Marginal productivity

Japanese: 限界生産力 - げんかいせいさんりょく(英語表記)marginal productivity
Marginal productivity

The increase in output obtained by increasing the input of a particular production factor by one unit from a certain level when the input of other production factors remains constant. Generally, marginal productivity tends to decrease as the input of production factors increases, which is called the law of diminishing marginal productivity.

Now, if the production volume is Y and the labor input is L , the production function is Y = f ( L )
As shown in (1) of the figure , when labor input increases from L0 to L1 , production increases from Y0 to Y1 .

Δ L = L 1 - L 0 , Δ Y = Y 1 - Y 0
In this case, because production volume increases by Δ Y for each Δ L unit increase in labor input, the marginal productivity of labor at this time is expressed as Δ Y / Δ L. If the increase in labor input becomes infinitesimally small, the slope of the production function will ultimately indicate the marginal productivity of labor. For a production function like Figure (1), as labor input increases, the slope of the production function gradually becomes more gentle. This is the law of diminishing marginal productivity of labor.

Next, let us consider how a firm decides on its labor input when the money wage rate w and the product price p are given. The firm's revenue is pY = pf ( L ), and its labor cost is wL . In Figure (2), profit (= pY - wL ) is shown as the vertical distance between the revenue curve pY and the labor cost line wL . The firm selects the labor input that maximizes this profit. As is intuitively clear, this is the labor input where the slope of the revenue curve is equal to the slope of the labor cost line. In other words, at this time, the marginal productivity of labor (the product of the marginal productivity of labor and the product price) is equal to the money wage rate. This can also be interpreted as the equality of the real wage rate ( w / p ) and the marginal productivity of labor. If the marginal productivity of labor is greater (smaller) than the money wage rate, profits can be increased by adding (reducing) labor employment.

This concept of marginal productivity plays an important role in production theory and distribution theory.

[Toshiyuki Uchijima]

[Reference] | Marginal productivity theory | Production function
Marginal productivity diagram (figure)
©Shogakukan ">

Marginal productivity diagram (figure)


Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

Japanese:

他の生産要素の投入量が不変であるときに、特定の生産要素の投入量をある水準から1単位増やすことにより得られる生産物の増加分のこと。一般に限界生産力は、生産要素投入量の増加とともに減少する傾向がみられ、これを限界生産力逓減(ていげん)の法則という。

 いま生産量をY、労働投入量をLとすると、生産関数は
  Yf(L)
と表される。の(1)に示されているように、労働投入量がL0からL1へと増加すると、生産量はY0からY1へと増える。

  ΔLL1L0ΔYY1Y0
とすると、労働投入ΔL単位の増加に対し、生産量はΔYだけ増えたのであるから、このときの労働の限界生産力は、ΔY/ΔLで示される。労働投入の増え分を無限に小さくしていくと、結局生産関数の傾きが労働の限界生産力を示すことになる。の(1)のような生産関数では、労働投入量が増えていくと生産関数の傾きはしだいに緩やかになる。これが労働の限界生産力逓減の法則である。

 次に、貨幣賃金率w、生産物価格pが所与であるときの企業の労働投入決定の仕方を考えてみよう。企業の収入はpYpf(L)であり、労働費用はwLである。の(2)において、利潤(=pYwL)は収入曲線pYと労働費用直線wLとの垂直距離として示される。企業はこの利潤が最大となる労働投入量を選択する。それは直観的に明らかなように、収入曲線の傾きと労働費用直線の傾きとが等しくなる労働投入量である。つまりこのとき、労働の価値限界生産力(労働の限界生産力と生産物価格との積)は貨幣賃金率に等しい。これはまた、実質賃金率(w/p)と労働の限界生産力との均等と読み替えることができる。労働の価値限界生産力が貨幣賃金率よりも大きい(小さい)ならば、労働雇用を追加(削減)することにより、利潤を高めることができる。

 このような限界生産力概念は、生産理論、分配理論において重要な役割を果たしている。

[内島敏之]

[参照項目] | 限界生産力説 | 生産関数
限界生産力説明図〔図〕
©Shogakukan">

限界生産力説明図〔図〕


出典 小学館 日本大百科全書(ニッポニカ)日本大百科全書(ニッポニカ)について 情報 | 凡例

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