Chapter 12 Welfare Theory and Valuation Public policies that lead to a reduction in the emissions of air and water pollutants or the protection of sensitive ecosystems presumably increase the well being of many members of society. Applied welfare economists are accustomed to measuring the welfare effects of policies that invoke price changes. If it is granted that the public good attributes of most dimensions of environmental quality preclude the development of well functioning markets for these service flows how are the monetary values of changes in environmental quality to be measured The past twenty to thirty years have seen the rapid development of the economic theory and techniques for measuring the demands for nonmarketed goods and in this chapter we attempt to sketch out the major results. We review the basic concept of economic welfare and derive measures of welfare change for both changes in prices of market goods and changes in quantities and qualities of nonmarket goods. We then describe the principal economic techniques for estimating the benefits of environmental quality improvements when these improvements either directly affect individuals well being or indirectly affect individuals through constraints they face. Perhaps the major class of measurement methods is based on the observation that changes in environmental quality may cause individuals to alter purchases of goods and services that are complements or substitutes for environmental quality in their preference orderings. These revealed preference methods are the primary focus of this chapter. A second major approach to obtaining estimates of the benefits and costs of environmental changes stated preference methods are addressed in detail in later chapters. Our treatment of welfare effects places special emphasis on the connection between the underlying economic theory and practical empirical models.