Chapter 4. Consumer Choice. A Consumer s Budget Constraint. Consumer Choice

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1 Chapter 4 Consumer Choice Consumer Choice In Chapter 3, we described consumer preferences Preferences alone do not determine choices We must also specifi constraints In this chapter, we describe how consumer choices are constrained, and how choices are made subject to constraints A Consumer s Budget Constraint A consumer is assumed to have a given income to spend in a single period on two goods The budget constraint sas the spending on the two goods will equal the income available The consumer could choose not to spend all income, but this will not happen, since more is better. 1

2 An Equation for the Budget Line P + P = I The Budget Line: Diagram I/P I/P The Budget Line: Diagram I/P Is Point A Affordable? A: Yes B: No A I/P 2

3 The Budget Line: Affordable Bundles I/P I/P Slope of the Budget Line Rearrange the equation for the budget line to more easil identif the slope: P + P = I I P = P P P Slope = P Interpretation of the Slope The slope tells us the rate at which goods and are echanged in the market How man units of good must be given up to obtain a unit of in the market? 3

4 Suppose that I can spend a fied budget on goods X and Y: Let P = 6 and P =2 How man units of good Y must one give up to purchase a unit of good X? A: 1/3 B: 3 C: 12 Suppose that I can spend a fied budget of $100 to spend on goods X and Y: Let P = 6 and P =2 How man units of good Y must one give up to purchase a unit of good X? A: 1/3 B: 3 C: 12 Budget Line Shifts When income, I, increases, the budget line shifts outward in parallel fashion. When P increases, the budget line rotates inward (the intercept becomes smaller). When P increases, the budget line rotates inward (the intercept becomes smaller) 4

5 Suppose that income, the price of good X, and the price of good Y all double. What happens to the consumer s budget line? A: Shifts outward, or to the right. B Shifts inward, or to the left. C: It does not move. Suppose that income, the price of good X, and the price of good Y all double. What happens to the consumer s budget line? A: Shifts outward, or to the right. B Shifts inward, or to the left. C: It does not move. Suppose that the budget line shifts from the blue line to the red line. Which event could have occurred? P rose P fell P rose P fell 5

6 Suppose that the budget line shifts from the blue line to the red line. Which event could have occurred? P rose P fell P rose P fell Consumer Optimization A consumer will wish to obtain the highest possible utilit that is feasible according to the budget constraint The consumer will choose a bundle to get on the highest-utilit indifference curve such that the chosen bundle must be on or inside of the budget line. C Which point maimizes utilit subject to the budget constraint? A: A B: B C: C B A 6

7 A B C Which point maimizes utilit subject to the budget constraint? A: A B: B C: C The Tangenc Condition Normall, the consumer s optimum occurs at a point of tangenc between the budget line and an indifference curve The Tangenc Condition At a tangenc, the following condition must hold: MU MU P = P This sas that the slope of the budget line is equal to the slope of an indifference curve 7

8 Alternativel MU P MU = P This sas: At the consumer optimum, marginal utilit per dollar should be the same for all goods consumed in positive quantities. A At point A, which condition holds? A: MU MU > P P B: MU MU < P P A At point A, which condition holds? A: MU MU > P P B: MU MU < P P 8

9 A Corner Solution In some cases, it is possible that the solution to a utilit maimization problem will involve consumption of a single good Such outcomes are called corner solutions although the actuall occur at the boundaries of the product space If indifference curves were not conve to the origin, then corner solutions would be the tpical outcome A Corner Solution The Composite Good Convention Let good Y be a composite good This means that it represents ependiture on all other goods (other than good X). It is measured in dollar s worth units, hence it has a price of $1. This is a convenient analtical assumption It allows us to focus attention on one good, X, when man goods are included in potential market baskets. B collapsing all other goods into one, we can still use diagrams that assume just two goods total. 9

10 Application Suppose consumers choose between gasoline and all other goods. Further, suppose that the government announces a program that will alwas pa half of a consumer s gas ependiture. Show the consumer choice problem before the subsid is introduced. Show the consumer choice problem after the subsid is introduced. How much does the government spend buing gas for this consumer? Suppose the government had instead given the consumer an equal amount of cash. Would the outcome have been better, worse, or the same for that consumer? Revealed Preference As consumers make choices, the reveal information about their preferences Sometimes a sequence of choices permits us to infer whether the assumptions we have made about preferences are correct (i.e., our theor could be rejected b facts) Revealed Preference Eample Suppose that a consumer bus wine and roses: I = 200, P w = 10, P r =10 The consumer chooses w = 8 and r = 2 Now suppose that income remains the same, but prices change: P w = 8, P r =12 The consumer chooses w = 3.5 and r = 6 Assuming unchanged preferences, are these choices consistent with our theor of consumer behavior? A: Yes B: No 10

11 Income and Head Taes Consider an income ta and a head ta, the sizes of which have been set so that the government collects the same amount of mone under each ta. Which ta does the consumer prefer? A:The consumer is indifferent between the two taes, since he pas the same amount of mone under each ta. B:The consumer prefers the head ta, because it does not lower the relative wage as does the income ta. C: The consumer prefers the income ta, because it can be avoided b increasing the amount of leisure time consumed. D: The consumer ma prefer either ta, depending on whether the income ta increases or decreases the number of hours of work at the optimum. Refer to the diagram. If the consumer purchased basket B last ear and purchases basket C this ear, we can conclude that A:The consumer is not behaving optimall. B The consumer's tastes changed between this ear and last ear. C: The consumer's indifference curves cannot be conve. D: The law of demand does not hold for this consumer. The End 11