Public Utility Pricing and Output Under Risk: Comment
In their paper in the March issue of this Reviewv, Gardner Brown, Jr. and M. Bruce Johnson argue that . . the optimal price will always be lower and, with linear demand, the optimal output will generally be higher than their counterparts in the riskless model of traditional theory. (Their analysis relates to a single product produced at a constant unit operating cost of b and with a constant unit capacity cost of 3. Thus in the riskless model, maximum welfare requires a price of b+i3.) Their result concerning price is an odd one. I accept that it follows from their assumptions but question the usefulness of these assumptions. The first step is to provide an intuitive understanding of their result. To do this, let us take the simplest possible case of risk where the demand curve has a probability of one half of being low and one half of being high. The price and capacity chosen must obviously be such that capacity falls between low demand and high demand at that price. If demand turns out to be low, consumers' surplus is maximized by producing up to the point where demand price equals b, since there is spare capacity and since capacity costs are fixed and hence irrelevant. If, on the other hand, demand turns out to be high, output will be limited by capacity, the excess demand being eliminated by rationing, so that price is irrelevant. Hence price can be determined so as to maximize consumers' surplus in the eventuality of low demand. Capacity, on the other hand, being excessive when there is low demand, can be determined so as to maximize consumers' surplus in the eventuality of high demand. It should be increased up to the point where the expected gain in consumers' surplus from a unit increase in capacity I (p-b) just equals the cost of that extra capacity A, where p is the (high) demand price at the level of capacity chosen. I hope that this adequately conveys the essence of Brown and Johnson's argument. It rests upon the explicit and reasonable assumption that price has to be fixed before it is known whether demand is going to be high or low. But it also rests upon the implicit assumption that rationing is always preferable to price as a means of restraining consumption at times of high demand. This assumption is not generally correct. A price greater than b will involve a loss of consumers' surplus at times of low demand but will diminish the amount of excess demand and hence the severity of rationing at times of high demand. There is thus a tradeoff between the sacrifice of consumers' surplus on the one hand and the stringency of rationing on the other hand. The terms of this trade-off and consumers' attitudes to it will depend on the circumstances of the case, so they can be usefully discussed only in terms of particular real cases. Rationing in the case of electricity means power cuts; in the case of gas it may mean a pressure drop which entails the danger of explosions; in the case of telephone service it means that some calls cannot be made. In all three of these cases, tariffs are usually set high enough to keep down the risk of failure to a very low level, i.e., they are at a level considerably in excess of operating costs.' This does not impugn the principle set out above for determining capacity,2 but it does suggest that Brown and Johnson's suggested
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