Behavior of the Dynamic Competition and Technical Progress model in special cases

Simulation will be the principal tool employed to explore the model. However, in certain simple cases it is possible to achieve analytic results.

Consider first the behavior of the model when firms make no e f­ forts to obtain new techniques- that is, when rin and rim are set to zero in all firms and all firms have the same unit production costs. If entry is impossible or is restricted to being strictly imitative of extant firms, the model’s behavior becomes independent of latent produc­ tivity. Also, since the only stochastic features of the full model are as­ sociated with the occurrence of technical change, the circumscribed model is fully deterministic. Since R&D expenses are the only non­ production costs, positive net investment can always be financed if

price is above unit cost. If all firms have identical productivity and unit cost levels, there will be equilibria in which N firms share the market equally. The equilibrium price-cost ratio will be determined by the investment equation (7), when Ki(t+1) = Kit , Ait = A, and Qit/Q = 1/N for all firms.

The picture is more complex if the firms have different productiv­ity levels Ait and hence different unit cost levels. If N different firms have N different cost levels but the differences are small, there can be equilibria in which all N firms survive but in which output shares are ranked inversely with unit cost levels. At the other extreme, suppose there are N1 firms at the lowest-cost level. Consider this lowest unit cost  marked  up  by  the  equilibrium  margin  determined  in  the manner just described, with Qit/Q = 1/N1. If this value is below the next- to-Iowest unit cost, then the “natural selection” process will operate unimpeded by the output restraint of the lowest-cost firms: they will drive the others entirely out of th e market and will wind up sharing the market among themselves. This result will necessarily occur if Nt is sufficiently large, since the equilibrium price-cost ratio tends to one as Qi/Q tends to zero.

Now suppose that rin is zero but that all firms display the same positive rim. The effects of the selection mechanism will be supple­ mented by imitative search. Ultimately, all surviving firms will dis­ play the same unit cost levee which will be the lowest of those dis­ played in the initial conditions (assuming that no mistakes are made in technique comparisons). The number of surviving firms (and hence the equilibrium margin) will depend on the exit specifica­ tions. If declining firms exit in finite time, the randomness of the imitation process may be reflected in a range of equilibrium results. If we now admit positive values of Yin, the link to latent productiv­ ity co mes into play and things become a great deal more compli­ cated. Much depends, obviously, on the relation between initial firm productivity levels and latent productivity and on the time path of la­ tent productivity. Radically different patterns of “historical” devel­ opment of the industry are implied by the different assumptions, and we contend that these differences are worthy of analysis and suggestive of possible interpretations of real events. For present pur­ poses, however, the temptations of steady- state analysis are irresist­ ible. Let us discuss what happens when latent productivity is advancing at a constant exponential rate.

Consider, specifically, the simplified model that arises if the in­ vestment mechanism (as well as entry and exit) is suppressed and firms remain the same size forever. This makes productivity behav­ ior independent of price and profitability . Each firm will have char­ acteristic (positive) levels of R&D expenditure, constant over time. Asymptotically, the average rate of productivity increase in each individual firm will equal the rate of increase of latent productivity. In other words, each firm’s productivity level will fluctuate around a particular long-run average ratio to latent productivity. Of course, the larger the firm’s R&D expenditures, the higher that ratio will be. But any maintained rate of expenditure- no matter how small-will yield, asymptotically, the same growth rate. This is because the ex­ pected productivity gain from an innovation or imitation draw keeps increasing as the firm falls further behind latent productivi ty, or fur­ ther behind other firms, and ultimately is sufficiently large to com­ pensate for the long average interval between draws.

If we abandon the simplifying assumption that individual firms stay the same size, the phenomena that appear include not only those of differenti al firm growth-which are central to our evolu­ tionary analysis-but also certain gross responses to demand by the industry as a whole. Assuming that demand is constant over time, a demand function of constant unitary elasticity has special signifi­ cance: a given percentage increase in productivity produces the same percentage decrease in unit cost and price, leaving the industry capi­ tal stock in the same state of equilibrium or disequilibrium it was be­ fore. That is, with unitary el asticity of demand, the advance of pro­ ductivity does not in itself produce a trend in industry capital. By contrast, if demand elasticity is constant and greater than tini ty, pro­ ductivity advance raises the price-cost ratio (at a given capital stock) and thus leads to an increased capital stock. Since information­ seeking efforts are proportioned to capital, this mechanism tends over time to produce an increase in the ratio of realized to latent pro­ ductivity. The corresponding implications of inelastic demand, or demand growth or decline, are obvious.

Source: Nelson Richard R., Winter Sidney G. (1985), An Evolutionary Theory of Economic Change, Belknap Press: An Imprint of Harvard University Press.

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