1. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 1 of 43 Theoretical Tools of Public Finance 2.4 Welfare Implications of Benefit Reductions: The TANF Example Continued 2.3 Equilibrium and Social Welfare 2.2 Putting the Tools to Work: TANF and Labor Supply Among Single Mothers 2.1 Constrained Utility Maximization Chapter 2 2.5Conclusion theoretical tools The set of tools designed to understand the mechanics behind economic decision making. empirical tools The set of tools designed to analyze data and answer questions raised by theoretical analysis.

2. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 2 of 43 Constrained Utility Maximization 2. 1 utility function A mathematical function representing an individual’s set of preferences, which translates her well-being from different consumption bundles into units that can be compared in order to determine choice. constrained utility maximization The process of maximizing the well-being (utility) of an individual, subject to her resources (budget constraint). models Mathematical or graphical representations of reality.

3. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 3 of 43 Constrained Utility Maximization 2. 1 Preferences and Indifference Curves

4. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 4 of 43 Constrained Utility Maximization 2. 1 Preferences and Indifference Curves indifference curve A graphical representation of all bundles of goods that make an individual equally well off. Because these bundles have equal utility, an individual is indifferent as to which bundle he consumes. Indifference curves have two essential properties, both of which follow naturally from the more-is-better assumption: 1.Consumers prefer higher indifference curves. 2.Indifference curves are always downward sloping.

5. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 5 of 43 Constrained Utility Maximization 2. 1 Preferences and Indifference Curves

6. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 6 of 43 Constrained Utility Maximization 2. 1 Utility Mapping of Preferences Underlying the derivation of indifference curves is the notion that each individual has a well-defined utility function. A utility function is some mathematical representation U = f(X 1, X 2, X 3, …), where X 1, X 2, X 3, and so on are the goods consumed by the individual and f is some mathematical function that describes how the consumption of those goods translates to utility.

7. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 7 of 43 Constrained Utility Maximization 2. 1 Utility Mapping of Preferences Marginal Utility marginal utility The additional increment to utility obtained by consuming an additional unit of a good. This utility function described exhibits the important principle of diminishing marginal utility: the consumption of each additional unit of a good makes an individual less happy than the consumption of the previous unit.

8. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 8 of 43 Constrained Utility Maximization 2. 1 Utility Mapping of Preferences Marginal Utility

9. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 9 of 43 Constrained Utility Maximization 2. 1 Utility Mapping of Preferences Marginal Rate of Substitution marginal rate of substitution (MRS) The rate at which a consumer is willing to trade one good for another. The MRS is equal to the slope of the indifference curve, the rate at which the consumer will trade the good on the vertical axis for the good on the horizontal axis.

10. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 10 of 43 Constrained Utility Maximization 2. 1 Utility Mapping of Preferences Marginal Rate of Substitution

11. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 11 of 43 Constrained Utility Maximization 2. 1 Budget Constraints budget constraint A mathematical representation of all the combinations of goods an individual can afford to buy if she spends her entire income. opportunity cost The cost of any purchase is the next best alternative use of that money, or the forgone opportunity. When a person’s budget is fixed, if he buys one thing he is, by definition, reducing the money he has to spend on other things. Indirectly, this purchase has the same effect as a direct good-for-good trade.

12. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 12 of 43 Constrained Utility Maximization 2. 1 Budget Constraints

13. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 13 of 43 Constrained Utility Maximization 2. 1 Putting It All Together: Constrained Choice Marginal analysis, the consideration of the costs and benefits of an additional unit of consumption or production, is a central concept in modeling an individual’s choice of goods and a firm’s production decision.

14. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 14 of 43 Constrained Utility Maximization 2. 1 The Effects of Price Changes: Substitution and Income Effects

15. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 15 of 43 Constrained Utility Maximization 2. 1 The Effects of Price Changes: Substitution and Income Effects Income and Substitution Effects substitution effect Holding utility constant, a relative rise in the price of a good will always cause an individual to choose less of that good. income effect A rise in the price of a good will typically cause an individual to choose less of all goods because her income can purchase less than before.

16. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 16 of 43 Constrained Utility Maximization 2. 1 The Effects of Price Changes: Substitution and Income Effects Income and Substitution Effects normal goods Goods for which demand increases as income rises. inferior goods Goods for which demand falls as income rises.

17. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 17 of 43 Putting the Tools to Work: TANF and Labor Supply Among Single Mothers 2. 2 Identifying the Budget Constraint

18. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 18 of 43 Putting the Tools to Work: TANF and Labor Supply Among Single Mothers 2. 2 The Effect of TANF on the Budget Constraint Effects of Changes in Benefit Guarantee

19. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 19 of 43 Putting the Tools to Work: TANF and Labor Supply Among Single Mothers 2. 2 The Effect of TANF on the Budget Constraint How Large Will the Labor Supply Response Be?

20. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 20 of 43 Putting the Tools to Work: TANF and Labor Supply Among Single Mothers 2. 2 The Effect of TANF on the Budget Constraint How Large Will the Labor Supply Response Be?

21. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 21 of 43 Equilibrium and Social Welfare 2. 3 Demand Curves welfare economics The study of the determinants of wellbeing, or welfare, in society. demand curve A curve showing the quantity of a good demanded by individuals at each price. Determinants of welfare Social efficiency Social welfare

22. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 22 of 43 Equilibrium and Social Welfare 2. 3 Demand Curves

23. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 23 of 43 Equilibrium and Social Welfare 2. 3 Demand Curves Elasticity of Demand elasticity of demand The percentage change in the quantity demanded of a good caused by each 1% change in the price of that good.

24. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 24 of 43 Equilibrium and Social Welfare 2. 3 Demand Curves Elasticity of Demand There are several key points to make about elasticities of demand:  They are typically negative, since quantity demanded typically falls as price rises.  They are typically not constant along a demand curve.  A vertical demand curve is one for which the quantity demanded does not change when price rises; in this case, demand is perfectly inelastic.  A horizontal demand curve is one where quantity demanded changes infinitely for even a very small change in price; in this case, demand is perfectly elastic.  The effect of one good’s prices on the demand for another good is the cross-price elasticity, and with the particular utility function we are using here, that cross-price elasticity is zero. Typically, however, a change in the price of one good will affect demand for other goods as well.

25. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 25 of 43 Equilibrium and Social Welfare 2. 3 Supply Curves supply curve A curve showing the quantity of a good that firms are willing to supply at each price. marginal productivity The impact of a one unit change in any input, holding other inputs constant, on the firm’s output. marginal cost The incremental cost to a firm of producing one more unit of a good. profits The difference between a firm’s revenues and costs, maximized when marginal revenues equal marginal costs.

26. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 26 of 43 Equilibrium and Social Welfare 2. 3 Equilibrium market The arena in which demanders and suppliers interact. market equilibrium The combination of price and quantity that satisfies both demand and supply, determined by the interaction of the supply and demand curves.

27. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 27 of 43 Equilibrium and Social Welfare 2. 3 Equilibrium

28. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 28 of 43 Equilibrium and Social Welfare 2. 3 Social Efficiency Social efficiency represents the net gains to society from all trades that are made in a particular market, and it consists of two components: consumer and producer surplus. consumer surplus The benefit that consumers derive from consuming a good, above and beyond the price they paid for the good.

29. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 29 of 43 Equilibrium and Social Welfare 2. 3 Social Efficiency

30. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 30 of 43 Equilibrium and Social Welfare 2. 3 Producer Surplus producer surplus The benefit that producers derive from selling a good, above and beyond the cost of producing that good.

31. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 31 of 43 Equilibrium and Social Welfare 2. 3 Producer Surplus

32. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 32 of 43 Equilibrium and Social Welfare 2. 3 Social Surplus total social surplus (social efficiency) The sum of consumer surplus and producer surplus.

33. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 33 of 43 Equilibrium and Social Welfare 2. 3 Social Surplus

34. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 34 of 43 Equilibrium and Social Welfare 2. 3 Competitive Equilibrium Maximizes Social Efficiency First Fundamental Theorem of Welfare Economics The competitive equilibrium, where supply equals demand, maximizes social efficiency. deadweight loss The reduction in social efficiency from denying trades for which benefits exceed costs. It is sometimes confusing to know how to draw deadweight loss triangles. The key to doing so is to remember that deadweight loss triangles point to the social optimum, and grow outward from there.

35. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 35 of 43 Equilibrium and Social Welfare 2. 3 From Social Efficiency to Social Welfare: The Role of Equity social welfare The level of well-being in society. Second Fundamental Theorem of Welfare Economics Society can attain any efficient outcome by suitably redistributing resources among individuals and then allowing them to freely trade.

36. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 36 of 43 Equilibrium and Social Welfare 2. 3 From Social Efficiency to Social Welfare: The Role of Equity equity–efficiency trade-off The choice society must make between the total size of the economic pie and its distribution among individuals. social welfare function (SWF) A function that combines the utility functions of all individuals into an overall social utility function.

37. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 37 of 43 Equilibrium and Social Welfare 2. 3 From Social Efficiency to Social Welfare: The Role of Equity Utilitarian SWF With a utilitarian social welfare function, society’s goal is to maximize the sum of individual utilities: SWF = U 1 + U 2 +... + U N The utilities of all individuals are given equal weight, and summed to get total social welfare.

38. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 38 of 43 Equilibrium and Social Welfare 2. 3 From Social Efficiency to Social Welfare: The Role of Equity Rawlsian Social Welfare Function John Rawls suggested that society’s goal should be to maximize the well- being of its worst-off member. The Rawlsian SWF has the form: SW = min (U 1, U 2,..., U N ) Since social welfare is determined by the minimum utility in society, social welfare is maximized by maximizing the well-being of the worst-off person in society.

39. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 39 of 43 Equilibrium and Social Welfare 2. 3 Choosing an Equity Criterion commodity egalitarianism The principle that society should ensure that individuals meet a set of basic needs, but that beyond that point income distribution is irrelevant. equality of opportunity The principle that society should ensure that all individuals have equal opportunities for success, but not focus on the outcomes of choices made.

40. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 40 of 43 Welfare Implications of Benefit Reductions: The TANF Example Continued 2. 4 Efficiency

41. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 41 of 43 Welfare Implications of Benefit Reductions: The TANF Example Continued 2. 4 Equity Governments have programs such as TANF because their citizens care not only about efficiency but also about equity, the fair distribution of resources in society. For many specifications of social welfare, the competitive equilibrium, while being the social efficiency-maximizing point, may not be the social welfare-maximizing point.

42. Chapter 2 Theoretical Tools of Public Finance © 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 42 of 43 Conclusion 2. 5 This chapter has shown both the power and the limitations of the theoretical tools of economics. On the one hand, by making relatively straightforward assumptions about how individuals and firms behave, we are able to address complicated questions such as how TANF benefits affect the labor supply of single mothers, and the implications of that response for social welfare. On the other hand, while we have answered these questions in a general sense, we have been very imprecise about the potential size of the changes that occur in response to changes in TANF benefits.