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In difficult words utility is measurable in an

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In difficult words: utility is measurable in an ordinal sense, but not in a cardinal sense Chapter 3: Consumers and their Preferences Slide 17 Example 3: If A=(10,5) and B= (7,6) and, for a certain consumer, U(A)=500 and U(B)=250, then. .. (a) Bundle A provides twice as much satisfaction as bundle B (b) This consumer is indifferent between A and 2 bundles of B (c) This consumer prefers bundle A over bundle B (d) This consumer prefers bundle A over bundle B (e) There is no way the consumer can rank these bundles because 10 is larger than 7 and while 5 is smaller than 6. Chapter 3: Consumers and their Preferences Slide 18 Rational Choice Rational Choice ± Trying to get the largest possible level of utility. In mathematical terms: In words: choose the consumption bundle (x,y) that maximizes utility subject to the budget constraint, taking prices and income as given , max ( , ) subject to xy Uxy px py M +≤ Example 4 : Let U(x,y)=2x+3y, px=6, py=3, and M=120. Graphically derive the optimal consumption bundle
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Chapter 3: Consumers and their Preferences Slide 19 Indifference curves ¾ Conclusion from the example: - It can still be painful to find the best bundle ¾ Solution for troubles: use indifference curves FIGURE 3-9 An Indifference Curve An indifference curve is a set of bundles that the consumer prefers equally. Chapter 3: Consumers and their Preferences Slide 20 Characteristics of Indifference Curves • Nonsatiation Æ IC’s slope downward • Nonsatiation + Transitivity Æ IC’s cannot cross each other • Nonsatiation Æ IC’s that are father from the origin represent higher levels of utility • Convexity Æ IC’s are bowed inward (they are convex) • See if you can prove these statements abouts ICs! Chapter 3: Consumers and their Preferences Slide 21 Rational choice once more Example 4 (continued): use the budget constraint and indifference curves to find the optimum to the consumer’s problem graphically Summary: Solving the consumer’s problem graphically • Move to IC that is the furthest away from origin (why this one?) that still has a point in the feasible set • Result: optimum bundle must be on budget line (nonsatiation) Solving the consumer’s problem mathematically • Note: the method below only works if IC’s have enough curvature and utility functions are not of the form min(ax,by) • Exploit the following two facts ¾ 1. Slope IC = slope budget line ¾ 2. Optimum lies on budget line
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Chapter 3: Consumers and their Preferences Slide 22 The slope of indifference curves 1) The marginal rate of substitution (MRS) Consider the bundle be (x 1 ,x 2 ). The marginal rate of substitution (MRS) of x 2 for x 1 is the amount of x 2 that the consumer must add to her bundle in order to compensate (i.e. keep the utility constant) for the loss of a small amount of x 1 Graphically: MRS is the absolute value of the slope of the IC Remarks: In general, the MRS is different for every different bundle (x 1 ,x 2 ) The convexity axiom implies that the MRS of x 2 for x 1 decreases as x 1 increases Interpretation: The more x 1 you have, the the more you are willing to give up in order to obtain an extra unit of x 2 Also: MRS of x 1 for x 2 decreases in x 2
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