Chapter 4 appendix PP152

# Chapter 4 appendix PP152 - CHAPTER 4 APPENDIX DEMAND THEORY...

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CHAPTER 4 APPENDIX DEMAND THEORY – A MATHEMATICAL TREATMENT EXERCISES 1. Which of the following utility functions are consistent with convex indifference curves and which are not? a. U(X, Y) = 2X + 5Y b. U(X, Y) = (XY) 0.5 c. U(X, Y) = Min(X, Y), where Min is the minimum of the two values of X and Y. Indifference maps for the three utility functions are presented in Figures 4A.1(a), 4A.1(b), and 4A.1(c). The first is a series of straight lines, the second is a series of hyperbolas and the third is a series of L-shaped curves. Only the second utility function has strictly convex indifference curves. To graph the indifference curves which represent the preferences given by U(X,Y) = 2X + 5Y, set utility equal to some level, U , and solve for Y to get X U Y 5 2 5- = . Since this is the equation for a straight line, the indifference curves are linear with intercept U 5 and slope 5 2- . The graph shows three indifference curves for three different values of U , where U < U 1 < U 2 . U U 1 U 2 U 2 U 1 2 U 2 2 U 5 U 1 5 U 2 5 Y X Figure 4A.1(a) To graph the indifference curves that represent the preferences given by U ( X , Y ) = ( XY ) 0.5 , set utility equal a given level U and solve for Y to get Y = U 2 X . By plugging in a few values for X and solving for Y, you will be able to graph the indifference curve for utility value U , which is illustrated in Figure 4A.1(b), along with the indifference curve for a larger utility value, U 1 . X Y U U 1 Figure 4A.1(b) To graph the indifference curves which represent the preferences given by U ( X , Y ) = Min ( X , Y ) , first note that utility functions of this form result in indifference curves that are L-shaped and represent a complementary relationship between X and Y. In this case, for any given level of utility U , the minimum value of X and Y will also be equal to U . If X increases but Y does not, utility will not change. If both X and Y change, then utility will change, and we will move to a different indifference curve. See the following table which illustrates how the utility value depends on the amounts of X and Y in the consumption bundle. X Y U 10 10 10 10 12 10 12 12 12 12 11 11 8 11 8 8 9 8 X Y U o U 1 U U 1 U U 1 Figure 4A.1(c) 2. Show that the two utility functions given below generate the identical demand functions for goods X and Y: a. U(X, Y) = log(X) + log(Y) b. U(X, Y) = (XY) 0.5 If two utility functions are equivalent, then the demand functions derived from them are identical. Two utility functions are equivalent if you can transform them are identical....
View Full Document

## This note was uploaded on 01/04/2012 for the course ECON 101 taught by Professor Pr.makushi during the Spring '11 term at San Diego Christian.

### Page1 / 11

Chapter 4 appendix PP152 - CHAPTER 4 APPENDIX DEMAND THEORY...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online