# 经济代写|劳动经济学代写Labor Economics代考|ECON656

## 经济代写|劳动经济学代写Labor Economics代考|Demand for Labor in the Short Run

This chapter argues that firms will maximize profits in the short run ( $K$ fixed) by hiring labor until labor’s marginal product $\left(M P_L\right)$ is equal to the real wage (W/P ). The reason for this decision rule is that the real wage represents the cost of an added unit of labor (in terms of output), while the marginal product is the output added by the extra unit of labor. As long as the firm, by increasing labor ( $K$ fixed), gains more in output than it loses in costs, it will continue to hire employees. The firm will stop hiring when the marginal cost of added lahor exceeds $M P_L$

The requirement that $M P_L-W / P$ in order for profits to be maximized means that the firm’s labor demand curve in the short run (in terms of the real wage) is identical to its $M P_L$ schedule (refer to Eigure 3.1). Remembering that the $M P_L$ is the extra output produced by one-unit increases in the amount of labor employed, holding capital constant, consider the production function displayed in Figure 3A.2. Holding capital constant at $K_a$, the firm can produce 100 units of $Q$ if it employs labor equal to $L_a$. If labor is increased to $L_a^{\prime}$, the firm can produce 50 more units of $Q$; if labor is increased from $L_a^{\prime}$ to $L_{\prime \prime}^{\prime \prime}$, the firm can produce an additional 50 units. Notice, however, that the required increase in labor to get the latter 50 units of added output, $L^{\prime \prime}{ }_a-L_a^{\prime}$, is larger than the extra labor required to produce the first 50 -unit increment $\left(L_a^{\prime}-L_a\right)$. This difference can only mean that as labor is increased when $K$ is held constant, each successive labor hour hired generates progressively smaller increments in output. Put differrently, Figure 3 A.2 graphically illustratēs thẽ diminishing marginal productivity of labor.

Why does labor’s marginal productivity decline? This chapter explains that labor’s marginal productivity declines because, with $K$ fixed, each added worker has less capital (per capita) with which to work. Is this explanation proven in Eigure $3 \mathrm{~A} .2$ ? The answer is, regrettably, no. Figure $3 \mathrm{A.} 2$ is drawn assuming diminishing marginal productivity. Renumbering the isoquants could produce a different set of marginal productivities. (To see this, change $Q=150$ to $Q=200$, and change $Q=200$ to $Q=500$. Labor’s marginal productivity would then rise.) However, the logic that labor’s marginal product must eventually fall as labor is increased, holding buildings, machines, and tools constant, is compelling. Further, as this chapter points out, even if $M P_L$ rises initially, the firm will stop hiring labor only in the range where $M P_L$ is declining; as long as $M P_L$ is above $W / P$ and rising, it will pay to continue hiring.

The assumptions that $M P_L$ declines eventually and that firms hire until $M P_L=W / P$ are the bases for the assertion that a firm’s short-run demand curve for labor slopes downward. The graphical, more rigorous derivation of the demand curve in this appendix confirms and supports the verbal analysis in the chapter. However, it also emphasizes more clearly than a verbal analysis can that the downward-sloping nature of the short-run labor demand curve is based on an assumption-however reasonable-that $M P_L$ declines as employment is increased.

## 经济代写|劳动经济学代写Labor Economics代考|The Own-Wage Elasticity of Demand

The own-wage elasticity of demand for a category of labor is defined as the percentage change in its employment $(E)$ induced by a 1 percent increase in its wage rate $(W)$ :
$\eta \mathrm{ii}=\% \Delta \mathrm{Ei} \% \Delta \mathrm{Wi} \times \mathrm{x} \quad(4.1)$
In equation (4.1), we have used the subscript $i$ to denote category of labor $i$, the Greek letter $\eta$ (eta) to represent elasticity, and the notation \% $\Delta$ to represent “percentage change in.” Since the previous chapter showed that labor demand curves slope downward, an increase in the wage rate will cause employment to decrease; the own-wage elasticity of demand is therefore a negative number. What is at issue is its magnitude. The larger its absolute value (its magnitude, ignoring its $\operatorname{sign}$ ), the larger the percentage decline in employment associated with any given percentage increase in wages.

Labor economists often focus on whether the absolute value of the elasticity of demand for labor is greater than or less than 1 . If it is greater than 1 , a 1 percent increase in wages will lead to an employment decline of greater than 1 percent; this situation is referred to as an elastic demand curve. In contrast, if the absolute value is less than 1 , the demand curve is said to be inelastic: a 1 percent increase in wages will lead to a proportionately smaller decline in employment. If demand is elastic, aggregate earnings (defined here as the wage rate times the employment level) of individuals in the category will decline when the wage rate increases, because employment falls at a faster rate than wages rise. Conversely, if demand is inelastic, aggregate earnings will increase when the wage rate is increased. If the elasticity just equals $-1$, the demand curve is said to be unitary elastic, and aggregate earnings will remain unchanged if wages increase.

Figure 4.1 shows that the flatter of the two demand curves graphed $\left(D_1\right)$ has greater elasticity than the steeper $\left(D_2\right)$. Beginning with any wage ( $W$, for example), a given wage change (to $W^{\prime \prime}$, say) will yield greater responses in employment with demand curve $D_1$ than with $\mathrm{D}_2$. To judge the different elasticities of response brought about by the same percentage wage increase, compare $\left(E_1-E_1^{\prime}\right) / E_1$ with $\left(E_2-E_2^{\prime}\right) / E_2$. Clearly, the more elastic response occurs along $D_1$.

To speak of a demand curve as having “an” elasticity, however, is technically incorrect. Given demand curves will generally have elastic and inelastic ranges, and while we are usually interested only in the elasticity of demand in the range around the current wage rate in any market, we cannot fully understand elasticity without comprehending that it can vary along a given demand curve.

## 经济代写|劳动经济学代写Labor Economics代考|The Own-Wage Elasticity of Demand

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