Capital coefficient

Japanese: 資本係数 - しほんけいすう（英語表記）capital coefficient

It is the amount of capital divided by the amount of output, and is also called the capital-output ratio. This concept is used for individual companies or industries, but is more commonly used for the economy as a whole, where output is usually interpreted as national income (gross domestic product, etc.). Capital coefficients are divided into average capital coefficients and marginal capital coefficients, depending on whether absolute levels or increases are used in the numerator and denominator. They are also called actual capital coefficients and required capital coefficients, depending on whether the actual amount of capital and output are used, or the amount of capital (or increase) required to produce one unit of output (or one unit increase in output), respectively.

R. F. Harrod, a pioneer in the field of growth theory, used this concept of capital coefficient to attempt to demonstrate the instability of the capitalist economy.

If we take the actual capital coefficient to be C , then the actual growth rate G can be expressed as G = s / C , where s is the savings rate. On the other hand, if the required capital coefficient is C _r (constant) and the appropriate growth rate (the growth rate of income just enough to allow full utilization of capital) is G _w , then G _w = s / C _r . From these two equations, we can say the following. If the actual growth rate G is greater than the appropriate growth rate G _w , then the required capital coefficient C _r will be greater than the actual capital coefficient C , and a capital shortage will occur. If we assume that entrepreneurs will try to make up for this shortage by increasing their investment, then this increase in investment will further increase G , making the gap between G and G _w even larger. Conversely, if the actual growth rate is smaller than the appropriate growth rate, that is, if the actual capital coefficient is greater than the required capital coefficient, then G will shrink further and deviate from G _w . Therefore, the growth rate can only be a constant value when the actual capital coefficient happens to match the required capital coefficient. However, the probability of this happening is extremely small and is governed by chance. This is how Harrod discussed the instability of the economy, and the problem of this instability is called the "knife edge problem."

Harrod also used the concept of capital coefficient to classify technological progress. Harrod's neutral standard was determined by the technological progress that would keep the capital coefficient constant at a constant interest rate (profit rate), and technological progress that would increase the capital coefficient was called labor-saving technological progress, and that which would decrease it was called capital-saving technological progress.

[Yuichiro Otsuka]

"Business Cycles" by R.F. Harrod, translated by Yoshikazu Miyazaki and Eiichi Asano (1963, Toyo Keizai Shinposha)

[References] | Technological progress | National income | Harrod

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

Japanese:

資本額を産出額で除した大きさをいい、資本産出高比率ともよばれる。この概念は個々の企業または産業レベルに関しても用いられるが、比較的利用度の高いのは経済全体についてであって、この場合には産出高は通常、国民所得（国内総生産等）の意味に解される。資本係数は、分母・分子に絶対水準がとられるか増加分がとられるかに応じて、平均資本係数と限界資本係数とに区別される。また、現実の資本額・産出高がとられるか、産出高1単位（または産出高1単位の増加分）を生み出すのに必要な資本額（またはその増加分）がとられるかに応じて、それぞれ現実資本係数、必要資本係数とよばれる。

　成長理論の分野で先駆的な業績を残したR・F・ハロッドは、このような資本係数概念を用いることによって、資本主義経済の不安定性を論証しようとした。

　いま現実の資本係数をCとすれば、現実の成長率Gは、G＝s／Cと表すことができる。ただしsは貯蓄率である。他方、必要資本係数をC_r(一定)、適正成長率(資本の完全稼働をちょうど許すに足るほどの所得の成長率)をG_wとすれば、G_w＝s/C_rである。この二つの式から次のことがいえる。もしも現実の成長率Gが適正成長率G_wよりも大であるとすれば、必要資本係数C_rは現実資本係数Cよりも大きくなり、資本不足の状態がおこる。このとき企業家は投資を増大させてこの不足を補おうとするものだと考えるならば、その投資増加はさらにGを高め、G、G_w間の乖離(かいり)をますます大きなものにしてしまう。逆に現実の成長率が適正成長率よりも小さい、すなわち現実資本係数が必要資本係数よりも大であれば、Gはますます縮小し、G_wから乖離してしまう。したがって成長率が一定の値をとりうるのは、現実資本係数が必要資本係数にたまたま合致したときに限られる。しかしその可能性はきわめて小さく、偶然に支配される。こうしてハロッドは経済の不安定性を論じたのであるが、この不安定性の問題は「ナイフ・エッジ問題」とよばれている。