Theoretical Background

This chapter starts by briefly presenting the theoretical background of welfare economics and introducing key aspects such as the indirect utility function, the expenditure function, or the concepts of compensating surplus or equivalent surplus.Next, it draws attention towillingness to pay andwillingness to accept, essential measures in environmental valuation. Finally, the chapter summarises the basic mathematical notation of the random utility maximisation models used throughout the book. 1.1 Welfare Economics Environmental valuation departs from the assumption that the goods and services provided by nature can be treated as arguments of the utility function of each individual. Themain purpose of environmental valuation is to obtain amonetarymeasure of the change in the level of utility of each individual as a consequence of a change in the provision of these goods and services (Hanemann 1984). These individual measures can subsequently be aggregated across society and compared against the costs of implementing the change and thereby inform policymakers whether the proposed change is value for money, or more formally constitutes a potential Pareto improvement to society (Nyborg 2014). For this purpose, it is imperative to establish a link between utility and income. In microeconomic theory, this is achieved by assuming that an individual derives utility from consuming goods and services provided by nature (e.g. clean water or recreation). Individuals maximise utility subject to a budget constraint. Hence, income and prices together define the feasible set of consumption patterns. The outcome of this optimisation process is a set of (Marshallian) demand functions, where demand depends on income, prices and environmental quality. An important distinction that needs to bemade is between direct and indirect utility. Direct utility is the utility obtained from consuming goods and is unconnected to prices and income. For a connection with income and prices, we thus need to look at changes in optimal behaviour. This is where indirect utility comes into play. That is, we know through the demand functions how individuals respond to price, income and quality changes. Hence, the term indirect utility represents the utility derived at the optimal demand © The Author(s) 2021 P. Mariel et al., Environmental Valuation with Discrete Choice Experiments, SpringerBriefs in Economics, https://doi.org/10.1007/978-3-030-62669-3_1 1 2 1 Theoretical Background levels. In the DCE literature, most authors refer to indirect utility functions when they mention utility functions. Benefit estimation departs from inferring the net change in income that is equivalent to or compensates for changes in the quantity or quality in the provision of environmental goods and services (Haab and McConnell 2002). More formally, we start by defining an individual’s direct utility function in terms of z, a vector ofmarket commodities and q, a vector of environmental services: