Chapter 03 - Rational Consumer ChoiceChapter 3RATIONAL CONSUMER CHOICEBoiling Down Chapter 3This chapter gets down to the nitty-gritty of decision making. The process of choosingamong alternatives requires, first, a clear understanding of the market baskets available toyou and the prices that apply. Second, it requires that you decide which of two alternativegoods you prefer.The first requirement can be depicted graphically with a budget line. Each intercept ofthe line shows how much of a good could be purchased if all of one's income was spent onthat commodity. The straight line connecting the two intercepts illustrates that the tradeoffrate between goods is constant, a fact that is true if each consumer is a price taker in themarket and can buy all she can afford at the constant market price.This graphical model can be shown algebraically if it is recognized that all incomemust go to only two commodities in a two-dimensional two-goods model. All of income(M) will be spent on good X and good Y. The amount spent on each will be the price of thegood times the quantity of the good purchased. Therefore M = PxX + PyY where Px andPy are the prices of goods X and Y, which then are multiplied times the quantities of X andY that are purchased. Simple algebraic manipulation of the equation shown above leads tothe equation that represents the budget line: Y = M/Py- (Px/Py) XWhen the income level and the prices of the two goods are known, then thecombinations of X and Y that are available with that income are determined.Experimenting on a graph with various income levels and prices, varying one at a time,will illustrate how these changes alter the set of possible market baskets available to theconsumer. Increasing M in the equation above will increase the X and Y intercepts but notaffect the slope of the line. Therefore an income increase is shown by a parallel rightwardshift of the budget constraint. A student should observe the change in slope and location ofthe budget line equation shown above as income and commodity prices are varied one byone. Graphing each change will help you see how the market baskets available to theconsumer are affected by income and price changes.Next is the task of representing the preferences of the consumer. It is assumed that1. consumers can decide between alternative market baskets with even very small changes in composition (completeness).2. if a consumer prefers A over B and B over C, he also will prefer A over C (transitivity).3. consumers want more rather than less.3-1Chapter 03 - Rational Consumer ChoiceIf all these assumptions apply, then it is possible to construct in a space of all possiblemarket baskets a set of points that are equally preferred because they result in the samelevel of pleasure, or utility, as it is usually called. All these points taken together are calledan indifference curve, because the consumer does not care which of the alternatives he has.Any baskets to the northeast of an indifference curve will have higher utility sinceinevitably such a basket has more of at least one of the goods. The absolute slope of theindifference curve specifies at each point the rate at which the consumer is willing to giveup good Y in exchange for more of good X without loss of pleasure. It is called themarginal rate of substitution of X for Y (MRS x for y).Indifference curves are usually curved in a manner convex to the origin in order toshow that consumers gain less benefit from an additional unit of a good if they alreadyhave large quantities of the good (diminishing marginal utility). These indifference curvescould be straight lines or even concave to the origin if more of a good does not diminishtaste for the good, or if people are inclined to want more the more they have of a good. When the constraint line and the indifference curve are put on the same graph, showingall possible market baskets, the maximization process becomes one of trying to move outto the highest possible level of pleasure (indifference curve) without exceeding theconstraint line, which is set by the income level of the consumer. This movement to thenortheast must necessarily stop when the indifference curve becomes tangent to the budgetline, because any further movement would give the consumer a market basket that shecould not afford. Since the slope of the indifference curve equals the MRS x for y and theslope of the budget constraint equals the price ratio between Px and Py, it is easy to seethat the following statement will be true when the consumer has maximized her utility:MRS x for y = the Px/Py. The basket for X and Y will be continuously juggled to fulfillthis equilibrium condition which maximizes utility subject to the budget limitations.Where multiple goods are available, one good can be traded off against a composite ofother goods, which is measured as the amount of income remaining after the commodity inquestion is paid for. In effect, the vertical axis of the graph measures the income remainingto spend on other goods when a specific amount of good X is consumed. The usefulness ofthese tools in understanding consumer choice and public policy outcomes is far greaterthan first meets the eye. In your text the food stamp case in Chapter 3 and demand analysisin Chapter 4 will illustrate this point.(Chapter 3 Appendix) The optimization process can also be developed by using autility function statement. Using this method, which in your text is shown as the equationU(F,S) = FS, a set of indifference curves can be derived. The slope of the indifferencecurves is shown to equal the ratio of the marginal utilities of the two commodities in theconsumer’s market basket. Equating the slope of the indifference curve (MUf/MUs) withthe slope of the budget line (Pf/Ps) will show where a person maximizes welfare byconsuming so that the last dollar spent on each item brings the same amount of utility(MUf/Pf = MUs/Ps). Indifference curve analysis requires a consumer to make ordinaljudgements about which market basket is preferred. No cardinal measurement of utility isrequired. Calculus can be used to show this maximization process. 3-2Chapter 03 - Rational Consumer ChoiceChapter Outline1. Rational consumer choice theory begins with a budget constraint or opportunity set.a. The slope of the constraint shows the relative price ratio of the two