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day2 - PADP 6950 Founda1ons of Policy Analysis Consumer...

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Unformatted text preview: PADP 6950: Founda1ons of Policy Analysis Consumer Choice Angela Fer1g, PhD Economic Theory of the Consumer We assume that consumers are ra1onal decision-makers They purchase the bundle of goods that maximizes their happiness, or u1lity, subject to what they can afford The u1lity-maximizing bundle of goods is also called the op1mal bundle 1 Basic assump1ons of the model of consumer choice There are 2 goods available to the consumer, X and Y The consumer has preferences over combina1ons (or bundles) of the 2 goods. The ordered pair (x,y) is intended to mean the consump1on bundle that has x units of good X and y units of good Y For example, let A=(1,15) denote the bundle where the consumer has 1 unit of good X and 15 units of good Y Y 15 10 5 5 10 15 X Basic assump1ons of the model of consumer choice We assume that consumer preferences sa1sfy a few basic rules: Preferences are complete Either bundle A is preferred to bundle B, B is preferred to A, or the consumer is "indifferent" between A and B Preferences are transi.ve If A is preferred to B and B is preferred to C, then A is preferred to C Preferences are con.nuous If A is preferred to B, then bundles that are sufficiently "close" to A must also be preferred to B 2 U1lity func1ons Here is a fundamental result from mathema1cal economics: If preferences are complete, transi1ve, and con1nuous, then they can be "represented" by a con1nuous "u1lity func1on." This means it is possible to construct a precise rela1onship U that maps consump1on bundles into levels of u1lity U1lity is the happiness or sa1sfac1on the consumer gets from consump1on ac1vi1es BUNDLE A B C U U U UTILITY 10 5 1 U(A) = 10 U(B) = 5 U(C) = 1 A is preferred to B, and B is preferred to C U1lity func1ons The units in which u1lity is measured do not ma`er it only ma`ers how the bundles are ordered according to the u1lity func1on The important thing is that A provides more u1lity than B (because this means A is preferred to B), not that A provides 5 more units of u1lity than B If we instead wrote U(A) = 20, U(B) = 18 and U(C) = 14, the u1lity func1on would s1ll represent the exact same preferences 3 Indifference Curves An indifference curve shows all bundles of goods that provide the consumer with the same u1lity Thus indifference curves map out the consumer's preferences The tables below illustrate two indifference curves: X 5 10 15 20 Y 15 10 6 4 Utility 10 10 10 10 X 5 10 15 20 Y 20 14 10 8 Utility 20 20 20 20 Graphing Indifference Curves Graph of the indifference curves from the previous table: Y 20 15 10 5 X 5 10 15 20 4 Important Features of Indifference Curves Indifference curves are downward-sloping Y < 0 X > 0 If you gain some X, you have to lose some Y in order to remain indifferent Indifference curves cannot cross each other B A C Consumer must be indifferent between A and B (because C is just as good as both) But B has more of both goods than A, so should prefer B to A The Slope of the Indifference Curve The slope of an indifference curve measures the amount of good Y the consumer is willing to give up for another unit of good X (while holding u1lity constant) 15 10 6 5 10 15 Another name for the absolute value of the slope of the indifference curve is the marginal rate of subs.tu.on The MRS diminishes as you move to the right 5 Diminishing MRS Diminishing MRS along an indifference curve means: The more units of X the consumer has, the fewer units of Y he or she is willing to give up for an addi1onal unit of X Basically, this means the consumer likes variety in consump1on Even though it is typically assumed, diminishing MRS does not always apply "Perfect subs1tutes": MRS is constant (plain socks vs. striped socks just care about total # of socks) "Perfect complements": MRS is either zero or infinite (lem shoes vs. right shoes cannot trade them off because you need both) Well-behaved preferences Are monotonic (or "non-sa1ated") If bundle B has more of each good than bundle A, then B is preferred to A Are bowed/convex (diminishing MRS) If bundle A has a li`le of both goods and bundle B has a lot of one good and very li`le of the other, then A is preferred to B Averages are preferred to extremes 6 How to Draw an Indifference Curve from a U1lity Func1on An Example of a U1lity Func1on: U=y2x2 Let U=10: y2x2=10 Solve this equa1on for Y in terms of X and you get: y = sqrt(10)/x Make table of plots: X 0 1 2 3 4 5 Y The Budget Line The consumer cannot simply choose whichever bundle he or she wants Consump1on decisions are limited by what is affordable What the consumer can afford depends on: Income Prices The consumer's budget constraint (or "budget line") shows all affordable combina1ons of X and Y 7 The Budget Line The equa1on for the budget line can be obtained by insis1ng that total expenditures on X and Y not exceed the consumer's income: I = PXX + PYY Income = Expenditure on X + Expenditure on Y Solve this equa1on for Y in terms of X and you get: Y = (I / PY) (PX / PY)X Recall: Y=b+mX (equa1on for a line) This is the equa1on of a line in X-Y space with slope -(PX/PY) and ver1cal intercept (I/PY) Graph of the Budget Line Graph the budget line if income is equal to I, the price of X is PX and the price of Y is PY: Y I / PY Slope = -PX / PY X I / PX 8 Changes in the Budget Line The loca1on of the budget line changes if prices or income change Suppose income increases: Y Suppose the price of good X increases: Y X X Changes in the Budget Line Suppose the price of good Y increases: Y X Suppose the price of X decreases: Y X 9 Consumer Equilibrium We use the theory of the consumer to locate the op1mal consump1on bundle Assume the consumer's objec1ve is to maximize u1lity This means the consumer tries to reach the highest possible indifference curve subject to staying on the budget line We say the consumer is in "equilibrium" when he / she consumes the u1lity-maximizing (or op1mal) bundle Consumer Equilibrium Y X The consumer's u1lity-maximizing bundle is at a point of tangency between the budget line and one of the indifference curves 10 Effects of Changes in Income Suppose the consumer has an increase in income. How does this affect the u1lity- maximizing bundle? Y1* 1 X1* Effects of Changes in Price Suppose there is an increase in the price of X. What happens to the op1mal bundle? Y1* 1 X1* 11 ...
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