1. 1 Stephen Chiu University of Hong Kong Utility Theory

2. 2 The cardinal approach The ordinal approach Consumer choice problem Intertemporal choice problem

3. 3 The cardinal approach In the 18 th century, Bentham proposed that the objective of public policy should be to maximize the sum of happiness in society Economics became the study of utility or happiness, assumed to be in principle measurable and comparable across people Marginal utility of income was higher for poor people than for rich people, so that income ought to be redistributed unless the efficiency cost was too high

4. 4 The ordinal approach Lionel Robbins (in 1932) argued that, Comparability of utility across people is not needed so long we are concerned about predicting choices Economics is about “the relationship between given ends and scarce means”, and how the “ends” or preferences came to be formed was outside its scope Only stable preferences are needed Robbins didn’t think that public policy could be analyzed within a formal economic framework

5. 5 The cardinal approach An agent’s utility level is like length or weight of an object that is objective and measurable An agent with utility level 3,000 is happier than another agent with utility level 200 But … John always looks happy and enthusiastic, and Smith unhappy and worrisome…

6. 6 The cardinal approach They both come to class... … given the same income and prices, John always spends his income the same way as Smith does

7. 7 The cardinal approach U 2 =600 U 3 =610 Food (units per week) Clothing (units per week) U 1 =500 W 1 =1000 W 2 =1M W 3 =1T Both John and Smith have the same indifference curve map!!!

8. 8 Why diversity in consumption? Cardinal approach – diversity because of diminishing marginal utility Ordinal approach – diversity despite no diminishing marginal utility; what is needed is MU/$ being equalized

9. 9 Consumer Choice problem Ordinal utility function indifference curve map Numbering of ICs unimportant, as long as they are order preserving Some regularity conditions (a.k.a. axioms) on ICs Budget constraint The problem becomes to max utility subject to budget constraint

10. 10 Perfect Substitutes Orange Juice (glasses) Apple Juice (glasses) 2341 1 2 3 4 0 Perfect Substitutes Perfect Substitutes Two goods are perfect substitutes when the marginal rate of substitution of one good for the other is constant.

11. 11 Perfect Complements Two goods are perfect complements when the indifference curves for the goods are shaped as right angles. Right Shoes Left Shoes 2341 1 2 3 4 0 Perfect Complements Perfect Complements

12. 12 Properties of ICs Map More is better Two ICs do not cross Bending toward origin Y X A C U1U1 U0U0 This is ruled out!

13. 13 Budget Constraints Budget Line F + 2C = $80 (I/P C ) = 40 Food (units per week) 406080 = (I/P F )20 10 20 30 0 A B D E G Clothing (units per week ) Pc = $2 P f = $1 I = $80 As consumption moves along a budget line from the intercept, the consumer spends less on one item and more on the other.

14. 14 Consumer Choice Budget Line U3U3 D Market basket D cannot be attained given the current budget constraint. Pc = $2 P f = $1 I = $80 Food (units per week) Clothing (units per week) 408020 30 40 0

15. 15 Consumer Choice Food (units per week) Clothing (units per week) 408020 30 40 0 U1U1 B Budget Line Pc = $2 P f = $1 I = $80 Point B does not maximize satisfaction because there exist some point A which is attainable and yields a higher satisfaction. -10C +10F A

16. 16 Consumer Choice V T U3U3 U1U1 B U Z R P OSQ A Optimal consumption budget is found where budget line and an IC are tangential to each other

17. 17 coffee tea U0U0 U1U1 U2U2 coffee Corner solutions are still possible Tangency condition need not hold

18. 18 The cardinal approach U 2 =600 U 3 =610 Food (units per week) Clothing (units per week) U 1 =500 W 1 =1000 W 2 =1M W 3 =1T Despite different numbering of ICs, John and Smith both choose the same bundle

19. 19 An application: Intertemporal Choice Our framework is flexible enough to deal with questions such as savings decisions and intertemporal choice. Suppose you live two periods: period 1 and period 2 You earn an income of 1,000 in period 1 and a pension of 500 in period 2 Interest rate r. That is, by saving $1 in period 1, you get back $(1+r) in period 2 You consider period 1 consumption and period 2 consumption perfect complement Question: how much should you save now?

20. 20 Intertemporal choice problem Income in period 2 C1C1 C2C2 1600 1000 500 Slope = -1.1 u(c 1,c 2 )=const Income in period 1 Intertemporal budget line

21. 21 1000-C 1 =S(1) 500+S(1+r)=C 2 (2) Substituting (1) into (2), we have 500+(1000-C 1 )(1+r)=C 2 Rearranging, we have 1500+1000r-(1+r) C 1 =C 2 > C Using C 1 =C 2 =C, we finally have Intertemporal choice problem

22. 22 Conclusions Ordinal utility theory is good enough so long as we want to study choice Cardinal utility theory is needed if we want to study public policy Happiness = subjective well being Happiness survey shows that average happiness in a nation remains the same level once per capita income reaches a certain level More on happiness if time permitted