Question 2: Channel Pricing (show all work)

A manufacturer sells a product to a retailer, who in turn sells the product to a group of customers. The manufacturers per unit cost is $4. The manufacturer sells the product to the retailer by charging a Wholesale Price. The retailer sells the product to the customers by setting a Retail Price. The demand curve of the customers is given by Quantity Sold by Retailer = 20 Retail Price. The retailer orders exactly the amount sold to customers from the manufacturer (so that the manufacturer sells the same quantity as the retailer).

What is the optimal linear wholesale price contract the manufacturer should offer the retailer? Calculate also the resultant profits for the manufacturer and the retailer.

(Answer: W=12, MProfit=32, RProfit=16)

Note: I may have a question that asks you about what are the profit outcomes if the manufacturer offers the retailer a 2-Block tariff or 2-Part Tariff (I will give you the specific offer, so its NOT a question of finding the optimal nonlinear pricing contract).