Price subsidies and guaranteed buys of a new technology

Abstract

We consider a problem of a government that wishes to stimulate the adoption of a new technology in order to replace an older, environmentally less desirable, technology. The new technology is manufactured by a monopolist firm which has learning-by-doing in its production process. The firm sells the new product to both private households and government institutions and wishes to determine an optimal pricing policy. The government has at its disposal two instruments: subsidizing the consumer price and making purchases of the new technology from the firm. We assume profit maximization on the part of the firm. The government wishes to maximize the cumulative number of units of the new technology sold to private households by the terminal date of the government program. The problem is set up as a Stackelberg differential game in which we identify an open-loop equilibrium, supposing that the government can credibly precommit to its subsidy and buying program.

Introduction

The paper deals with a problem of a government that wishes to accelerate the adoption of a new technology in the form of a newly invented product. The product can replace an older technology, in private households as well as in government institutions. The new technology is produced and marketed by a monopolist firm but households and government institutions have the option of continuing to buy an existing technology. To increase the diffusion of the new technology, a government has various instruments at its disposal (cf. Kalish and Lilien, 1983). In this paper we look at two specific instruments: price subsidies and guaranteed buys.

There can be several reasons for a government's wish to stimulate the use of new technologies. In the 1970s, much effort was expanded in western countries to make national economies less dependent on oil, by promoting the conservation of energy and encouraging the development of oil saving technologies. Here we have seen direct subsidies or tax rebates to convert, for example, traditional heating systems into dual-energy systems, to replace oil by natural gas, and to accelerate the use of wind and solar energy. Later on, governments' interest has also focused on environmental issues. For example, governments seek to enhance the use of “greener” energy sources (natural gas, biogas) or to reduce pollution (requiring catalysators in automobiles, subsidizing the price of unleaded petrol, subsidizing the replacement of older, polluting cars).

To assess the value to society of a particular governmental policy, an economist would introduce a welfare function. Since the specification of such a function presents some conceptual difficulties, this paper evaluates the effects of the government's subsidy program by two yardsticks: the level of the consumer price of the new technology and how many households have adopted the new technology by the end of the government subsidy program. Such objectives seem to be in line with the approach of public policy makers who would like to see a clear statement of the objectives that a government program is aimed at.

Kalish and Lilien (1983) were the first to approach the problem of government subsidies using an intertemporal marketing model. They studied an optimal control problem of the government but emphasized the need to develop dynamic games to handle the interactions between the government's subsidy policy and the firms' pricing strategies. Zaccour (1996) and Dockner et al. (1996) studied the subsidy problem as a differential game, employing a model of new product diffusion. (For this type of model, see Mahajan and Wind (1986)). Both these papers deal with the price decisions of the firm and the subsidy policy of the government. Zaccour (1996) identified Nash equilibria with open-loop strategies whereas Dockner et al. (1996) studied a case in which government acts as the Stackelberg leader and found feedback as well as open-loop equilibria. Kalish and Lilien (1983) and Zaccour (1996) incorporate the notion of cost experience (learning by doing), that is, the firm's unit cost of production decreases as cumulative sales increase. This phenomenon is quite often observed in the production of new technologies. This paper also employs the assumption of cost experience and extends previous work in two directions.

(1) We introduce an additional decision variable of the government: guaranteed purchases. The use of this instrument is two-fold. To equip its institutions, government needs to purchase units of the product category as such and, to the extent that governmental purchases favor the new product, government purchases help to decrease the firm's unit cost of production. A decreasing unit cost might give the producer an incentive to charge lower consumer prices.

(2) Consumers and government institutions have the option of buying an alternative product (say, a mature technology) that satisfies the same need, although in a less desirable manner from the government's point of view. To keep the model tractable, the alternative technology is introduced exogeneously in the model and has the same price to households and government. First we assume that the price of the mature technology remains constant over the planning period but later on we deal briefly with a case in which the price of the mature technology is monotonically decreasing.

As in previous work in the area, we impose a budget constraint on the government's expenditures. On the demand side we choose simple dynamics for the new product demand, involving only the current prices of the two technologies. This may be a limiting assumption for certain durable products since it does not allow for possible effects of previous adoptions on current sales (that is, imitation and/or saturation effects). However, when the planning period is relatively short, saturation effects might not yet be dominant. But it should be kept in mind that our choice of dynamics may be questionable if social interaction and communication with previous adopters is a major driving force of the adoption process of the new product.

The game is played in the Stackelberg leader–follower fashion and the two players are the government and the firm. We suppose that government takes the leader's role and announces its strategy before the firm makes its decisions. The players employ open-loop strategies which means that at the initial instant of time, each player decides upon a strategy which depends only on time. It is known that most open-loop Stackelberg equilibria have an inherent instability of being time inconsistent. This means that given the opportunity to revise his strategy at any instant of time after the initial one, the leader would like to choose another strategy than the one he chose at the initial instant of time. Thus, an open-loop Stackelberg equilibrium only makes sense if the leader can credibly precommit to his strategy. In the present game it seems plausible to assume precommitment on the part of the government: in practice a subsidy scheme is determined and announced from the outset and when the government's decision is irrevocable, the announcement will be credible. (There may be rare instances in which government changes, or even abandons, a program after its initiation. This could happen if, for some unforeseen reason, the very grounds of the program turn out to be unjustified.)

The rest of the paper is organized as follows. Section 2formulates the Stackelberg differential game and Section 3states our results concerning dynamic subsidy, purchasing, and pricing policies. Section 4concludes.