Academic journal article History of Economics Review

A Mathematical Approach to Malthus's Criticism of Adam Smith in 1798

Academic journal article History of Economics Review

A Mathematical Approach to Malthus's Criticism of Adam Smith in 1798

Article excerpt

Abstract: Against Smith, Malthus, in his First Essay on Population (1798), argued that every increase in national wealth does not always ameliorate the living standard of the working classes. If a nation increases investment in manufacture but not in agriculture, an increase in national wealth is not accompanied by an increase in 'the funds for the maintenance of labour', and thus physical wealth may increase, but happiness may decrease. In this paper, I formalise Malthus's criticism of Smith using a simple mathematical model so that Malthus's argument can be clearly understood.

1 Introduction

It is well known that John Maynard Keynes stated that Thomas Robert Malthus's first edition of Principle of Population (1798), referred to here as the First Essay, was 'a work of youthful genius' (Keynes 1933: 119). Through this work, Malthus stressed the importance of agriculture in an economy, rather than manufacture. It is in his criticism of Adam Smith in chapter sixteen of the First Essay that this is theoretically discussed. Although Malthus's discussion is important for understanding his early theory of economics, the topic has never been given the theoretical treatment it requires.

This paper formalises Malthus's criticism of Smith using a simple mathematical model. Some models of Malthus's economic theory have been produced by modem writers such as Eagly (1974), Eltis (1980), Costabile and Rowthom (1985), Waterman (1987), Watarai (1988), Negishi (1989), Dome (1992) and Pingle (2003), but most do not focus on his critique of Smith, despite its importance to economics. (1) The reason may be that Malthus's discussions in his First Essay are sometimes so obscure that it is difficult to interpret them. For example, Malthus argued about wealth in terms of exchangeable value or price, despite the fact that he obviously did not propose his own theory of value or price, nor a measure of value. (2) However, such a difficulty can be removed by modelling Malthus's arguments under certain specifications. First, we assume strong monotonicity of the social wealth function, which suppresses the need to explicitly treat prices in analysing wealth in Malthus's critique of Smith. In addition, we assume strong monotonicity of the 'happiness' function, which is also important in that critique as it establishes the key relationship between wealth and population increase. Through our model, we can more properly understand Malthus's statement that Smith was incorrect to argue that every increase of the national wealth (that is, the 'revenue or stock of a society') always tended to ameliorate the living standard of the working classes. More specifically, Malthus argued that, if a nation increased investment in the manufacturing sector, but not in agriculture, every increase in national wealth would not be accompanied by an increase in 'the funds for the maintenance of labour'. Thus physical wealth may increase, but happiness may decrease.

This paper provides a formal treatment of Malthus's concept of happiness and its relationship with population dynamics, which has been mostly absent in the literature. We share with Watennan (1998) the view that mathematical reconstructions of the ideas of Malthus 'can be a valuable tool' for interpreting the history of his 'intellectual formation'. Waterman states that 'in all his [Malthus's] work from beginning to end--with the sole exception of the second Essay--his thinking was generally deductive, a priori, philosophical, abstract, and ... implicitly mathematical' (Waterman 1998: 572). A mathematical approach in this paper is 'justifiable on the most rigorous intellectual-historiographic grounds' (Waterman 1998: 587).

The paper is organised as follows. In section 2 we present a simple mathematical model to analyse Malthus's critique of Smith mainly discussed in chapter sixteen of the First Essay. In section 3 we apply the model to analyse Malthus's critique. Our conclusion is presented in section 4. …

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