Friday, October 31, 2014

Fred Lee

Barkley Rosser, David Ruccio, and Matias Vernengo have obituaries. I find I had not known much about Lee's life.

I have been influenced by Lee's work on markup pricing (also known as full-cost pricing), the history of heterodox economics, and the suppression of heterodox economics by the mainstream through bullying and bureaucratic measures. I think highly of Lee's 2004 paper (written in collaboration with Steve Keen), "The Incoherent Emperor: A Heterodox Critique of Neoclassical Microeconomic Theory". I can only find one blog post of mine referencing this paper. Lee promoted pluralism in economics.

Friday, October 24, 2014

Marginal Productivity Theory of Distribution: Acknowledged Blatherskite

I was surprised at how many reviews of Thomas Piketty's Capital in the 21st Century draw on the Cambridge Capital Controversy to argue that Piketty's theoretical framework is grossly inadequate.

I like this Aspromourgos quote:

However classical the questions Piketty addresses, when he turns to explain the determination of r he has recourse to the conventional, post-classical marginal productivity theory of distribution: diminishing marginal capital productivity is 'natural' and 'obvious' (212–16). (He is much less willing to have recourse to time preference: 358–61; cf. 399–400.) The logical critique of capital aggregates – applied either at the macro or micro level – as supposed independent explanatory variables in the theory of profit rates, first coherently stated by Piero Sraffa (1960, pp. 81–7; see also Kurz and Salvadori 1995, pp. 427–67), is nowhere acknowledged or addressed. That such a relatively well-read economist as Piketty can so unhesitatingly apply this bankrupt approach, is testament to how completely a valid body of critical theoretical analysis can be submerged and forgotten in social science (a phenomenon for the sociologists of knowledge to contemplate). This is so, notwithstanding that Piketty offers a brief interpretation of the 'Cambridge' capital debates, making them turn upon the issues of whether there is substitutability in production (and associated flexibility of capital-output ratios), and whether or not 'growth is always perfectly balanced [i.e., full-employment growth]' (230–32). In fact, the participants on both sides of those debates were concerned with production systems in which substitution and capital-output variability occurred; and continuous full-employment growth was not entailed by recourse to orthodox, marginalist production functions, a point perfectly understood by the participants on both sides. -- Tony Aspromourgos

Update (27 October 2014): Added the Bernardo, Martinez, and Stockhammer reference.

Update (1 December 2014): Added the Foster and Yates reference.

Friday, October 17, 2014

r > g In A Steady State

1.0 Introduction

This post presents a model of distribution that Luigi Pasinetti developed. It is one of a family of models. Other important models in this family were developed by Richard Kahn, Nicholas Kaldor, and Joan Robinson. These models have been extended in various ways and presented in textbooks. One can see this family as having extended work by Roy Harrod, and as being related to the work of Michal Kalecki and even of Karl Marx.

2.0 The Model

2.1 Definitions

Consider a simple closed economy with no government. All income is paid out in the form of either wages or profits:

Y = W + P,

where W is total wages, P is total profits, and Y is national income. Total savings is composed of savings by workers and by capitalists, where capitalists are a class whose members receive income only from profits:

S = Sw + Sc

S is total savings. Sw is workers' savings, and Sc is capitalist savings. Profits are also split into two parts:

P = Pw + Pc,

where Pw is returns on the capital owned by the workers, and Pc is the return on the capital owned by the capitalists. The behavior assumption is made that both workers and capitalists save a (different) constant proportion of their income:

Sc = sc Pc
Sw = sw (W + Pw)

sc is the capitalists' (marginal and average) propensity to save. sw is the workers' (marginal and average) propensity to save. The propensities to save are assumed to lie between zero and one and to be in the following order:

0 ≤ sw < sc ≤ 1

Workers' savings are assumed to be insufficient to fund all the investment occurring along a steady-state growth path.

