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The mathematics of profit maximization is incorrect Philip George [India] Copyright: Philip George, 2022
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Abstract Profit maximization is one of the two main optimising principles of neoclassical economics, the other being utility maximization. In this paper we draw on Chapter 6 of J h Ma a d Ke e General Theory to show that the mathematics of profit maximization is incorrect. We show, moreover, that marginal cost, a variable fundamental to neoclassical economics, cannot be calculated. We explore the implications for sticky prices, increasing returns, the shape of the supply curve, and market clearing. Finally, we argue that an important reason for the failure of neoclassical economics is that while it pays a great deal of attention to the influence of future expectations on present decisions, it completely ignores the past.
1. Introduction Most critiques of profit maximization are empirical, arguing that firms in the real world seek to maximize, not profits, but revenue, market share or some other metric. Other critiques, e.g., by Kenneth Arrow (Arrow, 1979), have dwelt on the sociological and moral objections to the profit system. The mathematics itself is rarely challenged. The assumption is that firms can, if they wish to, abide by the mathematics of profit maximization. This paper shows that it is not possible to do so.
2. The Mathematics We e he a h f fi a i i a i a f d i Pa l Sa el Foundations of Economic Analysis (Samuelson, 1947). Current expositions do not vary from this in any significant manner. I take as a datum the maximum amount of gross total revenue which can be secured for each level of output. This may be written R = R( ) Let us define profit, net revenue, as the difference between gross revenue and total expenditure, = ( ,
1,
,
) = R( )
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