Eficiência Marginal do Capital

up:: 061e1 MOC Keynes

“The relation between the prospective yield of a capital asset and its supply price or replacement cost, i.e. the relation between the prospective yield of one more unit of that type of capital and the cost of producing that unit, furnishes us with the marginal efficiency of capital of that type. More precisely, I define the marginal efficiency of capital as being equal to that rate of discount which would make the present value of the series of annuities given by the returns expected from the capital-asset during its life just equal to its supply price.” (Keynes, 2013, p. 135; grifo meu)

Ou seja, dados os retornos (e.g.) anuais $\{Q_i{\}}_{i=1}^N$ de algum capital, temos que a eficiência marginal deste capital é a taxa de desconto que faz com que

$$P=\sum _{k=1}^N\frac{Q_k}{(1+EMgK{)}^k}$$

onde $P$ é o preço de substituição deste ativo — no tempo em consideração, pois se está trabalhando em valores de tempo presente.

$EMgK$ depende do rendimento total do capital

Destaque-se que a eficiência marginal do capital não depende somente de um rendimento $Q_i$, e sim de todos os rendimentos ao longo do “ciclo de vida” deste capital.

“The most important confusion concerning the meaning and significance of the marginal efficiency of capital has ensued on the failure to see that it depends on the prospective yield of capital, and not merely on its current yield. This can be best illustrated by pointing out the effect on the marginal efficiency of capital of an expectation of changes in the prospective cost of production, whether these changes are expected to come from changes in labour cost, i.e. in the wage-unit, or from inventions and new technique. The output from equipment produced to-day will have to compete, in the course of its life, with the output from equipment produced subsequently, perhaps at a lower labour cost, perhaps by an improved technique, which is content with a lower price for its output and will be increased in quantity until the price of its output has fallen to the lower figure with which it is content. Moreover, the entrepreneur’s profit (in terms of money) from equipment, old or new, will be reduced, if all output comes to be produced more cheaply.” (Keynes, 2013, p. 141; grifo meu)

Influências em $EMgK$

Note-se que o aumento no Investimento em certo capital vai

1. abaixar seus rendimentos (devido à concorrência)
2. aumentar seu preço de substituição

Ambos estes fatores farão com que $EMgK$ caia, embora o segundo seja mais propício ao curto prazo. Portanto, temos que $\Delta I⟹\Delta EMgK$. Note que $EMgK$ é uma função decrescente em $I$.

Pode-se analisar a equação da seguinte forma: tratam-se de preço de oferta do capital, $P$, e do preço de demanda dele, em que há descontos a valor presente de seus rendimentos. Note-se que o empresário continuará a comprar este bem enquanto $EMgK<r$, onde $r$ é a Taxa de Juros de mercado, da mesma forma que consumidores continuarão a comprar algo que esteja por um preço abaixo do esperado (pela demanda), até que os preços se normalizem.

Distinções entre $EMgK$ e taxa de juros

Porém, a eficiência marginal do capital e a taxa de juros formam-se autonomamente, são processos que se influenciam mas que não são idênticos uns aos outros!

“I would, however, ask the reader to note at once that neither the knowledge of an asset’s prospective yield nor the knowledge of the marginal efficiency of the asset enables us to deduce either the rate of interest or the present value of the asset. We must ascertain the rate of interest from some other source, and only then can we value the asset by ‘capitalising’ its prospective yield” (Keynes, 2013, p. 159; grifo meu)

“If the rate of interest were to rise pari passu with the marginal efficiency of capital, there would be no stimulating effect from the expectation of rising prices. For the stimulus to output depends on the marginal efficiency of a given stock of capital rising relatively to the rate of interest.” (Keynes, 2013, p. 143)

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References

• KEYNES, John Maynard. The collected writings of John Maynard Keynes: The General Theory of Employment, Interest and Money. Cambridge: Cambridge University Press for the Royal Economic Society, 2013. v. 7.