The value of the capital stock is divided up into that owned by the workers and by the capitalists:

K = Kw + Kc,

where K is the value of the capital stock, Kw is the value of the capital stock owned by the workers, and Kc is the value of the capital stock owned by the capitalists

2.2 Steady State Equilibrium Conditions

Along a steady-state growth path, in this model, all capital earns the same rate of profits, r:

r = P/K = Pc/Kc = Pw/Kw

It follows from the above set of equations that the ratio of the profits received from the workers to the profits received by the capitalists is equal to the ratio of the value of capital that each class owns:

Pw/Pc = Kw/Kc

Likewise, one can find the ratio of total profits to the profits obtained by the capitalists:

P/Pc = K/Kc

The analysis is restricted to steady-state growth paths where the value of the capitalists' capital and the value of the workers' capital is growing at the same rate:

S/K = Sc/Kc = Sw/Kw

The ratio of profits to savings is the same for the economy as a whole and for workers:

P/S = (P/K)/(S/K) = (Pc/Kc)/(Sc/Kc) = Pc/Sc

Or, after a similar logical deduction for workers:

P/S = Pc/Sc = Pw/Sw

Along a steady-state growth path, planned investment, I equals savings:

I = S
2.3 Deduction of the Cambridge Equation

The following is a series of algebraic substitutions based on the above:

P/I = P/S = Pc/Sc = Pc/(sc Pc) = 1/sc


P = (1/sc) I

The share of profits in national income is determined by the savings propensity of the capitalists and the ratio of investment to national income:

(P/Y) = (1/sc) (I/Y)

Recall that the rate of profits is the ratio of profits to the value of capital:

r = P/K = (1/sc) (I/K)

Recognizing that I/K is the rate of growth, g, one obtains the famous Cambridge equation:

r = g/sc

As long as the capitalists consume at least some of their income, the rate of profits is greater than the rate of growth along a steady-state growth path. And along such a path the share of income going to profits will be constant.

3.0 Discussion

If one assumes given investment decisions, the Cambridge Equation tells us what rate of profit is compatible with a steady state growth path in which the expectations underlying those investment decisions are satisfied.

Consider two steady states in which the same rate of growth is being obtained. Suppose that along one path workers have a higher propensity to save. Within broad limits, this greater willingness to save among workers has no effect on determining either the share of profits in income or the rate of profits. Only the capitalists' saving propensity matters for the steady state rate of profits, given the rate of growth. Would a capitalist economy have a tendency to approach such a growth path, given a sufficient length of time? I think such stability would entail the evolution of institutions, conventions, the labor force, and what is seen as common sense, including among dominant political parties.

The above model might have some relevance to current political economy discussions elsewhere.

Tuesday, October 14, 2014

Jean Tirole, A Practitioner Of New Industrial Organization

I have occasionally summarized certain aspects of microeconomics, concentrating on markets that are not perfectly competitive. Further developments along these lines can be found in the theory of Industrial Organization.

One can distinguish in the literature two approaches to IO know as old IO and new IO. Old IO extends back to the late 1950s. Joe Bain and Paolo Sylos Labini laid the foundations to this approach, and they were heralded by Franco Modigliani. I have not read any of Bain and only a bit of Sylos Labini. Sylos was a Sraffian and quite critical of neoclassical economics. He also had interesting things to say about economic development.

As I understand it, new IO consists of applying game theory to imperfectly competitive and oligopolistic markets. I gather new IO took off in the 1980s. Jean Tirole, the winner of this year's "Nobel" prize in economics, is a prominent exponent of new IO.

One can tell interesting stories about corporations with both old IO and new IO. For example, Tirole has had something to say about vertical integration which, based on what I've read in the popular press, might be of interest to me. (Typically, when I explore the theory of vertical integration, following Luigi Pasinetti, the integration is only notional, not at the more concrete level of concern in IO.)

I wonder, though, whether economists can point to empirical demonstrations of the superiority of new IO over old IO. Or have economists studying IO come to embrace new IO more because of the supposed theoretical rigor of game theory? Are specialists in IO willing to embrace the indeterminism that arises in game theory, what with the variety of solution concepts and the existence of multiple equilibria in many games? Or do they insist on closed models with unique equilibria?

  • Franco Modigliani (1958). New developments on the Oligopoly Front, Journal of Political Economy, V. 66, No. 3: pp. 215-232.

Update (same day): Corrected a glitch in the title. Does this Paul Krugman post read as a direct response to my post?