Suppose we have a wholesaler firm that charges a retailer r for the retailer's only input. The marginal cost of the wholesaler is $2. It takes one unit of the input to produce one unit of the retailer's output and in addition to the price of the input the retailer has an additional marginal cost of $2.
The retailer's demand curve is given as P = 40 - Q.
a) Write out the retailer's profits as a function of Q and r.
b) Maximize the retailer's profits still treating the wholesale price as r.
c) What is the retailer's profit maximizing price as a function of r?
d) What is the wholesaler's demand curve?
e) What is the profit maximizing wholesale price?
f) What is the retail price?
g) What are the profits for each firm?
h) Now, suppose the firms merge. What would the profit maximizing retail price be?
i) What are the profits of the new firm?
j) Describe how the retailer's pricing decision imposes an externality on the wholesaler.