Ronald Coase, Abba Lerner, and the Calculation Controversy
also the theory of the firm
The Calculation Controversy was an extended debate between a group of free market economists, including Ludwig von Mises and Friederich Hayek, and a group of socialist economists including Abba Lerner and Oskar Lange. It was set off by Mises’ article Economic Calculation in the Socialist Commonwealth, which argued that without markets and trade, rational economic calculation was impossible.
The most interesting response from the socialist side was the Lerner and Lange’s model of socialism with markets. In that system households allocate their income to consumption goods and their labor to jobs as in a free market. The Central Planning Board proposes a set of prices. Firms, government owned and worker managed, are instructed to produce the quantity of output for which marginal cost equals price, what a private profit making firm would do under perfect competition. If, at that price, supply of a good is more (less) than demand, the CPB lowers (raises) the price, the firm adjusts its output accordingly, consumers adjust the amount they attempt to buy. The process continues by trial and error until prices are such that supply equals demand for all goods. The idea is to take advantage of the mechanism of decentralized coordination used by capitalism, producing the same results as under perfect competition. The firms act as if they were maximizing their profit in a competitive market, the CPB plays the role of a market in determining prices.
A variety of criticisms can and have been offered for the idea and it has never been implemented in practice. The criticism that occurs to me, coming from a background in public choice theory, is that it is not incentive compatible, that it is not in the interest of the actors to do what the model requires them to.
Consider the firm. If it follows orders from the CPB it produces a profit which it turns over to the CPB. It has the alternative of spending the profit they were making on the workers themselves instead of turning it over to the planning board, deliberately raising costs by paying more to the workers or spending more on them to make their lives pleasanter. The firm’s cost curve, the lowest cost at which it can produce any quantity of output, is not public knowledge. The information needed to calculate it is dispersed among the workers and worker managers, all of whom share a common interest in inflating costs in ways that benefit themselves.
Contrast that to the private profit making firm whose behavior the government owned firm is supposed to mimic. Its owner and manager, in the simple case of an owner run firm, is its residual claimant. The firm’s profit, the difference between revenue and cost, goes to him, so it is in his interest to maximize it, which he does, in the perfect competition economy that the socialist economy is trying to copy, by producing the quantity at which marginal cost equals price and doing so at the lowest possible cost.
The same problem runs through the system. It works for robots who can be trusted to do whatever the rules of the system tell them to do. But it is populated by human beings, each of whom acts in his own interest. The beauty of the private market system is that it is in the interest of every actor to take the actions that produce the desired outcome for an efficient economy1 — perfectly in their interest in the ideal case of perfect competition, approximately in their interest in more realistic cases.2
Coase’s Critique of the Other Side of the Argument
Ronald Coase, in The Nature of the Firm, the article on which the modern theory of the firm is based, pointed out a problem with the claim that Mises and Hayek were arguing: If centrally planned coordination was impossible there would be no firms. A firm, after all, is a miniature socialist economy. It deals with the world outside it as a market participant, just as a socialist state such as the Soviet Union does, buying from and selling to other firms and individuals. But within the firm coordination is by central control, executives figuring out what workers should do and workers doing it as instructed. If that form of coordination was always and inevitably inferior to coordination by market transactions the result would be an agoric economy, each individual buying inputs and selling outputs, coordinating their activities by market transactions.
Why does that not happen? How is it possible for a firm coordinated from above by its owner-manager to compete with the market alternative?
Coase’s answer was that while centralized coordination indeed has costs, so does market coordination. In order to coordinate by market transactions the individual actor has to bear the costs of determining what goods and services are available, what their cost and quality are, how reliable the producer-seller is. He has to bear the costs of bargaining over price and other terms. If these costs are larger than the inefficiencies associated with coordination by central authorities, individuals coordinating through the market lose out to the competition of a similar group formed into a firm.
The main reason why it is profitable to establish a firm would seem to be that there is a cost of using the price mechanism. The most obvious cost of “organising” production through the price mechanism is that of discovering what the relevant prices are. … The costs of negotiating and concluding a separate contract for each exchange transaction which takes place on a market must also be taken into account. (“The Nature of the Firm”)
The Theory of the Firm
The costs of hierarchy tend to increase with the number of people being coordinated; the more layers of administrators between the boss and the factory floor the greater the ratio of administrators to workers, the more information lost going up and down between top and bottom of the hierarchy, the harder the problem of figuring out what everyone should be doing. It follows that, in a competitive market, firms tend to increase how much they coordinate within the firm until they reach a size at which taking more of the productive process in-house, making the tires for the cars they produce themselves instead of buying them from a tire company, costs more than the savings in transaction costs is worth. The same logic applies to economies of scale, respects in which costs fall with increasing volume of production, dividing the costs of designing a car among a million vehicles instead of half a million; the firm expands its output until further expansion costs more in organizational inefficiencies than it saves in efficiencies of production. Hence a competitive market is populated by firms of a variety of sizes, from one person up.
Implications
One implication of this is that the socialist alternative is less bad than Mises et. al. thought, possible if imperfectly efficient. Another is that the capitalist alternative is better than either side of the controversy realized, since it takes advantage of the advantages of centralized coordination where and to the extent that they exist. A third is that socialism is more workable the smaller the society being organized, more practical in a small country than a large, still more practical at the scale of a monastery or a religious commune, most practical at a still smaller scale. Almost all families are organized as miniature socialist communes, with little use of internal markets.
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“Efficient” in the sense explained and discussed in an earlier post.
I sketch the reasons this is true in my earlier post on market failure under the subhead “Market Failure as an Argument Against Government”.

I feasted on the Calculation Debate -- both sides -- when I was a student!
Your criticism is well taken. The closest thing to Lange-Lerner that has been implemented has been the EU Common Agricultural Policy [CAP] and it illustrates well how a real life Central Planning Board will set prices.
The CAP is a whole set of prices enforced by the government through buying product. Those are political prices, set to make the least efficient farmer vote for the party that gives him the bounty of the high price. Of course there were surpluses -- the wine lake, the butter mountain, and the milk ocean. Prices were kept in check only when it seemed politically feasible to do so.
The only other constraint on this behavior was the budgetary cost of financing the surpluses. High tariffs lowered the budgetary cost.
"If it follows orders from the CPB it produces a profit which it turns over to the CPB. It has the alternative of spending the profit they were making on the workers themselves instead of turning it over to the planning board, deliberately raising costs by paying more to the workers or spending more on them to make"
Thats more or less what happened with all the socialist and anarchist cooperatives on the Republican side during the Spanish Civil War. They didnt necessarily do marginal cost pricing but they did have arrangements where any profit was to be turned over to a central authority and redistributed among all the relevant cooperatives. Very quickly each individual cooperative found a way to make zero profit by driving up their own costs by driving up the wages. Since amount of "true" profit (before it was purposefully eliminated) varied by cooperative size and also by whether the factory/firm/farm they seized had previously modernized its equipment or not, this rapidly created a "workers aristocracy" within these cooperatives