20250710 Anotações sobre Keynes

up:: 061e1 MOC Keynes

Cap. 6: The definition of Income, Saving and Investment

During any period of time an entrepreneur will have sold finished output to consumers or to other entrepreneurs for a certain sum which we will designate as $A$.” (KEYNES, 2013, p. 52; grifo meu)

“He will also have spent a certain sum, designated by $A_1$, on purchasing finished output from other entrepreneurs.” (Ibid.; grifo meu)

“And he will end up with a capital equipment, which term includes both his stocks of unfinished goods or working capital and his stocks of finished goods, having a value $G$.” (Ibid.; grifo meu)

Portanto, o “empreendedor” terá a quantidade

$$(A-A_1)+G$$

ao final do processo de produção: $A$ do que produziu, $A_1$ do que precisou comprar para sua produção (Meios de Produção), e $G$ do que restou em estoque (Acumulação de Estoques), tanto do que ainda não foi utilizado para produzir, quanto o que foi produzido mas ainda não vendido.

“Here “$G$” is essentially what he could sell his capital, fixed and working, for at the end of the period” (FERGUSON, 2013, p. 2)

Parte dessa quantidade foi “herdada” do período anterior, de capital que ainda estava operante previamente e também neste período.

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“The actual value $G$ of the capital equipment at the end of the period is the net result of the entrepreneur, on the one hand, having maintained and improved it during the period, both by purchases from other entrepreneurs [i.e. $A_1$] and by work done upon it by himself, and, on the other hand, having exhausted or depreciated it through using it to produce output.” (Id., p. 52-3; grifo meu)

Da quantidade $G$ do estoque de capital herdado ao começo do período da produção, pode-se discernir

• $B^{\prime }$ com gastos em “maintenance and improvement” (Ibid.)
• $G^{\prime }$ sendo o valor que restaria (de onde vem!?)

Ou seja, $G^{\prime }-B^{\prime }$ é o valor máximo que poderia ser conservado no período seguinte, se não tivesse sido usado para produzir $A$ (Ibid.).

O problema de $G$ é de que ele mistura estoques prévios com estoques recém-produzidos. Note-se que ele produziu

$$(A-A_1)+G=A+(G-A_1)$$

O excesso que se obtém em $G^{\prime }-B^{\prime }$ quando comparado a $G-A_1$ é definido como o User Cost of Production $U$:

$$U:=(G^{\prime }-B^{\prime })-(G-A_1)$$

Os custos de Fatores de Produção $F$ são “The amount paid out by the entrepreneur to the other factors of production in return for their services” (Ibid.; grifo meu).

Reescrevendo-o, temos

$$U=A_1-\underset{=:I}{\underbrace{(G-(G^{\prime }-B^{\prime }))}}$$

Podemos descrever o investimento do empreendedor como $A_1-U$, que é igual a $G-(G^{\prime }-B^{\prime })$,

”$G-(G^{\prime }-B^{\prime })$, namely the increment in the value of the entrepreneur’s equipment beyond the net value which he has inherited from the previous period, represents the entrepreneur’s current investment in his equipment and can be written $I$. Thus $U$, the user cost of his sales-turnover $A$, is equal to $A_1-I$ where $A_1$ is what he has bought from other entrepreneurs and $I$ is what he has currently invested in his own equipment.” (Keynes, 2013, p. 66; grifo meu)

Diz-se que o prime cost da produção é $U+F$.

A renda [income] é então definida como

$$Y:=A-(U+F)$$

“…the excess of the value of his finished output sold during the period over his prime cost” (Ibid.)

Como a renda dos demais fatores de produção é igual ao $F$ por ele pago, a renda agregada é simplesmente $A-U(=Y+F)$.

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Definição de Consumo Agregado: $C:=\sum (A-A_1)$

Definição de Investimento Agregado: $I:=\sum (A_1-U)$

Neste sentido, a renda agregada é meramente igual a $Y=C+I$.

O investimento individual do empreendedor é $-U$:

“Moreover, $U$ is the individual entrepreneur’s disinvestment (and $-U$ his investment) in respect of his own equipment exclusive of what he buys from other entrepreneurs.” (Id., p. 54-5)

Há, portanto, relação entre Renda Agregada esperada com a Demanda Efetiva:

“Furthermore, the effective demand is simply the aggregate income (or proceeds) which the entrepreneurs expect to receive, inclusive of the incomes which they will hand on to the other factors of production, from the amount of current employment which they decide to give. The aggregate demand function relates various hypothetical quantities of employment to the proceeds which their outputs are expected to yield; and the effective demand is the point on the aggregate demand function which becomes effective because, taken in conjunction with the conditions of supply, it corresponds to the level of employment which maximises the entrepreneur’s expectation of profit.” (Ibid., p. 55; negrito meu)

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Supplementary costs:

Windfall costs:

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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.
• KEYNES, J.M. A Teoria Geral do Emprego, do Juro e da Moeda. São Paulo: Nova Cultural, 1996.
• FERGUSON, Brian S. Lectures on John Maynard Keynes’ General Theory of Employment, Interest and Money (5): Chapter 6, The Definition of Income, Saving and Investment; Appendix to Chapter 6, Appendix on User Cost; Chapter 7, The Meaning of Saving and Investment Further Considered. University of Guelph Department of Economics and Finance Working Paper, n. 2013-10, 2013. Disponível em: https://papers.ssrn.com/sol3/Delivery.cfm?abstractid=2313441.