Contrast between Welfare Conditions for Joint Supply and for Public Goods - Samuelson, Paul A. (The Review of Economics and Statistics, 1969)
1. THE theory of public goods 1 is sometimes confused with the theory of joint production. This is in the nature of a pun, or a play on words: for, as I have insisted elsewhere, as we increase the number of persons on both sides of the market in the case of mutton and wool, we converge in the usual fashion to the conditions of perfect competition. But when we increase the number of persons in the case of a typical public good, we make the problem more indeterminate rather than less. To elucidate the difference, I shall fill in what appears to be a minor gap in the literature, namely a needed statement in terms of modern welfare economics of the various optimality conditions as they appear in the case of joint products. The analysis is straightforward; and after it is before us, we can clearly see the difference between it and the well-known optimality conditions for the case of public goods. 2. I begin with an examination question given recently at the Massachusetts Institute of Technology: Corn is produced by land and labor; and so are wool-bearing mutton-bearing sheep. Assume the totals of available land and labor to be fixed. Write down the various welfare optimality conditions in the case where all people happen always to consume wool and mutton in the same proportions that sheep bear these products. And then, by contrast, write down the conditions that would have to prevail if individuals' indifference contours for wool, mutton, and corn involve the usual variability of proportions. This proved a difficult question for first-year graduate students in economic theory. Still many perceived that in the first case they could essentially work with two rather than three goods, substituting sheep as a kind of composite good for wool and mutton, and thereby ending up with the standard welfare conditions for two ordinary (private) goods, corn and sheep.