مالیات بر املاک و اثرات آن بر رفتار استراتژیک اجاره دادن و فروش برای انحصار گران کالاهای بادوام

This article analyzes how a property tax affects a lease-sell strategy of a durable-goods monopolist, and discusses its implications on social welfare. This paper presents some interesting results: (i) Contrary to the traditional view, social welfare can be enhanced by a tax when the time discount factor is low. (ii) Property tax causes the monopolist to spread production over two periods and increases the total stock of products, which enhances social welfare. (iii) The Coase conjecture fails and a monopolist produces only in period 1 and does not produce in period 2 when marginal cost is high. (iv) A mixed strategy of leasing and selling can be a unique solution, and a property tax encourages the monopolist to choose to sell even when the marginal cost is zero.

There has been much research that has explored the behavior of durable-goods producers. Most studies before Coase (1972) on durable goods focused on the choice of optimal durability (Kim, 2010 and Swan, 1970). Since Coase (1972) indicated that leasing can be more profitable than selling because leasing enables monopolist to commit to restricting quantities, many studies have examined the comparison between selling and leasing in durable goods. A number of studies on Coase's conjecture show that leasing is more profitable than selling under a monopoly since leasing can allow the monopolist avoid the time-inconsistency problem (see Bulow, 1982, Hirschey and Pappas, 1981 and Stockey, 1981). Moreover, a rather large number of studies have analyzed various conditions for mitigating the effect dubbed the time-inconsistency problem involving situations such as the constant inflow of new customers (Conlisk et al., 1984 and Sobel, 1991), the entry of new competitors (Bucovetsky and Chilton, 1986 and Bulow, 1986), discrete demand (Bagnolli, Salant, & Swierzbinski, 1989), increasing marginal cost (Kahn, 1986), different depreciation rates (Bond and Samuelson, 1984 and Desai and Purohit, 1998), a finite set of buyers (Bagnolli et al., 1989), the option of non-durable goods (Kuhn, 1998), market competition and product reliability (Desai & Purohit, 1998), heterogeneous firm efficiency in oligopoly (Saggi & Vettas, 2000), the monopolization of the maintenance market (Morita & Waldman, 2004), or network effects (Chien & Chu, 2008). This paper contributes to the literature by showing that the Coase conjecture fails when marginal cost is high even though we do not assume the existence of increasing marginal cost model as Kahn (1986) did. This paper shows that the monopolist produces only in period 1 and will not flood the market in period 2 when marginal cost is high even under a system in which there is no tax, which entails higher prices and lower social welfare. This is because the marginal cost can be interpreted as an excise tax imposed on production. In this context, our model can be considered as a generalized version of Goering and Boyce's model (1996), which shows that an excise tax gives rational consumers a sort of public notice that the monopolist will reduce production, and this leads to an increase in the monopolist's commitment power. However, most previous studies on the durable-goods market have analyzed leasing and selling policies separately. There are few studies considering leasing and selling together as a decision variable of the durable-goods monopolist. This paper shows that a combination of leasing and selling can be optimal in a monopoly with the constant marginal cost model, which differs from Desai and Purohit's (1998) depreciation rate model that is different for leased goods and sold goods, and Kahn's (1986) increasing cost function model. Desai and Purohit (1998) verify that the relative profitability of leasing and selling hinges on differences in the depreciation rates of leased and sold units. They argue that, if sold units depreciate at a significantly higher rate than leased units, a monopolist is better off taking a pure-selling strategy. They also assume that a monopolist's products are not homogeneous and identical durables. Kuhn (1998) tried to adopt genuine differences between durable and non-durable goods by incorporating non-durable goods of different quality and production costs and emphasized that the Coase conjecture fails, since non-durable goods act as an outside option that guarantees a minimum profit in the durable-goods market. We focus on homogenous and identical durable goods as Kim (2010), which differs from Desai and Purohit (1998) and Kuhn (1998). Heterogeneity in our model does not come from product characteristics such as depreciation rates, but mainly from a tax, which is different from Kim (2010) that considers different consumer types: careful and careless people. Recently