2_slides_ch3_Nicholson123_17Jan2024.pptx

Economics Charts

1. 1 Chapter 3 PREFERENCES AND UTILITY Copyright ©2005 by South-Western, a division of Thomson Learning. All rights reserved.

2. 2 Axioms of Rational Choice  

3. 3 Axioms of Rational Choice Transitivity if A is preferred to B, and B is preferred to C, then A is preferred to C assumes that the individual’s choices are internally consistent

4. 4 Axioms of Rational Choice Continuity if A is preferred to B, then situations suitably “close to” A must also be preferred to B used to analyze individuals’ responses to relatively small changes in income and prices

5. 5 Utility Given these assumptions, it is possible to show that people are able to rank in order all possible situations from least desirable to most Economists call this ranking utility if A is preferred to B, then the utility assigned to A exceeds the utility assigned to B U (A) > U (B)

6. 6 Utility Utility rankings are ordinal (not cardinal) in nature they record the relative desirability of commodity bundles Because utility measures are not unique, it makes no sense to consider how much more utility is gained from A than from B It is also impossible to compare utilities between people.

7. 7 Utility Assume that an individual must choose among consumption goods x 1 , x 2 ,…, x n The individual’s rankings can be shown by a utility function of the form: utility = U ( x 1 , x 2 ,…, x n ; other things) this function is unique up to an order-preserving transformation

8. 8 Indifference Curves An indifference curve shows a set of consumption bundles among which the individual is indifferent Quantity of x Quantity of y x 1 y 1 y 2 x 2 U 1 Combinations (x 1 , y 1 ) and (x 2 , y 2 ) provide the same level of utility

9. Monotonic Preferences Monotonic Preferences (Monotonicity) More of a good is preferred to less. Thus, utility increases as quantity of a good increases. 9

10. 10 Economic Goods In the utility function, the x ’s are assumed to be “ goods ” more is preferred to less Quantity of x Quantity of y x* y* Preferred to x*, y* ? ? Worse than x*, y*

11. 11 Consumer theory assumes: Monotonic preferences or local non-satiation

12. 12

13. 13 Indifference Curves An indifference curve shows a set of consumption bundles among which the individual is indifferent Quantity of x Quantity of y x 1 y 1 y 2 x 2 U 1 Combinations (x 1 , y 1 ) and (x 2 , y 2 ) provide the same level of utility

14. 14 Marginal Rate of Substitution The negative of the slope of the indifference curve at any point is called the marginal rate of substitution ( MRS ) Quantity of x Quantity of y x 1 y 1 y 2 x 2 U 1

15. 15 Marginal Rate of Substitution MRS changes as x and y change reflects the individual’s willingness to trade y for x Quantity of x Quantity of y x 1 y 1 y 2 x 2 U 1 At ( x 1 , y 1 ), the indifference curve is steeper. The person would be willing to give up more y to gain additional units of x At ( x 2 , y 2 ), the indifference curve is flatter. The person would be willing to give up less y to gain additional units of x

16. 16 Indifference Curve Map Each point must have an indifference curve through it Quantity of x Quantity of y U 1 < U 2 < U 3 U 1 U 2 U 3 Increasing utility

17. 17 Transitivity Can any two of an individual’s indifference curves intersect? Quantity of x Quantity of y U 1 U 2 A B C The individual is indifferent between A and C. The individual is indifferent between B and C. Transitivity suggests that the individual should be indifferent between A and B But B is preferred to A because B contains more x and y than A

18. 18 Convexity A set of points is convex if any two points can be joined by a straight line that is contained completely within the set. Quantity of x Quantity of y U 1 Balance bundle is preferred Diminishing MRS x* y*

19. 19 Convexity If the indifference curve is convex, then the combination ( x 1 + x 2 )/2, ( y 1 + y 2 )/2 will be preferred to either ( x 1 , y 1 ) or ( x 2 , y 2 ) Quantity of x Quantity of y U 1 x 2 y 1 y 2 x 1 This implies that “well-balanced” bundles are preferred to bundles that are heavily weighted toward one commodity (x 1 + x 2 )/2 (y 1 + y 2 )/2

20. 20 Utility and the MRS Suppose an individual’s preferences for hamburgers ( y ) and soft drinks ( x ) can be represented by Solving for y , we get y = 100/ x Solving for MRS = - dy / dx : MRS = - dy / dx = 100/ x 2

21. 21 Utility and the MRS MRS = - dy / dx = 100/ x 2 Note that as x rises, MRS falls when x = 5, MRS = 4 when x = 20, MRS = 0.25

22. 22 Marginal Utility Suppose that an individual has a utility function of the form utility = U ( x,y) The total differential of U is Along any indifference curve, utility is constant ( dU = 0)

23. 23 Deriving the MRS Therefore, we get: MRS is the ratio of the marginal utility of x to the marginal utility of y

24. 24 Diminishing Marginal Utility and the MRS Intuitively, it seems that the assumption of decreasing marginal utility is related to the concept of a diminishing MRS diminishing MRS requires that the utility function be quasi-concave this is independent of how utility is measured diminishing marginal utility depends on how utility is measured Thus, these two concepts are different

25. 25 Examples of Utility Functions Cobb-Douglas Utility utility = U ( x,y ) = x  y  where  and  are positive constants The relative sizes of  and  indicate the relative importance of the goods

26. 26 Examples of Utility Functions Perfect Substitutes utility = U ( x , y ) =  x +  y Quantity of x Quantity of y U 1 U 2 U 3 The indifference curves will be linear. The MRS will be constant along the indifference curve.

27. 27 Examples of Utility Functions Perfect Complements utility = U ( x , y ) = min ( x ,  y ) Quantity of x Quantity of y The indifference curves will be L-shaped. Only by choosing more of the two goods together can utility be increased. U 1 U 2 U 3

28. Q: The preference relation is rational if it satisfies the following properties: Completeness and transitivity e.g., If these properties are satisfied, a consumer can rank all possible bundles with consistent comparisons among all alternatives and each bundle can be put into one indifference set and no more than one indifference set. A preference relation can be represented by a utility function only if it is a rational. Ref: Mas-colell, Microeconomic Theory 28

29. Q: What is/are the axiom(s) that imply that the indifferences curves must have a negative slope of the indifference curve? Monotonicity Note: Non-satiation required Q: What is/are the axiom(s) that imply that the indifference curves exhibit a diminishing marginal rate of substitution?  Strict convexity Note: Convexity required 29