Robertson and the Cambridge Approach to Utility and Welfare

In the post-Second World War era, Robertson attempted to defend the Cambridge utilitarian tradition against the ‘new welfare economics’, developed earlier following Robbins’s influential criticism of the legitimacy of interpersonal comparisons of utility. Robertson claimed that welfare economics should be based on cardinal utility while rejecting the ordinalist revolution in consumer and welfare theories.

A main feature of Cambridge welfare economics uses the acceptance of interpersonal comparisons of welfare, though not necessarily associated with cardinal utility measurement. Robertson (1951 [1952]: 17, 38) saw himself as part of the ‘Cambridge set up’, coming from Marshall, the ‘Cardinal Club’, and the ‘Pigouvian world of measurable utility’. As both Robertson and Pigou (1953: Chapter 5) were aware, Marshall’s cardinalism was nuanced since he insisted that the utility of sensations cannot be measured directly, but only indirectly by their observable effects. This notion of utility as a ‘mental metric’ of desire was common to Marshall, Pigou, and Robertson, as noted by Sen (2000: 67). Its core assumption, according to Robertson (ibid.: 15, 1957: 72-73), was the psychological rule of diminishing marginal utility, based on ‘introspection and observation’ and interpreted as a corollary of the idea that utility is quantitative and measurable. Along with the requirement that utility is additively separable, diminishing marginal utility implies strict convexity of Edgeworth’s indifference curves. The Marshallian consumer is supposed to have a cardinal capacity of knowing the rate at which marginal utility declines, a knowledge that enables her to maximise her economic welfare or utility by distributing expenditure so that the marginal utility of a good is proportional to its price. This does not mean that marginal utility can be directly measured, but that the price a consumer pays for each good is an indirect measure of its marginal utility.

Robertson began with an examination of Pareto’s claim that lumps of utility can be set out in order of magnitude, but that one cannot ask how much greater one lump of utility is than another (Robertson 1951 [1952]: Section 2). However, Pareto and his followers did not consistently adhere to the postulate of ordinal utility, since the notion of marginal utility was still present in their assumption about the signs of the second derivatives of the utility function. Apart from the convexity assumption, Robertson also criticised the methodological principle of Occam’s razor. Although the theory of demand could be presented in an objective and behaviouristic fashion (as in Chapter 4 of volume 1 of the Lectures), Robertson did not accept the view that consumer theory should merely describe choices rather than explain them (see also Robertson 1954a).

Robertson’s attempt to protect Cambridge from the criticisms of new welfare economics was based on his view that the replacement of the law of diminishing marginal utility of income—which made possible interpersonal comparisons of utility—by compensation criteria and the social welfare function did not represent progress. His defence of cardinal utility was not restricted to welfare economics, but included also demand theory, since ordinal utility would not provide a better account of consumers’ behaviour, especially the crucial assumption that indifference curves are convex towards the origin, associated with his emphasis on material welfare as the proper domain of economics. Robertson had some influence over Cambridge students at the time, including Amartya Sen, who arrived at Trinity College in 1953. As recalled by Sen, his teachers at Trinity, Dobb, Sraffa, and Robertson, were his main influence:

And then Robertson was very important. He presented good, critical reasons for being sceptical of behaviourism, including the notion of revealed preference that had by then taken hold of economics. The idea that we can understand human beings in terms only of their behaviour, and then only their non-verbal behaviour, never through conversation...was very alien to the Marshallian part of the Cambridge tradition, a tradition I came to admire a lot. The natural heir to that tradition in my student days was Dennis Robertson (Sen quoted in Klamer 1989: 138).