Problem 2 (Channel coordination (10 Points))

There is a monopoly manufacturer of sporty sneakers who sells through two different. channels. The local channel is a brick and mortar retailer that has a monopoly. The online channel is served by two retailers that compete in prices. Assume that the two channels are online and local are completely separated such that there is no competition between channels. The two online retailers are perceived as homogeneous by consumers. Demand for sneakers is given by q=1-p in each of the channels. For the online channel p is the lowest price offered by the two online stores, while locally, it is the price offered by the local retailer. Assume that there are no costs of production or retailing.

The manufacturer offers two-part tariffs that consist of a fixed fee F and a per-unit

wholesale price . Suppose that the manufacturer offers take it or leave it contracts and that retailers value their outside option to the contract at zero.

a) Assume first that the manufacturer and all the retailers are integrated such that

they maximize the joint profits. What are the optimal prices in each channel for the

industry. b) Suppose from now on that each firm maximizes its own profits. What is an opti mal two-part tariff that the manufacturer offers to an online retailer. Verify that the resulting retail prices is the same as in the integrated solution you have just calculated.

c) Find an optimal two-part tariff that the manufacturer offers to the local retailer.

d) Suppose the manufacturer is not allowed to offer two different wholesale prices to online and local retailers. Find the optimal two-part tariffs of the manufacturer un der the constraint that the wholesale price has to be identical for each retailer. What are the resulting market prices. Compare the outcome to the case of differentiated two-part tariffs, who profits, who is harmed?

e) Discuss verbally, whether the manufacturer would like to use RPM if he cannot offer different wholesale price for the two different channels.