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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|Demand for Labor in the Short Run
本章认为，企业将在短期内实现利润最大化（ķ固定）通过雇佣劳动力直到劳动力的边际产量(米磷大号)等于实际工资（W/P）。这个决策规则的原因是实际工资代表增加的单位劳动的成本（就产出而言），而边际产量是增加的单位劳动增加的产出。只要企业通过增加劳动力（ķ固定），产出收益大于成本损失，它将继续雇用员工。当增加劳动力的边际成本超过时，公司将停止招聘米磷大号
要求米磷大号−在/磷为了使利润最大化意味着企业的短期劳动需求曲线（就实际工资而言）与其米磷大号时间表（参见 Eigure 3.1）。记住，米磷大号是在资本不变的情况下，雇佣劳动力增加一单位所产生的额外产出，考虑图 3A.2 所示的生产函数。保持资本不变ķ一个, 公司可以生产 100 单位问如果它雇用的劳动力等于大号一个. 如果劳动力增加到大号一个′, 公司可以多生产 50 单位问; 如果劳动力从大号一个′至大号′′′′，公司可以额外生产 50 台。但是请注意，要获得后 50 个单位的额外产出，需要增加劳动力，大号′′一个−大号一个′, 大于生产前 50 个单位增量所需的额外劳动力(大号一个′−大号一个). 这种差异只能意味着随着劳动力的增加，当ķ在保持不变的情况下，每个连续雇佣的工时都会产生越来越小的产出增量。换句话说，图 3 A.2 以图形方式说明了劳动的边际生产率递减。
为什么劳动力的边际生产率会下降？本章解释了劳动的边际生产率下降的原因是，ķ固定，每个增加的工人都有更少的资本（人均）来工作。这种解释是否在 Eigure 中得到证实3 一个.2? 遗憾的是，答案是否定的。数字3一个.2是在边际生产力递减的情况下绘制的。对等产量线重新编号可能会产生一组不同的边际生产率。（要看到这个，改变问=150至问=200, 并改变问=200至问=500. 劳动力的边际生产力随后会上升。）然而，劳动力的边际产品最终必须随着劳动力的增加而下降，同时保持建筑物、机器和工具不变的逻辑是令人信服的。此外，正如本章所指出的，即使米磷大号最初上升，公司将停止雇用劳动力，只有在米磷大号正在下降；只要米磷大号在上面在/磷并且不断上升，继续招聘将是值得的。
假设米磷大号最终下降，公司雇用直到米磷大号=在/磷是断言公司的短期劳动力需求曲线向下倾斜的基础。本附录中图形化的、更严格的需求曲线推导证实并支持了本章中的口头分析。然而，它也比口头分析更清楚地强调短期劳动力需求曲线向下倾斜的性质是基于一个假设——无论多么合理——米磷大号随着就业的增加而下降。
经济代写|劳动经济学代写Labor Economics代考|The Own-Wage Elasticity of Demand
对一类劳动力的自身工资需求弹性被定义为其就业的百分比变化(和)由于其工资率增加 1%(在) :
这一世一世=%D和一世%D在一世×X(4.1)
在等式（4.1）中，我们使用了下标一世表示劳动类别一世, 希腊字母这(eta) 表示弹性，符号 \%D表示“百分比变化”。由于前一章表明劳动力需求曲线向下倾斜，工资率上升会导致就业减少；因此，需求的自身工资弹性为负数。问题在于它的规模。它的绝对值越大（它的大小，忽略它的符号)，与任何给定的工资增长百分比相关的就业下降百分比越大。
劳动经济学家经常关注劳动力需求弹性的绝对值是大于还是小于 1 。如果大于 1，工资增加 1% 会导致就业下降大于 1%；这种情况称为弹性需求曲线。相反，如果绝对值小于 1，则称需求曲线是无弹性的：工资增加 1% 将导致就业下降幅度相应减小。如果需求是弹性的，那么当工资率增加时，该类别中个人的总收入（此处定义为工资率乘以就业水平）将下降，因为就业率下降的速度快于工资的上升速度。相反，如果需求缺乏弹性，当工资率增加时，总收入将增加。如果弹性刚好等于−1，需求曲线是单一弹性的，如果工资增加，总收入将保持不变。
图 4.1 显示了两条需求曲线中较为平坦的曲线(D1)比陡峭的弹性更大(D2). 从任何工资开始（在，例如），给定的工资变化（到在′′, 说) 将产生更大的就业需求曲线反应D1比与D2. 为了判断相同百分比的工资增长带来的不同反应弹性，比较(和1−和1′)/和1和(和2−和2′)/和2. 显然，更有弹性的响应发生在D1.
然而，将需求曲线说成具有“一种”弹性在技术上是不正确的。给定需求曲线通常具有弹性和非弹性范围，虽然我们通常只对任何市场当前工资率范围内的需求弹性感兴趣，但如果不理解弹性可以随给定需求变化，我们就无法完全理解弹性曲线。
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