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Employment theory does lacks a consensus concerning whether employment variation should be expressed as a change in the hours worked as a representative individual or as a change in the population of employed individuals. By appling the OLG model developed by Lucas [1] and Otaki ([2-4]), the present article describes a serious theoretical conesquence of distinction. The crucial factor that different employment theories are the intertemporal substitution effect and the indivisibility of labor force. Monetary expansion increases the rate of return for money if it is credible in the sense of Otaki [5]. This enhances the hours worked in the representative individual model, and thus, aggregate supply causes demand. Conversely, in the indivisible employees model, such an intertemporal substitution effect does not exist. The monetary expansion directly improves the purchasing power of money and thereby increases the aggregate demand for goods by the older generation. Thus, demand derives supply.

Independent of whether researchers adopt neoclassical or new Keynesian economic models, recent employment theories have rested on the assumption of a representative individual. However, it is important to note that the hours worked by a representative individual differs crucially from indivisible employees who each work equal amount of time. In this paper, we show that such a distinction has serious theoretical consequences.

The crucial factor is the existence of the intertemporal substitution effect. In the representative model, an expansion of money raises the rate of return as long as money is credible and stimulates the labor supply. Hence, apart from the spurious difference, both neoclassical and new Keynesian models seek the cause of employment variation for the supply-side incentive.

In contrast, there is no such substitution effect in the indivisible employees model^{1}. A monetary expansion directly increases the purchasing power of money as Otaki [

The rest of the paper is organized as follows. Section 2 constructs alternative models concerning the employment theory. Section 3 contains brief concluding remarks.

We consider a standard two-period deterministic OLG model in a production economy. In every period, a unit of individual is born. They can work only when they are young. A unit working hour produces unit goods.

The money supply obeys Lucas’s [

where is the nominal money stock per capita that is carried over from the previous period. is the gross increase rate of money. In this sense, new money is supplied as its own nominal interest rate.

We make the following alternative assumptions concerning the labor supply: 1) In the representative individual model, the representative individual can chooses his working hours and there is no unemployment problem; 2) In the indivisible employees model, each individual faces the discrete choice of whether to work.

For simplicity, we assume that the representative individual possesses the following utility function:

where is a well-behaved linear homogenous function. denote the consumption level sof generation during the young and old stages of life, respectively. is the hours worked.

has the following properties.

The shape of is illustrated in

The assumption that some lower limit exists for the disutility of labor is equivalent to the assumption that individuals do not incur any additional disutility by increasing in hours worked to some extent. As the classical economists presume. Its economic meaning of this assumption is that there is an urgent need to produce goods that correspond to the subsistent level, as shown below.

The lifetime budget constraint is

Since the lifetime utility function concerning the consumption stream is concave and homothetic, we obtain the following correspond indirect utility function:

Moreover, we can ascertain that

holds. This expression implies that, as long as is sufficiently small, the equilibrium hours worked always exceeds the subsistent lower limit, and that the problem of the indivisibility of hours worked never appears in the decision problem.

The optimality conditions are

We assume, according to Lucas [

In addition to the three optimality conditions, there is one independent market equilibrium condition. Here, we consider the condition for the money market equilibrium: that is,

Furthermore, we assume the credibility of money in the sense of Otaki [^{2}:

There are five endogenous variables, and five independent Equations (5)-(9). Hence, the model is closed, and the solution consists of a temporary rational expectation equilibrium.

From Equations (8) and (9), it is clear that increases with the nominal interest rate of money Equations (5) and (6) imply that is a monotonically decreasing function of the effective inflation rate (the inverse of the real interest rate). Thus, decreases as increases. It is also apparent from Equation (5) that equilibrium working hours increases with x^{3}.

To summarize, as long as money is credible, an easy monetary policy increases the real interest, and hence, the representative individual works more to enjoy more future consumption. Accordingly, a monetary expansion advances intertemporal substitution from current consumption and leisure into future consumption by raising the real rate of interest. As such, the expansionary effect of monetary policy is entirely based on the labor supply incentive, not on the expansion of the aggregate demand. In this sense, the representative individual model is inevitably classified as a neoclassical macroeconomic model.

Assume that the representative individual rationally expects that the real effective inflation rate is kept intact after period, since no economic environment is changed after period ^{4}. This assumption implies that

In addition

and

holds from the money market equilibrium condition (8). Thus, we obtain

That is, future consumption becomes time-independent. Hence, from Equations (5)-(7), are also time-independent. Consequently, the rational expectation equilibrium characterized by the initial condition and the expectation formulation (9) and (10) are stationary.

Here, we assume that labor supply is indivisible, and that each individual has the identical utility function:

where is the same consumption utility function as in Equation (1). denotes a definition function that takes the value unity when the individual works unit time and that is zero when the individual does not work.

According to Equation (1), the nominal minimal revenue that individuals decide to work is represented as

We must note that firms strictly prefer increasing employment to the upward adjustment in working hours per capita in any interior equilibrium in which unemployment exists and all individuals are indifferent to the decision of whether to work.

The reason is as follows. Even if a unit employment increases, as long as the working hours per capita are fixed, there is no appreciation of nominal wages. However, the concavity of requires nominal wages higher than to induce working hours that produce the same amount of output as in the case of employment adjustment. Thus, as long as unemployment exists, working hours per capita is fixed to the minimal level.

Accordingly, we obtain the following difference equation concerning the evolution of price sequence^{5}:

Hence, the equilibrium real interest rate

is independent of and takes a constant value.

The equilibrium condition for the money market is

where is the marginal propensity to save.

Assuming the credibility of money (i.e.,)an increase in the monetary growth rate increases the current value of money and empowers the purchasing power of old individuals as long as money is a credible asset. As such, the monetary expansion stimulates the economy through the multiplier effect developed by Otaki [

It is not difficult to show the time-independence of the equilibrium. Assume that people rationally believe that the price level grows proportionately with the monetary expansion rate, that is,

Then, the equilibrium real cash balance becomes time-independent, so does the real equilibrium GDP ^{6}.

In addition, as we previously mentioned, the individual employees model is similar to a Keynes’ [

This article analyzed how the aggregation problem affects the theory of employment. We obtained the following results.

First, because of the intertemporal substitution between goods and leisure, a change in working hours in the representative individual model is supply-side oriented even if money is credible and non-neutral. Furthermore, since it does not contain the concept of indivisibility of labor, this model cannot explain why unemployment occurs although it can spuriously trace the total output movement. An accelaration in monetary growth increases the real interest of money, and thus, intertermporal substitution occurs from leisure and current consumption to future consumption.

Second, the indivisible individual employees model possesses the demand-driven property deepened by Keynes [

In summation, Keynes’ [