Exchange rates and concurrent leasing and selling in durable-goods monopoly.(ORIGINAL PAPER)

Introduction

One of the more enduring puzzles of the theoretical durable-goods literature is the real world existence of large numbers of firms that simultaneously sell and lease their durable output. The durable-goods literature argues that monopolies would rather lease than sell, since leasing avoids any potential commitment problem with perspective buyers. As Coase (1972) first noted, a selling firm faces a commitment or dynamic consistency problem with buyers in that the firm cannot credibly convince buyers it will take the value of their existing stock into account in its future pricing decisions. Since the firm does not own the previously sold stock it has no incentive to account for this when selling units in a future period. Coase further conjectured that this consistency problem would force the monopolist to price at marginal cost in a "twinkling of an eye." This suggests that a selling firm may be forced to act in a competitive (zero profit) manner.

Later authors, such as Stokey (1981) and Gul et. al. (1986), show this will indeed occur if the time periods are sufficiently short. Although, other authors, such as Kahn (1986), Colangelo (1993), Bagnoli et. al. (1989), and Calem (1997), show there are a number of important caveats to this competitive scenario, the general theoretical conclusion remains that the a durable-goods monopoly seller tends to earn less profits than a renter. (1) However, we observe many firms selling their durable output. Indeed, many manufacturers, such as computer and automobile manufactures concurrently lease and sell output. This implies that selling certain units is more profitable than leasing all the firm's production.

There are a variety of traditional economic factors that impact the firm's lease versus sell decision. Moral hazard considerations can, in part, explain a firm's desire to sell units (see Goering 1997). Also, if a monopolist can commit itself to potential buyers through contracting, such as best-price provisions, they may wish to sell units (Butz 1990). Bhatt (1989) also shows that a risk-averse durable-goods monopolist may sell units if the in an attempt to shift demand uncertainty onto buyers. Additionally, Purohit (1995) argues that when the monopolist uses an intermediary to sell its output, selling may have a higher profit potential than leasing. Finally, Bulow (1986) and Bucovetsky and Chilton (1986) also argue that in an oligopoly setting, strategic considerations (locking-in future market share) may induce firms to concurrently rent and sell units.

In 1960 for the United States, Total Merchandise Trade (Merchandise Exports plus Merchandise Imports) relative to US GDP, equaled approximately 1.6%. Today United States total merchandise trade relative to US GDP equals approximately 6.25%. That is, today for the United States the volume of international trade in durable goods is an important aspect of overall economic activity in the U.S. (2)

Because of this increase in the importance of international trade in durable goods in this paper we present a simple and hereto unexplored rationale for concurrent leasing and selling, namely exchange rates. If a monopolist is engaged in trade with a foreign country, the value it receives for a unit of durable output depends in large part on the exchange rate. We show that by simultaneously selling and leasing output a monopolist without commitment ability may be able to earn higher profits than a pure leasing firm. If the exchange rate in a future period is expected to be less favorable to the foreign monopolist than the current rate, by selling units now the firm may effectively lock-in the higher exchange rate that tends to increase profits. Of course, as the firm sells units it also exacerbates its Coasian commitment problem, which tends to reduce profits. We show that in general these two opposing forces imply the firm wishes to concurrently sell and lease units, i.e., the firm does not wish to sell or rent all units when the current exchange rate is more favorable then the expected future exchange rate. On the other hand, our model indicates that if the future exchange rate is higher than the current rate a durable-goods monopolist will optimal lease all its units. (3)

Our model also provides a number of interesting comparative statics results. For example, we find that as the expected future exchange rate increases the current market sales price unambiguously increases. Thus, our analysis provides theoretical support for the empirical finding of Lee (1998). Lee (1998) examines the effect of exchange rates on the sales price of durable goods under duopoly and Cournot oligopoly and examines the sales equilibrium only and so does not directly examine the relationship between exchange rate expectations and the durable good monopolist's commitment problem and exchange rate expectations and the decision to rent or lease a durable good. However, Lee (1998) finds that an increase in the expected future exchange rate raises the current sales price of durable products. (4) We also show that the stock of available output in the future is increased (decreased) as the current (future) exchange rate increases. This implies that the future market price of the durable good tends to decline as the current exchange rate rises but increase as the expected future exchange rate rises. Finally, we explore the role of product durability in exchange rate pass-through.

