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# notes2 - Chapter 2 Consumer Theory Basics Recall that the...

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Chapter 2 Consumer Theory Basics Recall that the goal of economic theory is to account for behavior based on the assumption that actors have stable preferences, attempt to do as well as possible given those preferences and the constraints placed on their resources, and that changes in behavior are due to changes in these constraints. In this section, we use this approach to develop a theory of consumer behavior based on the simplest assumptions possible. Along the way, we develop the tool of comparative statics analysis , which attempts to characterize how economic agents (i.e. consumers, fi rms, governments, etc.) react to changes in the constraints they face. 2.1 Commodities and Budget Sets To begin, we need a description of the goods and services that a consumer may consume. We call any such good or service a commodity . We number the commodities in the world 1 through L (assuming there is a fi nite number of them). We will refer to a “generic” commodity as l (that is, l can stand for any of the L commodities) and denote the quantity of good l by x l . A commodity bundle (i.e. a description of the quantity of each commodity) in this economy is therefore a vector x = ( x 1 , x 2 , ..., x L ) . Thus if the consumer is given bundle x = ( x 1 , x 2 , ..., x L ) , she is given x 1 units of good 1, x 2 units of good 2, and so on. 1 We will refer to the set of all possible allocations as the commodity space , and it will contain all possible combinations of the L possible commodities. 2 Notice that the commodity space includes some bundles that don’t really make sense, at least 1 For simplicity of terminology - but not because consumers are more or less likely to be female than male - we will call our consumer “she,” rather than “he/she.” 2 That is, the commodity space is the L -dimensional real space R L . 5

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Nolan Miller Notes on Microeconomic Theory: Chapter 2 ver: Aug. 2006 economically. For example, the commodity space includes bundles with negative components. And, it includes bundles with components that are extremely large (i.e., so large that there simply aren’t enough units of the relevant commodities for a consumer to actually consume that bundle). Because of this, it is useful to have a (slightly) more limited concept than the commodity space that captures the set of all realistic consumption bundles. We call the set of all reasonable bundles the consumption set , denoted by X . What exactly goes into the consumption set depends on the exact situation under consideration. In most cases, it is important that we eliminate the possibility of consumption bundles containing negative components. But, because consumers usually have limited resources with which to purchase commodity bundles, we don’t have to worry as much about very large bundles. Consequently, we will, for the most part, take the consumption set to be the L dimensional non-negative real orthant, denoted R L + . That is, the possible bundles available for the consumer to choose from include all vectors of the L commodities such that every component is non-negative.
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notes2 - Chapter 2 Consumer Theory Basics Recall that the...

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