some studies consider a tax on durable goods. Goel and Hsieh (1999) demonstrate that imposition of a Pigouvian tax on durable goods can increase social welfare when there exists negative externality incurred by production of goods. Their model considers leasing only, and derives the conclusion that a tax can increase social welfare by reducing production. On the other hand, Goering and Boyce (1996) show that an excise tax on production may increase a durable-goods monopolist's profit. However, their models consider the pure-selling case and an excise tax on production. Although the excise tax can cause the monopolist to choose to sell, it also lowers the production level in every period. As a result, social welfare cannot increase as long as, among other assumptions, negative externality is not considered. However, what if an ad-valorem tax is imposed on goods? In real life, we can easily find ad-valorem taxes levied on durables such as houses, vehicles, boats, aircraft, computers and copiers. What is more, an ad-valorem tax is a comparatively welfare-dominant option compared to an excise tax that guarantees the same amount of tax revenue (see Suits & Musgrave, 1953). To date, however, few studies except Arnott and Young (1979) have addressed how imposition of an ad-valorem tax affects a durable-goods monopolist's strategy. In this context, we investigate the effects of the property tax as an example of an ad-valorem tax in a durable-goods monopoly using a two-period model. Many consumers pay property tax for their durable goods. Usually vehicle and boat registration fees are subsets of this kind of tax. In the USA, durable goods such as vehicles require property tax and recently some industries' including the motor industry and computer industry, and software industry including cloud computing companies are considering the lease or buy problem. From the government perspective, a property tax is an important tax source of local government entities, along with acquisition tax and registration tax. We examine how this property tax affects the lease-sale choice of the monopolist, whereas Arnott and Young (1979) focus on the monopolist's choice of durability. We also analyze the relation between tax and social welfare in terms of whether a property tax can enhance social welfare. Thus, our model differs from the previous ones in that we incorporate the lease-sale choice of a monopolist with an ad-valorem tax, which has rarely been tackled. We find that under some circumstances an ad-valorem tax can enhance social welfare by increasing the total production. This finding is a somewhat different when compared to Goering and Boyce's (1996) result that the excise tax can cause the monopolist to lower the production level in every period and thus, social welfare cannot increase, and Goel and Hsieh's (1999) result that a Pigouvian tax on durable goods increases social welfare by reducing production. This paper proceeds as follows: after introducing the basic model in Section 2, we analyze the benchmark model without taxation in Section 3. Using the results in Section 3, we derive the optimal strategies for leasing and selling under a property tax in Section 4. We explain the impacts of the tax on production and on social welfare in Section 5 and conclude the paper in Section 6. All proofs are in the Appendix.

This paper has examined how a property tax affects a durable-goods monopolist's production and lease–sale choice using a two-period model. As a benchmark, we analyzed the no-tax case in which the marginal cost can actually be interpreted as an excise production tax. In the no-tax case, it is shown that any combination of leasing and selling, including pure selling, can be optimal when the marginal cost is sufficiently high. Similar to this, in the property-tax case, concurrent leasing and selling occur. However, there are distinctive differences in the results of the two cases. A property tax encourages the monopolist to choose selling even when the marginal cost is zero. In addition, a property tax causes the monopolist to spread production over both periods. In other words, production occurs even in period 2. More importantly, the total stock of goods in period 2 increases, and this leads to a possibility of an increase in social welfare. The contributions of our model can be summarized as follows. First, we employ a property tax for the lease–sale decision in a durable-goods monopoly, which has rarely been tackled by previous studies. Second, we show that social welfare can be enhanced by a tax even without the assumption of negative externality or an increasing cost function. Although our model has some limitations, for example, the simple time span, or the assumption of no deterioration of goods, we expect that it can be used as an important benchmark for related studies.