“The Meaning of Utility Measurement,” A. Alchian (1953)

Armen Alchian, one of the dons from UCLA’s glory days, passed away today at 98. His is, for me, a difficult legacy to interpret. On the one hand, Alchian-Demsetz 1972 is among the most famous economics papers ever written, and it can fairly be considered the precursor to mechanism design, the most important new idea in economics in the past 50 years. People produce more by working together. It is difficult to know who shirks when we work as a team. A firm gives a residual claimant (an owner) who then has an incentive to monitor shirking, and as only one person needs to monitor the shirking, this is much less costly than a market where each member of the team production would need somehow to monitor whether other parts of the team shirk. Firms are deluded if they think that they can order their labor inputs to do whatever they want – agency problems exist both within and outside the firm. Such an agency theory of the firm is very modern indeed. That said, surely this can’t explain things like horizontally integrated firms, with different divisions producing wholly different products (or, really, any firm behavior where output is a separable function of each input in the firm).

Alchian’s other super famous work is his 1950 paper on evolution and the firm. As Friedman would later argue, Alchian suggested that we are justified treating firms as if they are profit maximizers when we do our analyses since the nature of competition means that non-profit maximizing firms will disappear in the long run. I am a Nelson/Winter fan, so of course I like the second half of the argument, but if I want to suggest that firms partially seek opportunities and partially are driven out by selection (one bit Lamarck, one bit Darwin), then why not just drop the profit maximization axiom altogether and try to write a parsimonious description of firm behavior which doesn’t rely on such maximization?

It turns out that if you do the math, profit maximization is not generally equivalent to selection. Using an example from Sandroni 2000, take two firms. There are two equally likely states of nature, Good and Bad. There are two things a firm can do, the risky one, which returns profit 3 in good states and 0 in bad states, and a risk-free one, which always returns 1. Maximizing expected profit means always investing all capital in the risky state, hence eventually going bankrupt. A firm who doesn’t profit maximize (say, it has incorrect beliefs and thinks we are always in the Bad state, hence always takes the risk-free action) can survive. This example is far too simple to be of much worth, but it does at least remind us of lesson in the St. Petersburg paradox: expected value maximization and survival have very little to do with each other.

More interesting is the case with random profits, as in Radner and Dutta 2003. Firms invest their capital stock, choosing some mean-variance profits pair as a function of capital stock. The owner can, instead of reinvesting profits into the capital stock, pay out to herself or investors. If the marginal utility of a dollar of capital stock falls below a dollar, the profit-maximizing owner will not reinvest that money. But a run of (random) losses can drive the firm to bankruptcy, and does so eventually with certainty. A non-profit maximizing firm may just take the lowest variance earnings in every period, pay out to investors a fraction of the capital stock exactly equal to the minimum earnings that period, and hence live forever. But why would investors ever invest in such a firm? If investment demand is bounded, for example, and there are many non profit-maximizing firms from the start, it is not the highest rate of return but the marginal rate of return which determines the market interest rate paid to investors. A non profit-maximizer that can pay out to investors at least that much will survive, and all the profit maximizers will eventually fail.

The paper in the title of this post is much simpler: it is merely a very readable description of von Neumann expected utility, when utility can be associated with a number and when it cannot, and the possibility of interpersonal utility comparison. Alchian, it is said, was a very good teacher, and from this article, I believe it. What’s great is the timing: 1953. That’s one year before Savage’s theory, the most beautiful in all of economics. Given that Alchian was associated with RAND, where Savage was fairly often, I imagine he must have known at least some of the rudiments of Savage’s subjective theory, though nothing appears in this particular article. 1953 is also two years before Herbert Simon’s behavioral theory. When describing the vN-M axioms, Alchian gives situations which might contradict each, except for the first, a complete and transitive order over bundles of goods, an assumption which is consistent with all but “totally unreasonable behavior”!

1953 AER final version (No IDEAS version).

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