A large literature in economics and marketing studies the problem of manufacturer's designing contracts that give a retailer appropriate incentives to make decisions that are optimal from the manufacturer's point of view (see, for example, Spengler 1950, Jeuland and Shugan 1983, McGuire and Staelin 1983, Lal 1990, Rao and Srinivasan 1995, Desai 1997, among others). An important result from this literature is that the manufacturer can coordinate retail price decisions by choosing a two-part tariff in which the wholesale price equals the manufacturer's marginal cost and the fixed fee extracts all the rents from the retailer. In other words, the manufacturer sells the firm to the retailer for the fixed fee and, thus, eliminates the double-marginalization problem. Although this result is well established for non-durables, researchers have not analyzed the coordination issue for durable goods manufacturers who have the added complexity of competition from used goods in secondary markets. In this paper, we show how the coordination problem for a durable goods manufacturer is fundamentally different from the traditional coordination problem of a non-durables manufacturer. In particular, the durable goods manufacturer has to solve not only the coordination problem but also the time-consistency problem (see, for example, Coase 1972, Bulow 1982, Purohit 1995). Our objectives in this paper are to investigate whether or not the insights from the channel coordination literature, that has developed principally with non-durable goods in mind, are also applicable to durable goods. In order to do this, we develop a dynamic, two-period model in which a manufacturer sells its products to a retailer who sells the product to consumers. Products sold in the first period become used goods in the second period and compete with sales of new units. Starting from consumer utilities, we derive inverse demand functions for new and used goods and consider a number of different contracts between the manufacturer and the retailer. We start with a simple contract in which the manufacturer offers a wholesale price for a period at the beginning of that period. As one would expect, this contract does not solve either the channel coordination problem or the time-consistency problem. We then consider a number of two-part tariff contracts. Given the well-established results from the existing channel coordination literature, we begin with a contract in which the manufacturer offers per-period two-part tariffs in which all wholesale prices are set at marginal cost. We find that not only does this contract fail to achieve channel coordination, but the retailer sells a higher quantity than an integrated manufacturer would sell. This is in contrast to the traditional double marginalization problem in which the retailer sells a lower quantity than an integrated manufacturer would sell. We then allow the wholesale prices to be different from marginal costs. We show that using this more general two-part tariff contract, the manufacturer can achieve channel coordination. That is, the total channel profit is the same as the profit of an integrated seller. However, the equilibrium wholesale price in the first period is strictly above the marginal cost. Next, we consider a contract in which the manufacturer uses a single fixed fee, announced at the beginning of the first period. The per-period wholesale prices are still at the marginal cost level in this contract. This contract is identical to "selling the firm to the retailer" at the price of the fixed fee. Here we find that the contract can achieve channel coordination. However, the contract is not an equilibrium solution. In particular, the manufacturer increases wholesale prices to above marginal cost levels. Although some of the contracts above solve the double marginalization problem, none of them mitigates the time consistency problem. In order to solve both these problems, the contract must yield total channel profit equal to an integrated renter's profit. Because the renter does not have a problem with time consistency, an integrated renter earns the highest profits in a durable goods channel. We derive a contract that solves both of these problems. In this contract, at the beginning of period 1, the manufacturer writes a contract with the retailer specifying a fixed fee and two per-period wholesale prices, both of which turn out to be strictly above the marginal cost. Interestingly, with this contract, the manufacturer makes more money by selling through the retailer rather than selling directly to consumers. We contribute to the coordination literature by examining coordination issues in a dynamic, durable goods context and identifying a new coordination problemunlike the traditional coordination models, a durable goods manufacturer may have to provide the retailer incentives to sell less rather than to sell more. Clearly, the traditional "selling the firm to the retailer," approach does not solve this new problem. We also contribute to the durable goods literature by showing how a durable goods manufacturer can sell its product and solve its time consistency problem. Effectively, this allows the manufacturer to earn the same profits as it would get if it could commit to prices or if it could rent its product. When committing to individual consumers or renting can only be achieved through additional costs, our solution is the optimal strategy for a durable goods manufacturer.
