Abstract
The theory of capital developed by Bohm-Bawerk and Wicksell emphasized the roundabout nature of the production process. The basic insight is that production necessarily involves time. One element of the production process is to determine the period of production, or the length of time from the start of production to its completion. Bohm-Bawerk and Wicksell emphasized the role of the interest rate in determining the period of production. In this paper, I develop an option games model of the decision to invest. Two firms have an opportunity to enter a market, but production takes time. Firms face a two-dimensional decision. Along one dimension, they determine the period of production and the prospective profit therefrom. Along another dimension, they determine whether or not they want to enter the market given the amount of time it will take to start generating revenue from production. Within this option games approach, the period of production can be understood as an endogenous time-to-build and I argue that this framework provides a tool for evaluating the claims of Bohm-Bawerk and Wicksell against the backdrop of competition and uncertainty. I evaluate the period of production decision and the option to enter decision when the real interest rate changes. I show that investment coordination failures are more likely to occur at lower levels of profitability when real interest rates are low. I conclude by discussing the implications of low interest rates for boom-bust investment cycles.
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Notes
In the model, I focus on entry, but one could just as easily use the model to consider the role of similar decisions, such as capacity expansion.
The option games literature incorporates strategic decision-making in the real option literature. For an overview of the real options approach, see Dixit and Pindyck (1994). For a collection of important papers in this literature, see Grenadier (2000). For a textbook treatment of this approach, see Chevalier-Roignant and Trigeorgis (2011).
Note that μ is restricted to be less than the real interest rate, r, to assure convergence. If μ > r, then it is always desirable to wait longer and the optimum would not exist. See (Dixit and Pindyck 1994, p. 138).
Grenadier (1996) rules out simultaneous entry by assuming that if both firms try to enter simultaneously, the first entrant is determined by a coin flip. He then considers the median time a follower firm will enter as a function of the volatility of demand. He interprets relatively short median entry times as “development cascades.” Thus, referring to simultaneously entry as an investment boom is similar in spirit.
Hendrickson and Salter (2016) develop a model that addresses similar issues to those addressed in this paper. In that paper, the central bank can influence the real interest rate by altering the relative rate of return on money and other assets.
Note that in the Austrian literature, the real interest rate is inversely related to the roundaboutness of production. In the Cambridge Capital Controversies, the Cambridge, U.K. economists argued that it was possible that the real interest rate could be positively related to the roundaboutness of production. For a discussion, see Garrison (2006). This model captures the Austrian view. In fact, as I note in the next subsection, the model is also capable of producing a definition of the value of capital consistent with the Austrian view.
Hirshleifer (1970) notes the close relationship between the implications of duration models and Bohm-Bawerk/Wicksell models of the length of production.
For a discussion, see Evans and Baxendale (2008).
Suppose that a does not change over some short time interval [t, t + d t). During this time interval, the probability of simultaneous entry is α 1 α 2. If neither firm enters, there is still a chance of simultaneous entry. It follows that the probability of simultaneous entry is α 1 α 2 + α 1 α 2(1 − α 1)(1 − α 2) + (1 − α 1)2(1 − α 2)2 α 1 α 2+… = α 1 α 2/(α 1 + α 2 − α 1 α 2). Since the firms are identical, this reduces to α/2 − α.
Note that this is due to the fact that the slope of the value functions, V L (a), V F (a), and S(a), get steeper as the real interest rate declines.
Note that the current model would not imply that the structure of production could be represented by a triangle. As discussed in Hirshleifer (1967), this is due to the use of discounting and the assumption about the timing of labor payments. Nonetheless, the general implications about the length of production and the value of capital remain consistent with the work of Bohm-Bawerk, Wicksell, and Hayek.
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Hendrickson, J.R. Interest rates and investment coordination failures. Rev Austrian Econ 30, 493–515 (2017). https://doi.org/10.1007/s11138-016-0368-6
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DOI: https://doi.org/10.1007/s11138-016-0368-6