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‘REVERSE HYSTERESIS’: R&D INVESTMENT WITH STOCHASTIC INNOVATION *

HELEN WEEDS
Fitzwilliam College, University of Cambridge

16 May 1999

Abstract
We consider optimal investment behavior for a firm facing both technological and economic uncertainty, in the context of a research project with unpredictable outcomes. The optimal investment strategy, in the form of a pair of trigger pointsfor investment and abandonment, is derived. As in Dixit (1989), the investment trigger exceeds the Marshallian investment point. However the abandonment trigger may exceed the Marshallian exit point, in contrast to the Dixit result, giving rise to ‘reverse hysteresis.’ Thus the firm tends to abandon research rapidly as profitability declines, at times despite the existence of positive expectedprofits. The model also provides a unified framework encompassing two existing models as limiting cases. Keywords: Real options, R&D, investment, hysteresis. JEL classification numbers: C61, D81, E22, O31.

Address for correspondence: Fitzwilliam College, Cambridge CB3 0DG, UK. Tel: (+44) (0)1223 332000; fax: (+44) (0)1223 464162; e-mail: hfw25@cam.ac.uk
The author wishes to thank Martin Cripps, DanMaldoom, Georg Rau, Hyun Shin and John Vickers for their comments and suggestions. Financial support was provided by the Americas’ Scholarship of Merton College, Oxford, and by the Economic and Social Research Council under grant number R00429524353.
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‘REVERSE HYSTERESIS’: R&D INVESTMENT WITH STOCHASTIC INNOVATION

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Introduction

When a firm invests in a research project it facestwo forms of uncertainty. In common with many other projects the economic value of the investment is uncertain. Since the return to a new product design or production process is derived from product market profits, the value of an invention is affected by fluctuations in market demand. However, in contrast to fixed capital investments, there is also technological uncertainty. Discovery occursrandomly, thus the relationship between the input of research effort and the creation of a marketable invention is uncertain. In this paper we consider optimal investment behavior for a firm facing both technological and economic uncertainty. As in other real options models, the stochastic nature of product market returns gives rise to option values which must be taken into account in making optimalinvestment and abandonment decisions. In addition the discovery of a marketable invention is a Poisson arrival. Uncertainty in the relationship between inputs and outputs drives a wedge between the firm’s decision to invest in research and the outcome of this investment. As a result, the active firm faces a probability distribution over possible discovery dates. Thus, when the firm exercises itsoption to invest in research it gains a second option, that of making the discovery itself, whose exercise time occurs randomly rather than being a single date chosen explicitly by the firm. The optimal investment strategy consists of a pair of trigger points for investment and abandonment. As in the Dixit (1989) product market model, sunk investment costs combined with uncertainty over market valuescause the trigger point for investment to rise and that for abandonment to fall relative to their Marshallian equivalents, widening the region of hysteresis. When technological uncertainty is also present, however, a second option effect arises. This option value is due to the irreversibility of the discovery itself and raises both trigger points. At the investment trigger the two effectsreinforce one another and research activity is further delayed compared with the Marshallian benchmark. At the abandonment trigger, however, the ‘discovery effect’ counteracts the sunk cost effect and the project is abandoned more rapidly than would otherwise be the case. When sunk costs are sufficiently small and the expected speed of discovery is high, the second effect dominates and abandonment takes...