The Labor Market and Supply Function
Labor Supply by Households
Next, let us formulate labor supply by households. For simplicity, we have so far assumed that labor income is fixed and households do not choose their leisure and labor supply optimally. In the neoclassical model, households optimally allocate leisure and labor supply among the initial holdings of time (24 h per day and so on). In the labor market, the wage rate is determined so as to attain full employment. The neoclassical macroeconomic model does not consider involuntary unemployment at least in the long run.
The standard utility function is given as
where c is consumption and L is labor. Utility U increases with c and decreases with L. The budget constraint is given as
where w is wage rate. The right-hand side of Eq. (3.11) means labor income. The household optimally determines its labor supply to maximize its utility (3.10) subject to its budget constraint (3.11).
As shown in Fig. 3.4, the point E, where the budget line is tangent to an indifference curve, is optimum. At this point, the marginal benefit of raising labor supply, the slope of the budget line, is equal to the marginal cost, the slope of the indifference curve.
An increase in wage raises the relative attractiveness of labor supply compared with leisure, a situation that is the substitution effect. However, such an increase raises the demand for leisure and reduces labor supply since leisure is a normal good. This corresponds to the income effect. Thus, if the substitution effect is greater than the income effect, it stimulates labor supply. See Chap. 8 for further explanations of substitution and the income effects on labor supply.
Let us now investigate the effect of the interest rate on labor supply. It seems that this effect is rather marginal in the static model discussed above. However, if we consider an intertemporal framework, this effect could be important. Suppose the agent chooses consumption and labor in two periods, the present and a future period. An increase in the interest rate causes an intertemporal substitution effect that attracts future goods and leisure consumption compared with current goods and leisure consumption. As explained in Sect. 1, if the rate of interest increases, future consumption is stimulated because of the substitution effect. We may regard leisure as a component of consumption. Then, because of an increase in the interest rate, the intertemporal substitution effect means that current leisure consumption declines and current labor supply increases.
Fig. 3.4 Labor supply
Thus, if the substitution effect is large enough, an increase in r or w stimulates labor supply, Ls. We assume this. Then, households’ labor supply increases with the interest rate, r, and wage rate, w.
