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Notes-04_Utility-2

# Notes-04_Utility-2 - Econ 3130 Spring 2012 R Masson Chapter...

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Econ 3130, Spring 2012, R. Masson Chapter 4: p. 1 Chapter 4: Utility I. What is the role of this chapter? A. One way to generate indifference curves which are “well behaved” (e.g., not crossing) is the use of mathematics 1. We can mathematically generate “Utility” as a function U=U(x 1 ,x 2 ) which has indifference curves in two-space as in Chapter 3 a. NB: The graphical functional forms are limited only by the imagination, mathematical functional forms are restricted by tractability B. Second, we may want to address the concept of indifference curves with more than two goods 1. If we have x 1 ,x 2 ,x 3 an indifference relationship is no longer a curve, it is a surface and cannot easily be graphed a. Recall gin, vermouth and whiskey C. Third we may want to use econometrics, which requires formulae 1. Characteristics of the formulae may be important to model. 2. Example a. Suppose we want to estimate demand for x 1 and x 2 given M,p 1 ,p 2 (1) We could regress x 1 on d 1 (M,p 1 ,p 2 ) where d 1 is some functional form, for example the regression x 1 = ± 0 + ± 1 M+ ± 2 p 1 + ± 3 p 2 (a) One would have linear demand. The slope of the demand curve would be 0 x 1 / 0 p 1 = ± 2 , where ± 2 <0 (b) For most goods (“normal goods”) one would expect ± 1 >0 (c) One would also expect ± 3 >0 (as costs of substitutes rise, buy less substitute and more x 1 ) (2) At the same time we could regress x 2 on some d 2 (M,p 1 ,p 2 ) (3) But there is a problem if we run two separate regressions, there is no guarantee that ( is the value from the estimated demand function for some specific M,p 1 ,p 2 ) unless we impose some mathematical

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Econ 3130, Spring 2012, R. Masson Chapter 4: p. 2 1 Strictly speaking there may be some caveats that are relevant here once one aggregates to multiple individuals. We leave that caveat to be pondered by those of you (if any) who intend to pursue a Ph.D. in Economics. restrictions that the estimates of the two demand functions are consistent with a cross equation restriction (simultaneity in econometrics). 1 (a) And even if one has , one may need restrictions to assure that for different values 3. So, mathematics can be useful for describing Preferences as in Chapter 3 II. Cardinal and Ordinal Utility A. Consider the following indifference curve map 1. If we generated these indifference curves from mathematical formulae, each of U 1 ,U 2 and U 3 would have numerical values. a. Assume x and y are both economic goods then all we would know is that U 3 >U 2 >U 1 would order these curves such that more preferred outcomes were assigned higher numbers b. Possible values (an infinite set of values are possible) include {U 1 ,U 2 ,U 3 }={1,2,3}, {U 1 ,U 2 ,U 3 }={101,102,103}, and {U 1 ,U 2 ,U 3 }={1,100,101} (1) Any of these would numerically say that U 3 >U 2 >U 1
Econ 3130, Spring 2012, R. Masson Chapter 4: p. 3 c. When we apply a mathematical function which generates numerical values of the U i s, all we care about is their order, so we call this Ordinal Utility d. If we assigned meaning to the numbers, like for {U 1 ,U 2 ,U 3 }={1,2,3} saying that if one achieves U 2

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Notes-04_Utility-2 - Econ 3130 Spring 2012 R Masson Chapter...

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