Chapter 3 lecture outline AAEC 3315, Benson 1 Pages 89-111 in Nicholson and Snyder 1. Preferences and utility 1.1. In this chapter we will lay the foundations for an economic model of consumer choice 1.2. The most fundamental concept is that of a preference relation, but we deal mostly with a utility function, which is built on the preference relation 1.3. Our main focus will be to define and describe an economic utility function 2. Axioms of rational choice – characteristics we assume define “rational” behavior 2.1. These are based on the concept of preference 2.1.1. For two situations A and B, an individual “prefers A to B” means that, all things considered, the individual feels better off under situation A 2.2. Preferences have 3 basic properties 2.2.1. Completeness 2.2.1.1. For any two situations A and B, the individual can specify exactly one of the following 2.2.1.1.1. A is preferred to B 2.2.1.1.2. B is preferred to A 2.2.1.1.3. A and B are equally attractive 2.2.1.2. This is an assumption about people’s abilities to make choices – that is, they can, always, in every situation 2.2.2. Transitivity 2.2.2.1. If an individual reports that A is preferred to B and B is preferred to C, then it must be the case that A is preferred to C 2.2.2.2. This is an assumption about logical consistency of preferences 2.2.3. ContinuityChapter 3 lecture outline AAEC 3315, Benson 2 2.2.3.1. If an individual reports that A is preferred to B, then situations suitably “close to” A are also preferred to B 2.2.3.2. This is an assumption that is necessary for the math we use to model economic choices to make sense 3. Utility – given rational preferences, it is possible to show that people can rank all possible situations from least desirable to the most 3.1. For each situation, a level of utility can be assigned 3.2. If A is preferred to B, then, we can say that the utility assigned to A exceeds the utility assigned to B 3.2.1. We can assign numbers to utility and say that ( ) ( ) 3.2.2. These numbers only have meaning as a comparison – it doesn’t matter if ( ) ( ) or if ( ) and ( ) , in either case, A is preferred to B 3.2.3. It doesn’t make sense to ask “how much more is A preferred to B?” 3.2.4. So it also doesn’t make sense to compare utilities of different people 3.3. We restrict analysis to choices among quantifiable options 3.3.1. Assuming other things that affect utility are held constant 3.3.2. Things like psychological attitudes, peer group pressures, personal experiences and general cultural environment 3.3.3. Example: an individual choosing among n consumption goods 3.3.3.1. The individual’s ranking of these goods can be represented by a utility function ( ) where the x’s refer to quantity of the goods that can be chosen 3.3.3.2. Usually, we write itChapter 3 lecture outline AAEC 3315, Benson 3 ( ) and just assume that everything not included in the equation is held constant 3.3.4. Utility – Individuals’ preferences are assumed to be represented by a utility function of the form ( ) Where are the quantities of n goods that might be consumed in a period 3.4. In the representation above, the variables are “goods” 3.4.1. No matter what the variables represent, more of any xi is better than less 3.4.2. Graph of region preferred to 4. Trades and substitution – most economic activity involves voluntary trading between individuals; here we discuss how trading can be illustrated in the context of utility 4.1. Voluntary trades can best be studied using an indifference curve 4.1.1. An indifference curve U1 represents all the alternative combinations of x and y for which the consumer is equally well off 4.1.2. The consumer is indifferent among all the possible combinations of x and y on the indifference curve x* y* Any point in this region is preferred to x*, y* Worse than x*, y*Chapter 3 lecture outline AAEC 3315, Benson 4 4.1.3. Each point on the indifference curve results in the same level of utility for the consumer 4.1.4. The slope of an indifference curve is negative 4.1.4.1. If an individual moves from ( ) to ( ), the consumer gains some of good x, but must give up some of good y to remain indifferent between the two points 4.1.4.2. The slope gets less steep as more x is consumed 4.1.5. The slope of the indifference curve is related to the marginal rate of substitution 4.1.5.1. The negative of the slope of the indifference curve (U1) at some point is the marginal rate of substitution 4.1.6. The slope of the indifference curve (or the MRS) shows what trades the consumer is willing to make 4.2. The x, y quadrant is dense with indifference curves 4.2.1. Each combination of x and y yields some level of utility 4.2.2. The amount of utility achieved on the different indifference curves isn’t important, only that it is possible to compare them and identify, for any two, which is higher than the other x1 y1 x2 y2Chapter 3 lecture outline AAEC 3315, Benson 5 4.2.3. Can any of those indifference curves intersect? 4.2.3.1. This would be a violation of the transitivity axiom. Why? 4.3. The indifference curves are convex 4.3.1. A convex set if any two points within the set can be joined by a straight line that is contained completely within the set 4.3.2. The assumption that MRS is diminishing is equivalent to assuming that indifference curves are convex 4.3.2.1. Or that the set of all combinations of x and y that are at least as preferred as is a convex set 4.3.2.2. Graph of all points at least as preferred as with diminishing MRS and without diminishing MRS 4.3.3. Convex indifference curves (and diminishing MRS) illustrate that consumers prefer balance in consumption 4.3.3.1. If is as preferred as , then “more balanced” bundles of x and y will be preferred to either or 4.3.3.2. All points on a straight line between and are “more balanced” than the endpoints, and all those points would like within the convex set of preferred point 4.4. Example: utility and the MRS 4.4.1. Assume a person’s ranking of hamburgers, y, and soft drinks, x, could be represented by the utility function √ 4.4.2. An indifference curve for the function above is found by identifying the set of combinations of x and y that yield the same level of