A fundamental externality in the labour market? Ragnar Frisch on the socially optimal amount of work

Abstract

In the late 1940s, Ragnar Frisch published two articles in Norwegian that constitute a pioneering attempt to apply welfare economics to a problem of economic policy. The main contention of the articles is that there exists a fundamental externality in the labour market because the marginal productivity of labour depends both on input in the individual unit and on total labour use in the economy. While inspired by the problems of post-war reconstruction, Frisch came to regard it as a general problem in a decentralized economy, and he explores its consequences for wage and tax policy. While Frisch attached great importance to the analysis, it has received little attention in the subsequent literature.

Keywords:

• Ragnar Frisch
• welfare economics
• labour supply
• externality

JEL CODES:

• B31
• D62
• J22

Acknowledgement

I am grateful to Olav Bjerkholt for his guidance in the use of the Frisch Archive at the University of Oslo. I also appreciate the helpful comments of Vidar Christiansen, Steven Medema, Bo Sandelin and Eskil Wadensjö on an earlier version of the paper. Two anonymous referees also helped to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 A pioneer of mathematical economics and econometrics, Frisch was one of the founders of the Econometric Society and the first editor of Econometrica. Most of his academic career was spent at the University of Oslo, while he also stayed for extensive periods of time abroad. Together with Jan Tinbergen, he received the first Nobel Memorial Prize in Economics in 1969. Early surveys of his work include the articles by Arrow (1960) and Johansen (1969), while the volume edited by Strøm (1998) contains articles on various aspects of his life and work. Particularly notable among these is the article by Chipman (1998) which discusses his central contributions to economic theory and econometrics. A recent survey that emphasizes Frisch’s methodological views is Bjerkholt and Dupont (2010).

2 Among these were Knut Wicksell, Gustav Cassel, Bertil Ohlin, Eli Heckscher, Gunnar Myrdal and Erik Lindahl. In 1965 the journal began publication in English and changed its name to the Swedish Journal of Economics. In 1976 it broadened its base and became the present Scandinavian Journal of Economics.

3 From the introduction to the article it appears that it was written as a response to the encouragement of “Swedish friends” who found his thoughts on this question interesting.

4 Erik Lundberg (1907–1987) was a prominent member of the Stockholm School of macroeconomics and a leading figure in Swedish economic research. His international reputation was established with his Studies in the Theory of Economic Expansion (Lundberg 1937).

5 All translations from Norwegian are my own.

6 At the time that Frisch wrote his articles, his Institute in Oslo enjoyed a visit from Lawrence Klein, who based on his econometric work at the Cowles Commission had gone against the majority view among American economists to predict almost no increase in unemployment, a prediction that proved to be largely correct.

7 The possibility of such comparisons had been the subject of a long debate in economics, recently been revived by Robbins (1932), but Frisch does not refer to any of this literature. In his own work on the measurement of utility (Frisch 1932), the discussion of tax progressivity clearly implies the possibility of interpersonal comparisons of utility.

8 Several Norwegian cities were severely damaged both during the German invasion in 1940 and by allied air attacks during the occupation 1940–1945. The northern county of Finmark was burnt down as German forces retreated before the Red Army in 1944–1945. An early estimate (which Frisch clearly knew) of the loss of real capital for the country as a whole amounted to 18.5% of the capital stock in 1939 (Aukrust and Bjerve 1945).

9 In his first article, Frisch (1947) proceeds directly to the theoretical model, while the reference to reconstruction only appears later. The second article is more explicit with regard to the contemporary economic situation, strongly emphasizing the problem of reconstruction in the introductory paragraph (Frisch 1948, 63).

10 In his 1947 article, Frisch refers to the two concepts as the direct and indirect productivity of labour, while the 1948 article uses the terms internal and external. (The Norwegian words are practically identical to the English terms.) I follow here the latter usage.

11 Frisch notes that since the second argument of the production function is assumed to represent the labour of “the others”, this should more accurately be written as Nx. However, as he also notes, in a large economy, the two measures become practically identical.

12 In order to make it more intuitive, I have made some changes to Frisch’s notation, which, in any case, is somewhat different in the two articles.

13 Frisch actually writes utility as depending on disposable income, but since there is no saving in the model, this must be equal to consumption, so that it is natural to write the utility function in this more conventional manner.

14 The Norwegian word “frampressing” that I have translated as “generation” could alternatively and more literally have been rendered as “squeezing forth”.

15 Maximizing the utility function Ω(c)-U(x) subject to the budget constraint c = wx, it is a simple exercise in comparative statics to show that the wage effect ∂x/∂w can be written as the sum of a negative income effect and a positive substitution effect. Moreover, given the additive form of the utility function the sign of the total effect can be shown to be determined by the elasticity of the marginal utility of consumption, -Ω’’(c)c/Ω’(c). The wage effect is positive if and only if the elasticity is less than one. The possibility of empirically measuring this elasticity was analyzed in some detail in Frisch (1932).

16 The Norwegian word – literally “effort-unaffected” – is one of Frisch’s own invention, and I have not seen it used elsewhere.

17 The statement that the tax should be higher for a smaller consumption potential may be somewhat counterintuitive, but Frisch’s intention is obviously to say that for a given income, the tax should be higher, if smaller is the family size. This interpretation requires that a small consumption potential is defined as implying a small family.

18 However, he presented his recommendations with a number of qualifications related to the possibility of their actual political implementation. For a brief summary of these, see e.g., Sandmo (2011, 230).

19 Interestingly, he does not consider the design of the income tax in this connection but refers to the argument that advertising may serve a social purpose in encouraging people to work more, so as to be able to reap the benefits of mass production (Chipman 1970, 373.)

20 In Frisch (1948), he refers to such a memorandum as having been presented to the Sub-Commission some time in 1947, so it must have had some kind of circulation before the publication of the 1949 version.

21 Klein was, at this time, in the beginning of his distinguished career as a macroeconometric model builder, and it was his interest in this topic that attracted him to the University of Oslo with the prospect of collaboration with Frisch and Trygve Haavelmo; see Bjerkholt (2014). However, before embarking on this career that gained him the Nobel Memorial Prize in 1980, he was known chiefly for his development of Keynesian ideas. His book The Keynesian Revolution (1947) was especially influential.

22 This state of affairs actually continued during the decade of the 1950s; see the discussions in Sandmo (2015) and Medema (2015).