The durable goods monopoly problem was identified by Coase [44].
Consider a monopolist selling a durable good to a fixed set of buyers.
If the monopolist could commit to selling at one date only, it would choose the monopoly price (and quantity) to maximize profits. Con-sumers who value the product more than the monopoly price would buy at that price. Any consumers with values below the monopoly price would not buy. If the monopolist cannot commit to selling at one time only, however, consumers would be na¨ıve to purchase at the monopoly price initially. This is because once the monopolist has sold to the high-valuation customers, it then has an incentive to reduce price and sell to lower-valuation customers. The high-valuation customers, anticipat-ing the reduction in price, will rationally delay their purchases. The monopolists’ pricing power is undone because sales in the second (and future) periods essentially compete with sales in the first period. The monopolist competes with its future self.
The Coase conjecture is that as the time between selling dates converges to zero, the monopolist’s price converges to the competi-tive price, which is marginal cost. Bulow [29] reviews this topic and discusses related issues.
Dudine et al. [59] focus on a parallel intertemporal demand incentive. The monopolist’s inability to commit again drives the dynamics. While the durable goods monopoly problem focuses on buyers’ incentive to delay purchases, the “storable goods monopoly”
problem focuses on buyers’ incentive to advance purchases by stockpil-ing goods for future consumption. While the operations and inventory literature has analyzed numerous incentives to stockpile inventory (long production lead times, fixed costs, and so on), the stockpiling incentive in this monograph is driven purely by strategic considerations. The argument in Dudine et al. [59] is the following. Suppose a monopo-list faces an identical linear demand curve in each of two periods; let qt(pt) = 1− pt, t = 1, 2 where t refers to the time period. The demand is that of a single buyer. Assume that the marginal production cost is zero. If the monopolist could commit to prices in both periods, then it
would simply charge the monopoly price in each period, i.e., p∗t = 1/2 and q∗t = 1/2 for t = 1, 2.
Now suppose that commitment to future prices is not feasible. This provides an opportunity and incentive for buyers to influence future prices by buying goods in the first period for use in the second. Suppose the monopolist sets p∗1= 1/2. The buyer, acting strategically, buys q1= 1/2 + , where > 0. Because the buyer has stockpiled units for use in period 2, the demand function in period 2 is now q2(p) = 1− − p.
The monopolist in this second period will maximize profits at a price p2= (1− )/2. As a consequence of the buyers ability to store the good, the price in period 2 is lower than the price that the monopolist could have charged if the monopolist had been able to commit up-front to the second period price.
The monopolist’s inability to commit allows the buyer effectively to lower the second period price by stockpiling inventory. This lower price benefits the buyer on all units purchased in the second period. As long as the cost of stockpiling inventory is sufficiently low, the trade-off between the cost of stockpiling inventory and the benefit of a lower price in the second period works to the buyer’s advantage. In response to the buyer’s strategic behavior, the monopolist will attempt to deter the stockpiling by raising prices in the first period. In the equilibrium, however, the inability to commit to the second period price will always leave the buyer with an incentive to stockpile inventories.
10.1.1 Related Papers
Both the durable goods and the storable goods problems have been analyzed in the supply chain management literature. In particular, ref. [182] addresses intertemporal pricing with customers delaying pur-chases (the durable goods effect) and ref. [183] deals with customer stockpiling (the storable goods effect). In ref. [182] the monopolist has a fixed amount of inventory that has to be sold over a finite time horizon.
Customers vary along two dimensions: their valuation for the product and their willingness to wait. Su demonstrates that prices can decrease or increase over time, depending on whether the high-valuation cus-tomers are less or more patient than the low-valuation cuscus-tomers. In ref. [183], customers can stockpile inventory and the manufacturer can
commit to a price path. However, the manufacturer may benefit from offering period price promotions as long as frequent shoppers are willing to pay more than occasional shoppers.
Su and Zhang [184] consider a newsvendor setting in which cus-tomers, anticipating ex post markdowns on unsold inventory, may strategically delay purchases. The monopolist’s choice of low quantity, i.e., high price, can alleviate this problem, but the monopolist may not be able to commit credibly. Su and Zhang introduce a commitment device that we have explored earlier in this review: decentralization of decision-making. A decentralized supply chain with a simple uniform pricing contract can, by introducing a vertical externality on price and inventory decisions, credibly commit to keeping prices high and quan-tities low. Arya and Mittendorf [13] also argue that “channel discord,”
i.e., strategic decentralization serving as a commitment device, can mit-igate the durable goods monopolists’ problem.
Anand et al. [5] analyze the storable goods problem using a supply chain model with an upstream seller and a single downstream buyer facing a downward sloping market demand. The downstream firm can strategically hold inventory in order to lower future prices. Anton and Varma [8] consider an oligopoly version of this problem. Buyers’ incen-tives to stockpile, the basic problem as perceived by the seller, are exacerbated here because each firm bears only part of the future cost of consumers stockpiling inventory and each firm has therefore low incentive to suppress stockpiling.
Several recent papers consider related dynamic issues. Most consider strategic incentives to delay purchases: see refs. [185, 186, 187]. The strategic incentives to stockpile inventory, however, have received less attention in the supply chain literature. Inventory dynamics are central to supply chain coordination in reality and deserve further attention in the theory literature.
The classic Clark and Scarf [41] article develops a serial multi-echelon model, i.e., a model with one firm at each of many stages.
By establishing the concept of echelon stocks1 Clark and Scarf show
1The echelon inventory level at any stage of the supply chain is the inventory available at that stage and at all downstream stages.
that the multi-dimensional problem can be solved as a sequence of one-dimensional problems. Lee and Whang [119], Chen [40], Cachon and Zipkin [39] and Porteus [157] all analyze the coordination problem of attaining the optimal centralized outcome through appropriate trans-fers for each echelon.