Labor demand

In economics, the labor demand of an employer is the number of labor-hours that the employer is willing to hire based on the various exogenous (externally determined) variables it is faced with, such as the wage rate, the unit cost of capital, the market-determined selling price of its output, etc. The function specifying the quantity of labor that would be demanded at any of various possible values of these exogenous variables is called the labor demand function.^[1] The sum of the labor-hours demanded by all employers in total is the market demand for labor.

Perfect competitor

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The long-run labor demand function of a competitive firm is determined by the following profit maximization problem:

${\displaystyle {\text{Maximize}}\,\,pQ-wL-rK\,\,{\text{with respect to}}\,\,Q,\,L,\,{\text{and}}\,K}$

${\displaystyle {\text{subject to}}}$

${\displaystyle Q=f\,(L,K),}$

where p is the exogenous selling price of the produced output, Q is the chosen quantity of output to be produced per month, w is the hourly wage rate paid to a worker, L is the number of labor hours hired (the quantity of labor demanded) per month, r is the cost of using a machine (capital) for an hour (the "rental rate"), K is the number of hours of machinery used (the quantity of capital demanded) per month, and f is the production function specifying the amount of output that can be produced using any of various combinations of quantities of labor and capital. This optimization problem involves simultaneously choosing the levels of labor, capital, and output. The resulting labor demand, capital demand, and output supply functions are of the general form

${\displaystyle L(p,w,r),}$

${\displaystyle K(p,w,r),}$

and

${\displaystyle Q(p,w,r).}$

Ordinarily labor demand will be an increasing function of the product's selling price p (since a higher p makes it worthwhile to produce more output and to hire additional units of input in order to do so), and a decreasing function of w (since more expensive labor makes it worthwhile to hire less labor and produce less output). The rental rate of capital, r, has two conflicting effects: more expensive capital induces the firm to substitute away from physical capital usage and into more labor usage, contingent on any particular level of output; but the higher capital cost also induces the firm to produce less output, requiring less usage of both inputs. Depending on which effect predominates, labor demand could be either increasing or decreasing in r.

The short-run labor demand function is the result of the same optimization except that capital usage K is exogenously given by past physical investment rather than being a choice variable.

Monopolist

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If the firm is a monopolist, its long-run optimization problem is different because it cannot take its selling price as given: the more it produces, the lower will be the price it can obtain for each unit of output, according to the market demand curve for the product. So its profit-maximization problem is

${\displaystyle {\text{Maximize}}\,\,pQ(p)-wL-rK\,\,{\text{with respect to}}\,L,\,K,\,{\text{and}}\,p}$

${\displaystyle {\text{subject to}}}$

${\displaystyle Q(p)=f\,(L,K),}$

where Q(p) is the market demand function for the product. The constraint equates the amount that can be sold to the amount produced. Here labor demand, capital demand, and the selling price are the choice variables, giving rise to the input demand functions

$L(w,r),}$

${\displaystyle K(w,r),}$

그리고 가격 결정 기능

$(\displaystyle p(w,r)).}$

공급함수는 외생가격의 존재를 미리 공급하기 때문에 독점자에 대한 출력공급기능이 없다.

단기 노동 수요 함수는 물리적 자본 K가 외생적이라는 점을 제외하면 동일한 방식으로 도출된다.

노동시장의 단협주의자들

이 절은 출처를 인용하지 않는다. 신뢰할 수 있는 출처에 인용문을 추가하여 이 섹션을 개선할 수 있도록 도와주십시오. 공급되지 않은 재료는 도전하여 제거할 수 있다. (2020년 4월) (이 템플릿 메시지를 제거하는 방법과 시기 학습)

만약 그 회사가 상품 시장에서 완벽한 경쟁자지만 노동 시장에서 단일주의자라면, 즉 노동 시장의 유일한 구매자여서 그것이 요구하는 양이 임금율에 영향을 미친다는 것을 의미한다면, 그것의 장기적인 최적화 문제는 다음과 같다.

${\displaystyle {\textimize}\,\,pQ-wL(w)-rK\,\,{\text{w},{\text{and}}\,K}$

${\displaystyle {\text{data}}$

${\displaystyle Q=f\,(L(w),K),}$

여기서 L(w)은 회사와 마주보고 있는 노동자의 시장 노동력 공급 기능이다. 여기서 기업은 임금률과 독립적으로 요구할 노동량을 선택할 수 없다. 왜냐하면 노동공급기능은 고용할 수 있는 노동의 양을 임금률과 연계하기 때문이다. 따라서 노동수요기능이 없기 때문이다.

물리적 자본 K가 선택 변수가 되기보다는 외생적이라는 점을 제외하면 단기 최적화는 동일하다.

참고 항목

• 인자시장
• 조건부 요인 요구
• 신고전주의 미시경제 모델
• 임금 노예제
• 인원선택

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