (h) Show that the double marginalisation problem in part (g) disappears as n∞. Interpret your result.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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1. Consider a vertically related market. Demand for the final product is given by P
abQ. A manufacturer sells an input to a retailer. The retailer uses 1 unit of input
to make 1 unit of output and then sells the final good to the consumer. Both the
manufacturer and the retailer have zero production costs. The timing of the game
is that at the wholesale stage, the manufacturer sets a contract. After observing the
contract, at the retail stage, the retailer sets a final product price.
(a) What are the joint-profit maximising final good quantity and price?
(b) Suppose both parties act as independent profit maximisers. In the first stage, the
manufacturer sets a wholesale price w. After observing w, in the second stage,
the retailer sets a retail price P. In the retail stage, what is the profit maximising
retail price as a function of w?
(c) In the wholesale stage, what is the profit maximising wholesale price, w? Hence,
what is the retail price in equilibrium? Compare your answers with those in part
(a) and comment.
(d) What would the outcome be if the two suppliers are vertically integrated?
(e) If the manufacturer could charge the retailer a two-part tariff {w, F}, where w is
a per-unit charge and F is a fixed fee, discuss how the optimal tariff should be
set.
(f) Explain how the manufacturer could use a maximum retail price to maximise
profit. That is, in the wholesale stage, the manufacturer specifies a wholesale
price w together with a maximum retail price.
(g) Now, suppose there exist n > 1 retailers downstream, who compete in quantities.
The timing is that in the wholesale stage, the manufacturer sets the wholesale
price w. In the retail stage, all n retailers observe w and compete by choosing
quantities simultaneously. Let b = 1. Show that the double marginalisation
problem still exists.
(h) Show that the double marginalisation problem in part (g) disappears as n∞.
Interpret your result.
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