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The formal analysis in this chapter lays the foundation for the welfare analysis in the remainder of the book. A conventional welfare equation for marginal policy changes is obtained in a competitive general equilibrium model of a tax-distorted closed economy. Initially, the distributional effects are removed by adopting the ‘dollar-is-a-dollar’ assumption used by Harberger. The analysis is extended in the following chapters to include distributional effects, time, internationally traded goods, externalities, non-competitive behaviour, price-quantity controls, public goods, and other market distortions. The Hatta decomposition is generalized to show that the shadow prices of goods are equal to their compensated shadow prices multiplied by the shadow value of government revenue. Any income effects are isolated in the shadow value of government revenue.

This chapter provides a set of questions drawn from material presented in previous chapters. Most are designed to emphasize important points, and to illustrate practical examples of applied welfare analysis. A number of questions are quite long and are intended as assignments, while others are more suitable for tutorial exercises.

Governments rarely raise revenue with lump sum transfers. Instead, they use distorting taxes, and this must be reflected in cost-benefit studies. The conventional welfare analysis in previous chapters is revised to include changes in tax inefficiency when distorting taxes are used to balance the government budget. This involves a simple revision to the conventional (lump sum) shadow prices, in which the revised shadow price of any good is its conventional shadow price plus the change in tax inefficiency on the revenue transfers made with distorting taxes. This adjustment is used in the next chapter to demonstrate the role played by the marginal social cost of public funds (MCF) in project evaluation. Finally, the Hatta (1977) decomposition is extended to revised shadow prices where the income effects are isolated in the revised shadow value of government revenue. It is used in following chapters to measure the distributional effects of policy changes when governments make revenue transfers with distorting taxes.

In public economics applications, the MCF is frequently used to compute the cost to private surplus of raising an additional dollar of government revenue. One of the most common examples is provided by the revision to the Samuelson condition that follows the approach recommended by Pigou (1947). The MCF is rarely used in the applied welfare literature to compute shadow prices. By doing so in this chapter, it is possible to demonstrate the separate, but related roles of the MCF and the shadow value of government revenue. While the MCF is the cost to private surplus of transferring a dollar of revenue to balance the government budget, the shadow value of government revenue is the change in social welfare from endowing another dollar of revenue on the government. Thus, the MCF is the welfare effect of transferring given resources between the private and public sectors of the economy, while the shadow value of government revenue is the welfare effect of expanding the economies’ resources. That is why the shadow value of government revenue, and not the MCF, converts efficiency gains into utility. The relationship between the MCF and the shadow value of government revenue is used to reconcile different measures of the MCF used in the public economics literature.

This chapter is somewhat unrelated to the rest of the book, since it does not deal with taxation policies but with the calculation of the shadow cost of labour (shadow wage) in less developed countries (LDCs). During the last two decades, there has been growing consensus on the usefulness as well as the limitations of social cost–benefit analysis for project and expenditure evaluation in developing economies, and on the general procedures for determining shadow prices for such analyses. The objective here is to illustrate how the models and approaches developed in the rest of the book can be used for purposes other than taxation analysis, rather than to present a comprehensive shadow price model. The model presented addresses the case of an open economy facing fixed international prices, in which the government cannot (or does not) set different prices in the rural and urban sectors, and in which tariffs are fixed.

This chapter describes the theory of two-person, zero-sum games invented by John Von Neumann in 1928. It begins with an application to the computation of economic shadow prices. It shows that a two-person game is strictly competitive if, and only if, it has a zero-sum representation. Such a game can be represented using only the first player's payoff matrix. The minimax and maximin values of the matrix are defined and linked to the concept of a saddle point. The ideas are then related to a player's security level in a game. An inductive proof of Von Neumann's minimax theorem is offered. The connexion between the minimax theorem and the duality theorem of linear programming is explained. The method of solving certain two-person, zero-sum games geometrically with the help of the theorem of the separating hyperplane is introduced. The Hide-and-Seek Game is used as a non-trivial example.

This chapter discusses ‘pure theory’ analysis, so-called because it mostly ignores many important features of underdeveloped countries in order to concentrate on one relationship. The discussion also explores implications for the shadow pricing of labour, both in urban and rural production.

Due to distortions in market economies shadow prices are necessary to properly value consumption and capital assets, especially natural capital. The chapter examines the key elements of shadow prices, and their role in measuring wealth and in government policy (through instruments such as environmental taxes), as well as the importance of social or institutional capital (such as the legal system) in underpinning markets. It addresses why the conventional economists’ treatment of consumer preferences is inadequate for addressing sustainable consumption: the existence of habits; the omission of ‘conspicuous consumption’ (interpersonal externality leading to overconsumption); and role of ‘social consumption’ which signals group membership. The chapter demonstrates how the traditional economic model must be expanded to capture consumer behaviours and the attendant policy implications, and argues social well-being increases only if wealth per capita increases.