Abstract

The basic issue concerning production in welfare economics is whether a market solution will yield the socially optimum kinds and quantities of commodities. It is well known that problems can arise for three broad reasons: distributive justice; external effects; and scale economies. This paper is concerned with the last of these. The basic principle is easily stated.' A commodity should be produced if the costs can be covered by the sum of revenues and a properly defined measure of consumer's surplus. The optimum amount is then found by equating the demand price and the marginal cost. Such an optimum can be realized in a market if perfectly discriminatory pricing is possible. Otherwise we face conflicting problems. A competitive market fulfilling the marginal condition would be unsustainable because total profits would be negative. An element of monopoly would allow positive profits, but would violate the marginal condition.2 Thus we expect a market solution to be suboptimal. However, a much more precise structure must be put on the problem if we are to understand the nature of the bias involved. It is useful to think of the question as one of quantity versus diversity. With scale economies, resources can be saved by producing fewer goods and larger quantities of each. However, this leaves less variety, which entails some welfare loss. It is easy and probably not too unrealistic to model scale economies by supposing that each potential commodity involves some fixed set-up cost and has a constant marginal cost. Modeling the desirability of variety has been thought to be difficult, and several indirect approaches have been adopted. The Hotelling spatial model, Lancaster's product characteristics approach, and the mean-variance portfolio selection model have all been put to use.3 These lead to results involving transport costs or correlations among commodities or securities, and are hard to interpret in general terms. We therefore take a direct route, noting that the convexity of indifference surfaces of a conventional utility function defined over the quantities of all potential commodities already embodies the desirability of variety. Thus, a consumer who is indifferent between the quantities (1,0) and (0,1) of two commodities prefers the mix (1/2,1/2) to either extreme. The advantage of this view is that the results involve the familiar ownand cross-elasticities of demand functions, and are therefore easier to comprehend. There is one case of particular interest on which we concentrate. This is where potential commodities in a group or sector or industry are good substitutes among themselves, but poor substitutes for the other commodities in the economy. Then we are led to examining the market solution in relation to an optimum, both as regards biases within the group, and between the group and the rest of the economy. We expect the answer to depend on the intra- and intersector elasticities of substitution. To demonstrate the point as simply as possible, we shall aggregate the rest of the economy into one good labeled 0, chosen as the numeraire. The economy's endowment of it is normalized at unity; it can be thought of as the time at the disposal of the consumers.