Uncertain innovation with uncertain product durability

Abstract

This paper adds to two strands of the economics literature, the literature on product durability and on technical change, in a small way by introducing the possibility that an uncertain invention may be exogenously durable. Durability makes otherwise fully appropriable innovation porous. We consider a duopoly where firms maximize the present discounted rewards from innovation that might turn out to be a durable good or a non-durable good. Comparative-static results show that greater appropriability of rewards from the durable good innovation induces the firm to increase its profit-maximizing research spending. The effect of a change in the probability of the durable innovation is shown to depend on the degree of appropriability. The consideration of the effect of changes in the probability of durable innovation is unique to the literature. The effects of change in R&D competition are ambiguous and in line with earlier findings. Two special cases are considered and policy implications discussed.

Notes

¹ The research rewards may be viewed as revenues net of production costs. Later in this paper we shall consider a scenario with research spillovers.

² The revenues of a durable goods monopolist may be sensitive to its sales–lease decision. We abstract from this issue to focus on the influence of innovation and durability uncertainties.

³ Alternately, (1 – δ) will be the extent of spillovers to the inventor from second-hand sales.

⁴ The different values of δ may be seen as capturing market uncertainty associated with the durable good (see Bhatt, 1989; Goering, 2000).

⁵ We are focusing on the firm with research outlays x; while the rival firm has R&D y.

⁶  When the probability of innovation is exponentially distributed, m(t) = 1 and v(t) = t.

⁷ Without loss of generality, pre-innovation market competition can be added to this set-up.

⁸ The probability of durable innovation may alternately be viewed as the probability that a used goods market (e.g., county flea market, access to Internet auction sites, etc.) will exist.

⁹ Note that this is a sufficient, but not necessary, condition.

¹⁰ Obviously, the comparative-static effect of a change in rival R&D cannot be considered in this case.

¹¹ See Griliches (1992) for a review of the innovation spillovers literature.

¹² This is obviously a simple model of innovation spillovers. One could alternately model the revenues from rival innovation to be different from those from own innovation.