Full Unemployment

I find amusing the political slogan with which I title this post. We want the engineers to do their job in applying control theory to stepping motors, in creating Artificial Intelligences, in developing techniques of information management, etc. such that nobody need work out of necessity. Maybe in some future day, machinery will produce all we need, including more machinery. When the economic problem is solved:

"Man will be faced with his real, his permanent problem - how to use his freedom from pressing economic cares, how to occupy the leisure, which science and compound interest will have won for him, to live wisely and agreeably and well." -- John Myanard Keynes (1930)

Marx and Engels envision a post-capitalist society:

"Where nobody has one exclusive sphere of activity, but each can become accomplished in any branch he wishes, society regulates the general production and thus makes it possible for me to do one thing today and another tomorrow, to hunt in the morning, fish in the afternoon, rear cattle in the evening, criticize after dinner, just as I have a mind, without ever becoming hunter, fisherman, shepherd or critic. -- Karl Marx (1947, p. 22)

Bruce Sterling (1989) imagines that, in such a world, one will cultivate ones taste for "The Beautiful and the Sublime". At any rate, in this pleasant world of tomorrow, all will be able to devote themselves to great cooking, fostering social relationships, art, or whatever one may choose.

Curiously enough, the classical tradition in economics, as exemplified, for example, in Sraffa or Von Neumann, provides tools for analyzing how prices might be formed in a post-scarcity world. For example, Joan Robinson, in her first essay in (Robinson 1962) has a section titled "A model for the future" with a subsection on "The Robots". This is a model of a (maybe impossible) capitalist economy. In my version, all production is carried out in automated factories, and these factories are owned by firms traded on a stock exchange. Everybody owns shares, and the trading of these shares sets up a tendency torwards a uniform rate of profits.

I have described before some formulation of a price system consistent with this institutional set up. For now, I want to describe prices when the managers of each firm in an industry have chosen a process for producing the firm's output. As usual, I assume, for simplicity that all processes require the same time to operate, say, a year. Inputs must be purchased at the beginning of the year, and outputs become available at the end of the year. A reference set of prices satisfies the following system of equations:

p A β = p B

where

• A is a square matrix; a_i,j is the quantity of the ith commodity used as input when the jth process is operated at a unit level.
• B is a square matrix; b_i,j is the quantity of the ith commodity produced as output when the jth process is operated at a unit level.
• p is a row vector of prices; p_i is the price of the ith commodity.
• (β - 1) is the rate of profits.

This formulation allows for robots to last for more than one year. The quantity of a dated robot enters as an input, and the output includes a robot one year older, as well as whatever other outputs are produced by that process. The use of such robots is a special case of the more general model of joint production encapsulated in the above system of equations.

Various conditions must be imposed on the coefficients of production A and B to ensure a solution simultaneously exists for prices and the dual problem of the choice of technique. Von Neumann, in fact, assumes that each commodity is either used as an input or produced as an output in a poisitive amount in each process. Joan Robinson assumes the existence of "some standard physical elements (say, nuts and bolts) that enter into the production both of robots and of salable goods." But I do not want to discuss more of the mathematics in this post.

References

• D. G. Champernowne (1945-1946) "A Note on J. v. Neumann's Article on 'A Model of Economic Equilibrium'", Review of Economic Studies, V. 13, N. 1: pp. 10-18.
• John Maynard Keynes (1930) "Economic Possibilities for our Grandchildren", in Essays in Persuasion, W. W. Norton & Company
• Karl Marx and Frederick Engels (1947) The German Ideology: Parts I & III, International Publishers
• Joan Robinson (1962) Essays in the Theory of Economic Growth, Macmillan.
• Piero Sraffa (1960) , Cambridge University Press.
• J. v. Neumann (1945-1946) "A Model of General Economic Equilibrium", Review of Economic Studies, V. 13, N. 1: pp. 1-9.
• Bruce Sterling (1989) Crystal Express, Ace Books