Basic Model

We suppose a foreign monopolist manufactures a durable product over a two-period horizon. (5) The exogenously specified product durability is given by [delta] [member of] [0, 1]. The parameter 6 is the percentage of first period output that is available for use in the second period. Thus, if first period production is perfectly durable [delta]= 1, and if [delta]=0 the output is non-durable and zero period one units will survive for second period use.

In terms of the domestic market demand for the durable good is given by:

[p.sub.1] = a - [bx.sub.1] and [p.sub.2] = a - b([delta][x.sub.1] + [x.sub.2]) (1)

represent the lease (rental) price in each period, where [x.sub.1] [greater than or equal to] 0 and [x.sub.2] [greater than or equal to] are the firm's production levels in period one and two respectively. The demand specification in (1) assumes that the lease price is linearly related to the available stock output in each period. Note that if the firm sells a unit of durable output it receives the discounted stream of the lease prices, i.e., the first period sales price [p.sup.s.sub.1] of a unit of output with durability [delta] is:

[p.sup.s.sub.1] = [p.sub.1] + [beta][delta][p.sub.2] = a - [bx.sub.1] + [beta][delta](a - b([delta][x.sub.1] + [x.sub.2]) (2)

where [beta] [member of] [0, 1] is the discount factor. From (1) and (2) it is apparent that if the firm's output is non-durable ([delta] = 0) there is no difference in this setting between leasing and selling a first period unit. (6)

For simplicity, suppose that the single foreign firm leases or sells all its output in the domestic country (i.e., foreign firm is a pure monopolist in the domestic market). The foreign firm is thus interested in market prices denominated in its own currency. The exchange rate in each period is given by [e.sub.1] and [e.sub.2], where [e.sub.t] represents the amount of foreign currency per unit of domestic currency (e.g., pounds per dollar) in period t. (7) We further assume that the foreign monopolist chooses, not only the output levels [x.sub.1] and [x.sub.2], but also the percentage of period one units it wishes to lease [lambda] [member of] [0, 1] abroad. If [lambda] = 1 the firm chooses to lease all period one units while [lambda] = 0 indicates the firm will sell all period one units.

Finally, we assume the firm has zero production costs. Although the assumption of zero production costs is a strong one, it removes the influence of cost on the timing of production and allows us to focus on the impact of exchange rates. Obviously, the time path for costs will also play a large role in any observed behavior. If, for example, costs in the next period are considerable lower then they are today, the firm will ceteris paribus, choose to manufacture more in the future and sell less today. Previous studies have explored the impact of production costs extensively (e.g., Kahn 1986), thus we do not repeat this analysis here. Rather, we abstract from the influence of such cost changes by assuming zero marginal costs in both periods to focus solely on the influence of exchange rates.

Given these assumptions we can write the foreign firm's discounted profit in terms of its own currency as:

[pi] = ([gamma][p.sub.1] + (1 - [lambda])[p.sup.s.sub.1]) [e.sub.1][x.sub.1] + ([lambda][delta][x.sub.1] + [x.sub.2])[beta][e.sub.2][p.sub.2] (3)

where [p.sub.1], [p.sub.2], and [p.sup.s.sub.1] are given by (1) and (2). The firm, of course, wishes to maximize the present value of profits given in (3) through its choice of rental fraction [lambda] and output levels [x.sub.1] and [x.sub.2]. However, if the firm sells any period one units ([lambda] < 1), buyers' expectations about the future behavior of the firm become important as Coase (1972) showed.

Note that in period two the foreign monopolist's profits denominated in its own currency is given by:

[pi].sub.2] = ([lambda][delta][x.sub.1] + [x.sub.2])[p.sub.2][e.sub.2] = (([lambda][delta][x.sub.1] + [x.sub.2])(a- b([delta][x.sub.1] + [x.sub.2]))[e.sub.2] (4)

The firm's period two profit in (4) is simply the total stock of production still owned by the firm times the exchange rate adjusted market price. Potential period one buyers will rationally expect the firm to maximize (4), which places an expectational constraint on the firm. In other words, the firm cannot simply maximize (3) if it sells any units since the resulting solution will be dynamically inconsistent. Consumers realize that in period two any units previously sold by the firm are water under the bridge and that the firm will maximize (4) not [[pi].sub.2] = ([delta][x.sub.1] + [x.sub.2])[e.sub.2][p.sub.2] as suggested by (3). (8) Using (3) and (4) in the next section we solve for the dynamically consistent solution in reverse order starting in period two.

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