In economics, welfare often refers to the level of utility. Therefore, our analysis begins with how much satisfaction a consumer derives from a commodity or a basket of commodities. Other factors, such as the wellbeing of others, may affect utility but a discussion of these factors is not undertaken here. Utility or satisfaction is a property that is common to all commodities that are desired. However, utility is a subjective concept in the sense that we cannot observe how much utility or satisfaction a consumer derives from his consumption. Moreover, it is not obvious how to compare utility levels across individuals. Nonetheless, as economists we can analyse consumer choice in terms of utility. This is one of the purposes of this appendix. The second purpose is to introduce the production side of the economy. In the main text, we use these tools in an analysis of aggregate welfare (or social welfare) in a multi-household economy. Before proceeding, a warning is justified. In this apperdix, we will use some simple mathematics. The formulas presented here are extremely useful points of reference for many of the results derived in a more intuitive way in the main text. The reader who nevertheless prefers a non-technical introduction to household and firm behaviour can either skip the mathematics and just read the text or read the corresponding chapter(s) in an introductory microeconomics textbook.

A1 Preferences and the utility function

In order to be able to say something about consumer choice, we must start by making some assumptions. Four assumptions relating to choices of commodities will be introduced.