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# notes_2150_sep_23S.docx

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Economics
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Economics 2150A/B
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Prof
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Fall

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Ch. 3 Goal: Develop a Model of Consumer behaviour to Derive demand curves Called theory of Rational Consumer Choice Ch. 3 – Develop a way to model consumer preferences with utility curves Ch. 4 – Add a budget constraint to get consumer maximization problem and the Ordinary Demand Curve Ch. 5 – Applications of Demand Theory I. Consumer Theory assumes self-interest and rationality among consumers -self-interest: the consumer will behave in a way that maximizes his or her satisfaction (utility). -Indifference curves (I.C.) represent the level of utility that the consumer derives from consuming particular bundles of goods in a world where there are only two goods. -Shape of the indifference curves will represent the relative preference that the consumer has for one good over the other good. II. Self-interest assumption is a strong assumption. Says Individuals always make choices to make themselves better off. A. Experimental economics Reality: preferences are less well-defined in children. B. The theory of self-interest does not eliminate the possibility of charitable giving. Charitable giving can be explained with self-interest if we: -Express the consumer’s utility/satisfaction as a function of someone else’s utility. -Donating to charity and making others happy may raise the utility of an individual if that individual cares about the consumption (or utility) of another individual. III. Bundle of Goods A. Assume there are only 2 Goods: Clothing and Food The point H represents a consumption bundle in which the person consumes 0 units of Food (F) and 30 untis of Clothing (C). Point D = bundle with 20 units of F and 10 units of C. (20,10) B. Consumer preferences tell us how a consumer would rank these Market baskets assuming the baskets are available at no cost. IV. Preference postulates: If a consumer is rational, then we assume that the preferences possess three important characteristics: 1. Completeness 2. Transitivity 3. More is Better These are the 3 underlying assumptions behind utility functions. 1) Preferences are complete *The consumer can always rank any 2 bundles in the space. (A > B) or (B > A) or (A=B) Either 1) bundle A is preferred to bundle B, 2) bundle B is preferred to A, or 3) the consumer is indifferent between A and B. Completeness is a strong assumption as it -implies familiarity with every good. -compares bundles with trivial differences. 2) Preferences are Transitive (i.e. consistent): If bundle A is at least as good as B, and B is at least as good as C, then A is at least as good as C. If (A > B) and (B > C), then (A > C). 3) More is better – (i.e. Nonsatiation) Consumer prefers to have a bundle with more of a good as long as there is not less of the other good. Having more of both goods is better. (MUx>0) and (MUy>0) See figure 3.1 above. – Does the Consumer prefer E (20,30) to D(20,10) Why? -Does the consumer prefer G(40,20) to D(20,10) Why?. V. Ordinal v. Cardinal Ranking 1.Ordinal rankings – give info about the order, not intensity, in which a consumer ranks baskets. Ex: consumer likes (3,3) better than (1,1) bec more is better, but we can’t say how much more she likes (3,3) over (1,1). We can’t say she likes (3,3) three times as much as (1,1). 2. Cardinal rankings – give info about the intensity of preferences. Ex: we not only know she prefers (3,3) to (1,1), but we can measure the strength with which she prefers (3,3) to (1,1). Consumers often can’t tell you how much they prefer a bundle with pizza and beer over a bundle with a hamburger and a soft drink. 3. So preferences are ordinal, not cardinal, even though we may calculate levels of utility as an exact number. A number like U(F,C)=3 and U(F,C)=5 only tells you that U=5 represents a higher level of satisfaction than U=3. 4. Can’t compare preferences across different individuals, bec U not cardinal. VI. Properties of Indifference Curves Bec of the assumptions about rationality made above, we know that indifference curves will follow four properties: 1) When the consumer likes both goods (MUx >0 and MUy >0), all of the indifference curves will have negative slopes. Q: What if the good on the x axis is a “bad,” like pollution (MUx<0). How would you graph the preferences? 2) Indifference Curves cannot intersect. 3) Every consumption basket lies on one and only one indifference curve. -From property that indifference curves cannot intersect. 4) Indifference curves are not “thick.” B has more of both goods and must be preferred to A; so they cannot lie on the same IC. What do the utility functions look like? A. U is function of One good, written U(y) 1/2 1. Suppose Utility takes the following form: U(y) = y Utility function measures the level of satisfaction that a consumer receives from any basket of goods. Suppose y =# of ice cream cones. U measures the level of satisfaction that he gets from consuming a particular number of ice cream cones. Q: Does this function satisfy our definition of preferences? 1. Complete – defines a level of utility for every basket of Y. 2. More is better – more ice cream consumption leads to higher utility Bundle A: y = 1 cone then U = (1) ½ = 1 Bundle B: y = 4 cones then U = 2 Bundle C: y = 9 cones then U = 3 As the no. of cones increases, satisfaction increases; so more is better. – U is a monotonically increasing function of x. Monotonically increasing means that the function f(x) always increases as x increases and each value of x maps to only one point on f(x). Monotonically increasing; if for all x and y such that x ≤ y one has f(x) ≤ f(y), so f preserves the order. 3. Transitivity – B (U=2) > A(U=1) and C(U=3) > B(U=2) ; so C > A. 2. Marginal Utility a. MUy = ΔU/ΔY = slope of total utility curve = the additional utility from consuming one more unit of y. = The change in total utility from a change in the consumption of good y. This slope changes depending on how much y has already been consumed. Derivative=slope dU(y) MU = dy is another way to express MU. -1/2 MU = dU/dy = (1/2)y -1/2 At y= 4, U’(y) = ΔU/Δy = ½(y) = ¼. b. Principle of Diminishing Marginal Utility - as we consume more of the good, we eventually reach a point where MU begins to fall for each additional unit of the good consumed. Ex: you get less satisfaction from eating another ice cream cone if you have already consumed 10 cones instead of 0 cones. c. Marginal utility is always positive implied by more is better – not realistic because you become satiated with ice cream cones at some point. In fact, you may get negative marginal utility from the 11 th cone if your stomach is hurting (total utility starts to decrease). We will assume that consumers will never experience negative MU because they will not pay for a good if it reduces their pleasure. C. Utility with two goods U(x,y) These are graphs of U(x,y) = x ½ y 1/2 Now Utility is a function of the consumption of two goods, x = food and y= clothing. All of the points A(2,8), B(4,4), and C(8,2) yield the same utility = 4. At point A: U=(2) ½ (8)1/= 4 Each level of utility is represented by an Indifference Curve (IC) – every bundle on the IC gives the same level of utility. These points are on the same IC where U=4. See 2-D graph. 2. Marginal Utility with two goods U(x,y) - partial derivative. ∂U (x, y) ∂U MUx = ∂x and MUy = ∂ y MUx= rate of cha
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