Groucho Marxism

The socialist calculation debate was a discourse held in the 1930s and 1940s that centred on how a socialist economy would perform economic calculation in the absence of private ownership of the means of production. The debate was primarily between the ‘Austrian School’, represented by economists Ludwig von Mises and Friedrich Hayek, who argued against the feasibility of such calculation; and neoclassical and Marxian economists, most notably Cläre Tisch, Oskar R. Lange, and Abba P. Lerner, who argued that such calculation was feasible. Although primarily a debate between proponents of capitalism and proponents of socialism, a significant portion was also between socialists who held differing views regarding the utilization of markets and money in a socialist system.

Hayek and von Mises argued that centrally planned socialist economies cannot efficiently allocate resources because they lack market-determined prices for factors of production (like labour, land, capital). According to them, without private ownership and competition creating price signals reflecting supply and demand, planners can’t know how to best use resources, which leads to inefficiency, unlike in market economies where prices convey crucial information. The problem of efficiently allocating resources in an economy is referred to as the ‘economic calculation problem’. In a recent (2022) article, the Finnish economist Jussi Lindgren came up with a mathematical formulation of the problem, which I will now briefly describe.

Lindgren formulates the problem of economic planning as that of minimizing a loss function over a specific time period. He considers an economy in which there are M commodities and N agents. For such an economy, a price vector is an Mx1 vector specifying the price of each commodity. For each price vector p there will be an expenditure vector e(p), an Nx1 vector specifying the minimum expenditure each agent must make in order to meet their demand for goods and services. The loss function is then given by L(p,u) = mu^Tu/2+ne(p), where u(t) = p(t+1)-p(t) is the Mx1 vector of rates of change of prices, m is a constant, and n is a 1xN vector of constants. The aim of the economic planner is to pick a sequence {u(t)} so as to minimize the quantity J = ∑ L(p(t),u(t)), where the sum is over a fixed time period.

In words, Lindgren formulates economic planning as a dynamic minimization problem where the aim is to find an optimal trajectory for prices, given the individual expenditure functions and a quadratic common penalty cost related to the time-derivative of the price vector. This quadratic penalty cost can be understood as a transaction cost for changing prices. In theory, the problem can be solved using a technique known as ‘dynamic programming’. In practice, it is not possible to do this, for two reasons. First, the expenditure vector depends on individual preferences of every agent in the economy, which can’t possibly by known by a central planner. And second, even if it was possibly to know these preferences, the problem suffers from something known as the ‘curse of dimensionality’.

The term ‘curse of dimensionality’ was coined by the American applied mathematician Richard E. Bellman, the inventor of dynamic programming, and refers to computational issues that arise when the dimension of a problem becomes large. The dimension of a problem represents the number of independent variables, parameters, or degrees of freedom required to define it. The economic calculation problem as formulated above has a dimension which is astronomically large, as it includes expenditure functions for each individual which must be specified at each possible price level. This renders the problem insoluble in practice. Lindgren concludes that the economic calculation problem would be “impossible for a central planner to solve”.

However, Lindgren’s formulation reveals more than he realizes. In his model, the expenditure vector defined using utility functions. A utility function represents a preference ordering by assigning a real number to each alternative in such a manner that alternative A is assigned a number greater than alternative B if and only if the individual prefers alternative A to alternative B. Lindgren’s formulation is based on the assumption that each individual in the economy has such a function available to them (and only them) which is both immutable and fully specified for every possible combination of commodities. This is obviously nonsense. Never mind his problem being impossible for the central planner to solve; it would be impossible to specify, even in principle.

The implicit claim that capitalism is somehow able to solve this problem is therefore also nonsense. All Lindgren has done is devise a problem which neither capitalism nor socialism can solve, because it cannot even be specified in the first place! Sadly, this is what passes for ‘research’ in mainstream academic economics. In any case, the idea that capitalism as a system acts so to minimize expenditure for individual consumers whilst still satisfying their demands, as Lindgren’s model implies, is for the birds. The optimization protocol driving capitalism is not minimization of the discrepancy between supply and demand; it is maximization of profits. This should be clear to anyone who has lived under capitalism for any length of time.