Theoretical Tools of Public Finance

1. Theoretical Tools ofPublic Finance P R E P A R E D B Y FERNANDO QUIJANO AND SHELLY TEFFT

2. 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 of 44

3. 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.

4. Constrained Utility Maximization 2.1 Preferences and Indifference Curves • FIGURE 2-1

5. 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.

6. Constrained Utility Maximization 2.1 Preferences and Indifference Curves • FIGURE 2-2

7. 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(X1, X2, X3, …), where X1, X2, X3, 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.

8. 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.

9. Constrained Utility Maximization 2.1 Utility Mapping of Preferences Marginal Utility

10. 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.

11. Constrained Utility Maximization 2.1 Utility Mapping of Preferences Marginal Rate of Substitution • FIGURE 2-4

12. 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.

13. Constrained Utility Maximization 2.1 Budget Constraints • FIGURE 2-5

14. Constrained Utility Maximization 2.1 Putting It All Together: Constrained Choice • FIGURE 2-6 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.

15. Constrained Utility Maximization 2.1 The Effects of Price Changes: Substitution and Income Effects • FIGURE 2-7

16. 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.

17. 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.

18. 2.2 Putting the Tools to Work: TANF and Labor Supply among Single Mothers Identifying the Budget Constraint • FIGURE 2-8

19. 2.2 Putting the Tools to Work: TANF and Labor Supply among Single Mothers The Effect of TANF on the Budget Constraint Effects of Changes in Benefit Guarantee • FIGURE 2-9

20. 2.2 Putting the Tools to Work: TANF and Labor Supply among Single Mothers The Effect of TANF on the Budget Constraint How Large Will the Labor Supply Response Be? • FIGURE 2-10

21. 2.2 Putting the Tools to Work: TANF and Labor Supply among Single Mothers The Effect of TANF on the Budget Constraint How Large Will the Labor Supply Response Be? • FIGURE 2-11

22. Equilibrium and Social Welfare 2.3 welfare economics The study of the determinants of well-being, or welfare, in society. Demand Curves demand curve A curve showing the quantity of a good demanded by individuals at each price.

23. Equilibrium and Social Welfare 2.3 Demand Curves

24. 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.

25. 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.

26. 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.

27. 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.

28. Equilibrium and Social Welfare 2.3 Equilibrium • FIGURE 2-13

29. 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 consumer surplus The benefit that consumers derive from consuming a good, above and beyond the price they paid for the good.

30. Equilibrium and Social Welfare 2.3 Social Efficiency Consumer Surplus • FIGURE 2-14

31. Equilibrium and Social Welfare 2.3 Social Efficiency Producer Surplus producer surplus The benefit that producers derive from selling a good, above and beyond the cost of producing that good.

32. Equilibrium and Social Welfare 2.3 Social Efficiency Producer Surplus • FIGURE 2-15

33. Equilibrium and Social Welfare 2.3 Social Efficiency Social Surplus total social surplus(social efficiency) The sum of consumer surplus and producer surplus.

34. Equilibrium and Social Welfare 2.3 Social Efficiency Social Surplus • FIGURE 2-16

35. 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 preventing 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.

36. 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.

37. 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.

38. 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 = U1 + U2 + . . . + UN The utilities of all individuals are given equal weight, and summed to get total social welfare.

39. 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 (U1, U2, . . ., UN) 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.

40. 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.

41. Welfare Implications of Benefit Reductions: The TANF Example Continued 2.4 Efficiency • FIGURE 2-17

42. Welfare Implications of Benefit Reductions: The TANFExample 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.

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.