This chapter is loosely grouped into four parts.

Part one is composed of Sections 8.1 through 8.5. Part two consists of a single long Section 8.6. Part three is made up of Sections 8.7 and 8.8, and part four is Section 8.9. The first part of this chapter collects a number of bare-bones models and topics that are loosely tied to the notion of growth, market shares, and fluctuations.

The bare-bones models in this part may be used, singly or in some com­binations, to construct more fully specified models of growth or fluctuation. For example, Aoki and Yoshikawa (2001) describe a model that uses some of the bare-bones models as components to show how demand saturation limits growth. A second example is described in Section 8.6. The third example is discussed in Chapter 9.

We begin this chapter by discussing two mini-models, called Poisson and urn models, for explaining how economies grow by inventing new goods or creating new industries. These models provide different explanations of growth from those in the literature on endogenous growth models.

The two models in Section 8.1 provide two explanations of economic growth that are different from standard ones based on technical progress, that is, total factor productivity models or endogenous growth models. The flavor of the difference may be captured by saying that in the endogenous growth models an economy grows by improving the quality of existing goods, whereas in our models it grows by introducing new goods.

Inthe first model, firms or sectors independently inventnew goods or improve on the existing ones. The numbers of new goods are then functions of the number of the firms, or the size of the economy. The growth rate of this model eventually converges to the rate at which new goods are being introduced to the economy. In the second model, the numbers of goods that are introduced are independent of the numbers of the existing goods, and the rate of introduction of new goods decreases as the number of goods grows.

increasing ratio of the total production of the economy. Their maturity does imply that economic effects of further improvements will necessarily be more limited than in the past.”

These two linear models are followed by another set of two related models. In the first one the exit rate of goods is nonlinear, to quantify the idea that older goods disappear from the markets more quickly than newer goods. In the second, demand saturates as time goes on.

We then turn to discuss a simple stochastic business-cycle model, after taking a quick look at a deterministic version suggested by Iwai (1984a, b, 1996). His model considers an economy composed of two sectors of firms with a fixed total number of firms. The rates of change of shares of the market change in response to gaps between demands and supplies of the two sectors. The share converges monotonically to one. This generates no business-cycle-like fluctuations of the total output.

A stochastic version of this model, which keeps the central idea that shares change in response to the gaps, is next discussed for comparison. A simplified two-sector version of this model has been described in Section 4.1. The model generalizes this to a K-sector model in which sectors respond to gaps between supplies and demands of individual sectors. It is an open business-cycle model. Unlike the deterministic ones, it generates fluctuations. The expected output of the economy responds to changing patterns of demand shares. It increases as more demands are shifted to more productive sectors of the economy.

We accomplish two things by this model. First, we illustrate a possibility that fluctuations of the aggregate economy arise as an outcome of interactions of many agents/sectors in a simple model. Second, we demonstrate that the level of the aggregate economic activity depends on the structure of demand.

There are two ways for demand to affect the aggregate level of economic activities. One is externality associated with demand, which might produce multiple equilibria as in Diamond (1982). We return to his model in Chapter 9. The other is differences in productivity across sectors/activities. Recent works by Murphy et al. (1989) and Matsuyama (1995), for example, emphasize the importance of increasing returns in order to demonstrate the role of demand in determining the level of the aggregate production. They, in effect, allow differences in productivity across sectors to draw their conclusions. In this chapter, we keep Iwai's idea and assume that productivities differ across sectors in the economy. Here, we just show how the output of the economy is maximized for a suitable choice of the demand shares by assuming that the productivity coefficients of the two sectors are not equal.

8.1