Business enterprises routinely calculate the profitability of their activities, weighing the costs of producing a good or service against the revenue it generates. The objective of cost- benefit analysis is the evaluation of the "production activities' of the public sector. The "social profitability' of public sector projects is calculated in a manner similar to the way a business enterprise would calculate the profitability of its activities, but the resources used and the outputs produced are valued differently. In a cost-benefit appraisal, "shadow prices', which reflect the social value of goods, replace the market prices that are used in the private calculation. In a perfectly competitive economy market prices and shadow prices will coincide, if we ignore complications introduced by issues of income distribution. Cost-benefit analysis and calculation of private profitability will yield the same result in this case.
Market distortions, however, will cause shadow prices and market prices to differ. This makes cost benefit analysis difficult, since "shadow prices' or "social values' cannot be directly observed. In Discussion Paper No. 41 Programme Director Alasdair Smith examines the relationship between market and shadow prices when market distortions take the form of a tax or subsidy that causes consumers and private producers of a good to face different prices. An example of such a tax might be an excise tax. The price which consumers pay for a good is one measure of social value of the good, as it measures what a consumer is willing to pay for an extra unit of the good. The price which producers face is an alternative measure of social value, since in a competitive market it is equal to the marginal cost of the resources used in producing the good. In the presence of a consumer tax or other distortion these two measures will not coincide. How can one calculate the correct shadow price in this situation? One plausible procedure is the use of a "weighted-average' rule, in which the shadow price of the good lies between the consumer and producer prices. The weights of the two market prices in the shadow price formula depend on the relative impact on consumers and on private producers of a change in public sector production of the good.
Smith argues that this procedure is invalid when the effects of distortions in other markets must be taken into account. He derives a shadow price formula in a general equilibrium model which takes into account such market interactions. As an illustration he uses this formula to calculate the appropriate shadow prices in a small model with a variety of different tax structures. When market distortions are large, Smith finds that the shadow price of a good need not lie between the consumer and producer prices. He also finds that the calculated shadow prices are quite sensitive to the exact specification of the consumer tax.
Smith argues that the weakness of the "weighted average' rule is its assumption that the marginal cost faced by producers of a particular good is a proper measure of the social marginal cost of producing that good. The partial equilibrium argument takes the good's supply curve as a measure of its marginal social cost. This is not appropriate if there are distortions elsewhere in the economy. Large agricultural subsidies, for example, will lead to expansion of the agricultural sector and will drive the market price of land above its social value. The private marginal cost of producing other goods which use land will therefore exceed the social cost of production; this makes the weighted-average argument invalid. The policy implication is that one should be cautious of using tools based on the logic of partial equilibrium in situations where there are significant links between markets.

Public Sector Shadow Prices in Distorted General Equilibrium Models
Alasdair Smith

Discussion Paper No. 41, January 1985, (IT)