As indicated in Figure 1, massive migration from agricultural to industrial areas terminates in the early 1970s in Japan. This termination of migration coincides with the end of that country’s rapid economic growth. Unemployment rates also increase after the termination of migration. The first aim of this paper is to provide a simple framework that is consistent with these phenomena.

The framework that we present is a modified Harrod-Domar model. Although this model might be regarded as an elementary framework in old textbooks, this paper demonstrates that it still gives insights into dynamic economies. In his seminal paper, Harrod [1] argues that the warranted growth rate does not coincide with the natural rate of growth¹. Even though the warranted rate exceeds the natural rate, an industrial economy can grow at the warranted rate so long as large numbers of migrants flow into the industrial areas. However, once this migration terminates, a discrepancy between the warranted rate and the natural rate inevitably emerges as an actual

disparity requiring resolution². The current paper suggests that in these circumstances, a fall in the employment rate may play a central role in adjusting the warranted rate of growth.

Using a model with fixed coefficients, Kaldor [2] proposes an adjustment mechanism through income distribution. He argues that the rate of savings is higher out of profits than out of wages; as a result, the average saving rate positively relates to the profit share in income. If the profit share moves adequately, the warranted rate becomes equal to the natural rate through a change in the average savings rate. The adjustment mechanism proposed by the current paper is similar to Kaldor’s to the extent that the savings rate is variable. However, profit share is constant in our model. We emphasize that the consumption of individual households is not proportional to their income. Accordingly, the average savings rate of the whole economy decreases with a fall in income per household, which depends on the employment rate. Thus, a fall in employment rate can reduce the savings rate, and thereby adjust the warranted rate to the natural rate.

The second aim of the paper is to investigate the multiplier effect of government spending in the circumstance of underemployment. Ono [3] provides a clear explanation of the balanced budget multiplier, which is unity in the short run. Our comparative statics show that the balanced budget multiplier exceeds unity, and accordingly, government spending enhances households’ disposable income and consumption.

Let us consider a simple model consisting of two economies: an agricultural economy and an industrial economy. Suppose that each economy is self-sufficient and has no connection to the other except with regard to possible migration. Our focus is upon economic growth in the industrial economy where a market economy prevails. For the agricultural economy, we assume that local communities guarantee individual households a living standard that slightly exceeds the subsistence level. When jobs are available in the industrial economy and the wage rates are more satisfactory than the earnings in the agricultural economy, migration occurs from the agricultural to the industrial economy. We also assume that one household has successors in both economies; consequently, the total population grows at the gross rate of.

Now, consider the first stage of industrial development, when an abundant supply of labor is available through migration from the agricultural economy. We assume that

Wage rate given by (2) is higher than reservation wage that is based on earnings in the agriculture

economy. Then, equilibrium employment rate would be determined by the well-known Har-

ris-Todaro mechanism⁷:

Taking (1), (3), and (5) into account, aggregate consumption is given by

Note that the aggregate consumption is proportional to aggregate income, while the individual consumption

given by (1) involves a positive constant.

Now, let us investigate the warranted rate of growth. The goods market equilibrium is given by. Then, using (6), we have

where denotes the saving rate:. Then, from (7) and, we obtain the

warranted growth rate:

Following Harrod, let us assume that this warranted rate is higher than the natural rate of growth. Since we ignore technical progress, it implies that, i.e.,

Even if this inequality holds, the industrial economy can grow at the rate of as long as the inflow of migrants continues.

Since, the industrial economy growing at the rate of will completely absorb agricultural labor sooner or later. After the agricultural economy disappears, the industrial economy can grow at the rate of in the long run. Now, let us examine how the warranted growth rate can be adjusted to natural rate.

Let denote the employment rate in the second steady state without migration. Aggregate consumption can be indicated by

Accordingly, the equilibrium output becomes

where. Then, from (11) and, the warranted rate of growth is

. However, the growth rate in the steady state is bound to be, and therefore it must hold that

. This means that has to be

Comparing (5) and (12) under condition (9), we obtain the following proposition.

Proposition 1: The employment rate in the second steady state is lower than the employment rate in the first steady state:.

This examination reveals that the warranted growth rate can be adjusted toward the natural growth rate by a

decrease in the employment rate. A fall in output raises consumption rate, and

thereby reduces the saving rate. Further, the fall in decreases employment. Hence, a particular employment rate exists under which. Note that there is a paradoxical aspect: the higher the growth rate of

population, the higher the employment rate:.

Now we investigate how government spending affects macroeconomic performance. Let denote per capita government spending. Aggregate spending is given by, and the goods market equilibrium is indicated by. We examine a simple balanced budget policy, i.e. the government levies a lump-sum tax on each household. Then, instead of (10), aggregate consumption is

Taking (13) into account, we can derive the following employment rate in the second steady state:

which means that government spending raises the employment rate through its demand-expansion effect.

Per capita output is given by

Note that: the balanced budget multiplier exceeds unity. This is because

government spending enhances investment as well as consumption in the steady state. Defining per capita dis-

posable income as, we have. Thus, the following proposition is obtained.

Proposition 2: The balanced budget multiplier is greater than unity. Accordingly, government spending increases households’ disposable income and consumption.

By taking into account individual consumption that is not proportional to income, the current paper examines two steady states: one is characterized by a high employment rate accompanied by rapid economic growth with migration; the other is characterized by a lower employment rate accompanied by slower economic growth without migration⁸. Since insufficient demand for goods restricts the economy in the second steady state, it might not be surprising that Keynesian fiscal policy improves the situation. However, it would be worth noting that the balanced budget multiplier exceeds unity in the second steady state.

I wish to thank Makoto Mori, Hideki Nakamura, and Friday Seminar participants at Osaka City University for their valuable comments on an early version of this paper. I would like to thank an anonymous referee for his/her useful suggestions.