Consider the following model of a vertical market. In a market for a good, there exists a monop- olist manufacturer with a marginal cost of 5 who charges a wholesale price of pm to a monopolist retailer. The retailer's only marginal cost is the manufacturer price; however, the retailer must pay a fixed cost F in order to sell the manufacturer's goods. (For example, he must remodel parts of his store.) The retailer charges a price to consumers of pr. Demand is linear with pr = 15 - Q. a. Write down the retailer's profit function. (Hint: Don't forget fixed costs!) b. What is the price the retailer charges as a function of pm? c. Write down the manufacturer's profit function as a function of pm. What is the optimal pm set by the wholesaler? d. Given pm, what is the retailer's profit? At what level of F will the retailer no longer be willing to purchase from the manufacturer? (Hint: At what F is the retailer's profit negative?) e. Consider the vertically integrated monopolist. At what level of F will the vertically inte- grated monopolist no longer be willing to stock the good in his retail division? (Hint: At what F are profits positive?) At what values of F will the manufacturer carry the good if and only if it is vertically integrated with the retailer? (Hint: Use the answer you just found as well as the answer from d.)
Consider the following model of a vertical market. In a market for a good, there exists a monop- olist manufacturer with a marginal cost of 5 who charges a wholesale price of pm to a monopolist retailer. The retailer's only marginal cost is the manufacturer price; however, the retailer must pay a fixed cost F in order to sell the manufacturer's goods. (For example, he must remodel parts of his store.) The retailer charges a price to consumers of pr. Demand is linear with pr = 15 - Q. a. Write down the retailer's profit function. (Hint: Don't forget fixed costs!) b. What is the price the retailer charges as a function of pm? c. Write down the manufacturer's profit function as a function of pm. What is the optimal pm set by the wholesaler? d. Given pm, what is the retailer's profit? At what level of F will the retailer no longer be willing to purchase from the manufacturer? (Hint: At what F is the retailer's profit negative?) e. Consider the vertically integrated monopolist. At what level of F will the vertically inte- grated monopolist no longer be willing to stock the good in his retail division? (Hint: At what F are profits positive?) At what values of F will the manufacturer carry the good if and only if it is vertically integrated with the retailer? (Hint: Use the answer you just found as well as the answer from d.)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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I need help with part e
Transcribed Image Text:Consider the following model of a vertical market. In a market for a good, there exists a monop-
olist manufacturer with a marginal cost of 5 who charges a wholesale price of pm to a monopolist
retailer. The retailer's only marginal cost is the manufacturer price; however, the retailer must
pay a fixed cost F in order to sell the manufacturer's goods. (For example, he must remodel parts
of his store.) The retailer charges a price to consumers of pr. Demand is linear with pr = 15 – Q.
a. Write down the retailer's profit function. (Hint: Don't forget fixed costs!)
b. What is the price the retailer charges as a function of pm?
c. Write down the manufacturer's profit function as a function of pm. What is the optimal pm
set by the wholesaler?
d. Given p, what is the retailer's profit? At what level of F will the retailer no longer be
willing to purchase from the manufacturer? (Hint: At what F is the retailer's profit negative?)
e. Consider the vertically integrated monopolist. At what level of F will the vertically inte-
grated monopolist no longer be willing to stock the good in his retail division? (Hint: At
what F are profits positive?) At what values of F will the manufacturer carry the good if and
only if it is vertically integrated with the retailer? (Hint: Use the answer you just found as well
as the answer from d.)
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