Knowledge that Transforms

In his comment, Stanley Reynolds provides a very interesting application of subgame perfect equilibrium concept to my 1981 model.' Reynolds claims that contrary to my analysis, the Sylos Postulate and excess capital investment need not be inconsistent with Nash equilibrium (p. 896). It is not overly surprising if characteristics of equilibrium are altered by applying a different solution concept. However, conclusions arrived at in my earlier paper regarding Sylos Postulate and Excess Capacity Hypothesis are quite robust to changes in equilibrium. Reynold's assertion that behavior of incumbent at subgame perfect equilibrium is consistent with Sylos Postulate or Excess Capacity Hypothesis is based on a misunderstanding of these concepts. As Reynolds notes, two-period, openloop Nash equilibrium with capacity as an upper bound on output, which was examined in my earlier paper, is also a subgame perfect equilibrium. Thus, all of results for this case still hold. In particular, monopolist will deter only if capacity level without threat of exceeds entry-deterring level. This requires capacity to be relatively inexpensive as compared to discounted marginal profit evaluated at blocking output (Proposition 1 and equation (4) of my paper). Thus, the Sylos Postulate is only satisfied in this limited sense (p. 506). The established firm may choose, however, to permit entry. When occurs, established firm always operates at full capacity before entry, thus contradicting Excess Capacity Hypothesis. When capacity is relatively inexpensive, established firm lowers its output to accommodate entrant and holds excess capacity after entry, thus contradicting Sylos Postulate. For case where capacity investment affects production costs, entrant and incumbent firm behavior at subgame perfect equilibrium reinforces my conclusion that the Sylos Postulate ignores both strategic interaction between firms and dynamic aspects of entry (p. 503). The established firm at subgame perfect equilibrium will not deter whether or not it is profitable to do so. Rather, will be deterred only if

Two behavioral assumptions that are often made in the industrial organization literature are that an established firm (or group) may deter entry either through limit pricing (the Sylos Postulate) or by holding excess capacity (the Excess Capacity Hypothesis). In an interesting recent article in this Review (1981), Daniel Spulber examines these behavioral assumptions to see whether they are consistent with rational behavior by an established firm. Spulber's analysis is based on a two-firm, two-period game model in which the established firm is given a first-in advantage. By introducing this dynamic element into the model, Spulber is able to explicitly address the issue of the optimality of entry-deterring behavior. Spulber finds that the use of limit pricing and/or excess capacity to deter entry is rational only under a very limited set of circumstances.' In particular, when the second-period outcome is determined by a Cournot-Nash equilibrium, he derives the following results. 1) The first-period output of the established firm is always less than or equal to the first-period output produced by a firm not anticipating entry. The established firm essentially accommodates entry and limit pricing does not occur. 2) The established firm never holds more capital than the amount that would minimize its production costs, given its output choices in periods one and two. This comment takes issue with Spulber's conclusions about the Cournot-Nash case. It will be shown that the two results cited above may be reversed when the production technology is characterized by variable proportions. This reversal hinges on the particular type of Nash equilibrium employed in the analysis of the two-period model. Spulber implicitly uses a Nash equilibrium that is not subgame perfect.2 It is shown below that, when one requires the Nash equilibrium to be subgame perfect, both limit pricing and excess capital investment outcomes are possible for the variable proportions technology case. The subgame perfection property thus seems to capture an important strategic element in decision making for the established firm. In some cases, this type of strategic behavior leads to entry barriers that would not exist under innocent profit maximization by the established firm. Strategic entry barriers are discussed by Steven Salop (1979). Spulber's notation and assumptions about demand and costs are adopted below.

Eric Blair's forecast from the 1940's called for a 1984 international political economy with constant war between three global powers, designed to use up resources otherwise so abundant that the masses would be free to reflect on, and consequently depose, the bureaucratic elite (George Orwell, 1949). Orwell's forecast was wrong, although perhaps in part only because it was a self-negating prophecy: one that induces corrective measures. Undoubtedly the most successful long-term economic forecast was Joseph's prediction to the Pharaoh of the fourteen-year agrarian business cycle. Others with less privileged information have fared less well. A founder of our own profession, Malthus, erroneously predicted long-term stagnation at the subsistence level, because he underestimated technical change (although for Sub-Saharan Africa and parts of South Asia, the Malthusian projection appears closer to the mark). This essay reviews long-term forecasts from the last several decades in the area of international economics, to see whether patterns can be distinguished in their success or failure.

In his 1983 paper, Jeremy Siegel derives a seemingly implementable policy rule involving optimal responses to interest rates. The existence of such a rule would be of tremendous interest to central banks whose monetary policies place heavy weight on responses to interest rates. The Siegel rule is especially appealing because it is (i) an optimal combination policy in the sense of William Poole (1970), and (ii) the proposed implementation of the rule does not require detailed knowledge of the structure of the economy. All that is required is a calculation of the covariance between innovations in prices and interest rates. Within the confines of a rational expectations equilibrium model, in which Siegel assumes agents do not make use of information embodied in the current nominal interest rate, he is able to design an optimal combination policy that does not require detailed information about the economy. That such an optimal policy exists is not new, but that it can be easily implemented is novel.' The policy rule depends solely on the covariance between innovations in the aggregate price level and innovations in the nominal rate of interest, normalized by the variance of innovations in the interest rate. When this index is zero, policy has been set optimally. When the index is positive the feedback term on interest rates in the money supply rule is too large, and when the index is negative the feedback term is too small. Given that one can obtain reduced-form expressions for prices and interest rates, the index is easily computed. Unfortunately, Siegel's proposal violates Robert Lucas's (1976) critique. That is, he implicitly treats as invariant certain aspects of economic behavior that will generally change when one moves to an operational interest rate This note shows in detail that in a model where prices are flexible and agents observe local market prices (i.e., the model at least employed verbally by Siegel), that the coefficients in the aggregate supply and demand functions are not invariant to the form of the money supply rule. This lack of invariance will cause Siegel's rule to be nonoperational. The sensitivity of parameters in aggregate supply functions to policy is not restricted to equilibrium models with flexible prices. This property also extends to contracting models with endogenous indexing (see, for example, Jo Anna Gray, 1976). Therefore, Siegel's rule will not be implementable in a wide variety of commonly used macro models.