Maximizing Total Utility: Law of Diminishing Marginal Utility

1. Chapter 5 Consumer choices The Benefit Side of Demand

2. Recall: The Law of Demand • People do less of what they want to do as the cost of doing it rises • The benefit of an activity equals the highest price we’d be willing to pay to pursue it (i.e., the reservation price). • As the cost of an activity rises and exceeds the reservation price, less of the activity will be pursued.

3. The difference among needs, wants and demand • Needs: minimum requirement to stay alive • Wants: • “tastes” or “preferences” • quality of life • living standard • satisfaction • Demand: • Willingness • Ability

4. Translating Wants into Demand • Measuring Wants: The Concept of Utility • Utility • The satisfaction people derive from their consumption activities • Assumption • People allocate their income to maximize their satisfaction or total utility

5. Utility • Total utility: • Total satisfaction from consuming a certain amount of goods and services • Average utility: • Average satisfaction from consuming each unit of goods and services • AU = TU / Q • Marginal utility: • Additional utility from consuming one additional unit of goods and services • MU = change in TU / change in Q

6. Example:

7. Sarah’s Total Utility from Ice Cream Consumption Figure 5.2, p.130 Based on table 5.1, p.129

8. Diminishing Marginal Utility Figure 5.3, p. 131 Based on Table 5.2, p.130

9. Key Points • TU first increases then max out and starts to decrease • TU increases at a slower pace • TU is maximized when MU=0 • MU is decreasing but positive when TU is increasing • MU is decreasing and negative when TU is decreasing • MU = 0 when TU is maximized

10. Decision Rule • The goal: max TU • Decision rule: • Increase Q as long as MU > 0 • consume up to Q when MU = 0

11. In the example • Did not consider cost • One product: no trade-off introduce cost include other products --to represent consumption bundle --to show trade-off

12. Translating Wants into Demand • The Law of Diminishing Marginal Utility • The tendency for the additional utility gained from consuming an additional unit of a good to diminish as consumption increases beyond some point

13. Translating Wants into Demand • Allocating a fixed income between two goods • Assume • Two goods: Chocolate and vanilla ice cream • Price of chocolate equals $2/pint • Price of vanilla equals $1/pint • Sarah’s budget = $400/yr • Currently Sarah is consuming 200 pints of vanilla and 100 pints of chocolate • Question • Is Sarah maximizing her total utility?

14. Marginal Utility Curves for Two Flavors of Ice Cream (II) Figure 5.5, p. 133

15. Translating Wants into Demand • At 200 vanilla and 100 chocolate • Marginal utility vanilla/P • $12/1 = 12 utils/$ • Marginal utility chocolate/P • 16/2 = 8 utils/$ • MU/P for vanilla not equal to MU/P for chocolate • MU/P for vanilla higher than MU/P for chocolate • Increase Q for vanilla to reduce MU for V • Decrease Q for chocolate to increase MU for Ch Until MU/P for vanilla = MU/P for chocolate

16. Optimal Consumption Figure 5.6, p.134

17. Translating Wants into Demand • The Rational Spending Rule • Spending should be allocated across goods so that the marginal utility per dollar is the same for each good.

18. Translating Wants into Demand • The Rational Spending Rule • How is the rational spending rule related to the cost-benefit principle? • How should Sarah respond to a reduction in the price of chocolate ice cream?

19. Translating Wants into Demand • Assume • Budget = $400 • PC = $2 & PV = $1 • QC= 75 & QV = 250

20. Translating Wants into Demand • Assume • Price of chocolate falls to $1