Chapter 2. Theoretical Tools of Public Finance. Introduction CONSTRAINED UTILITY MAXIMIZATION. Constrained Utility Maximization: Constrained choice

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1 Chapter 2 Theoretical Tools of Public Finance Introduction Theoretical Tools of Public Finance Theoretical tools are a set of tools used to understand economic decision making. They are primarily graphical and mathematical. Empirical tools allow you to examine the theory with data. (will do in chapter ) Jonathan Gruber Public Finance and Public Policy Aaron S. Yelowitz - Copyright 2005 Worth Publishers CONSTRAINED UTILITY MAXIMIZATION Constrained utility maximization means that all decisions are made in order to maximize the well-being of the individual, subject to his available resources. Utility maximization involves preferences and a budget constraint. One of the key assumptions about preferences is non-satiation that more is preferred to less. Constrained Utility Maximization: Constrained choice What is the highest indifference curve that an individual can reach, given a budget constraint? Preferences tells us what a consumer wants, and the budget constraint tells us what a consumer can actually purchase. This leads to utility maximization, shown graphically, in Figure 8. 8 Q CD (quantity of CDs) 2 This bundle of goods gives the highest utility, subject to the budget constraint. This indifference curve gives much higher utility, but is not attainable. This indifference curve is not utility-maximizing, because there are bundles that give higher utility. Constrained Utility Maximization: Putting it together: Constrained choice In this figure, the utility maximizing choice occurs where the indifference curve is tangent to the budget constraint. Y = PMQM + PCQC This implies that the slope of the indifference curve equals the slope of the budget constraint, where the marginal rate of substitution equals the ratio of prices: Figure Utility Maximization (quantity of ) MU M P MRS = = MU P C M C

2 The Effects of Price Changes: Substitution and income effects Consider a typical price change in our framework: Increase the price of,. This rotates the budget constraint inward along the x-axis. Figure 0 illustrates this. Q CD (quantity of CDs) 2 Andrea Increase is worse in rotates off, and the consumes budget constraint less inward. on x-axis. 0 2 (quantity of ) Figure 0 Increase in the Price of Movies The Effects of Price Changes: Substitution and income effects A change in price consists of two effects: Substitution effect change in due to change in relative prices, holding utility constant. Income effect change in due to feeling poorer after price increase. Figure illustrates this. Q CD (quantity of CDs) 2 Movement from one indifference curve to the other is the income effect. Movement along the indifference curve is the substitution effect 0 2 Decline in due to income effect Decline in due to substitution effect (quantity of ) TANF and labor supply among single mothers TANF is Temporary Assistance for Needy Families. Cash welfare for poor families, mainly single mothers. For example, in New Mexico, family of three receives $89 per month. Assume the two goods in utility maximization problem are leisure and food. Whatever time is not devoted to leisure is spent working and earning money. Identifying the budget constraint What does the budget constraint look like? Assume the person can work up to 2000 hours per year, at a wage rate of $0 per hour, and that TANF is not yet in place. Price of food is $ per unit. 2

3 Identifying the budget constraint The price of one hour of leisure is the hourly wage rate. Creates a direct tradeoff between leisure and food: each hour of work brings her 0 units of food. Figure 2 illustrates this. Food 500 hours of leisure, units of food,000 hours of leisure, units of food The slope of the budget constraint is w/p F, or -0.,500 hours of leisure, units of food is a good just as were more is preferred to less Figure 2 is a good and labor is a bad. The effect of TANF on the budget constraint Now, let s introduce TANF into the framework. TANF has two key features: Benefit guarantee, G amount that a recipient with $0 earnings gets. Benefit reduction rate, t rate at which benefit guarantee falls as earnings increases. The effect of TANF on the budget constraint Assume that benefit guarantee, G, is $ per year. Assume the benefit reduction rate, τ, is 50%. Figure illustrates this. Food Slope on this section of the budget constraint is -0. At,000 hours of work, TANF benefits fall to zero. The benefit reduction rate of 50% reduces the guarantee as earnings increase. Green area represents new bundles from TANF. Slope on this section of the budget constraint is -5. $5000 guarantee means that a recipient could now consume (2000,5000). The effect of changes in the benefit guarantee One possible policy experiment is reducing the benefit guarantee level G. What happens when G falls from $ to $,000, holding all other parameters constant? Figure 4 illustrates this ,000,500 Figure Introduce Temporary Assistance to Needy Families

4 Food 6,000,000 The earnings level where TANF ends falls from $ to $6, ,000,400,500 Lowering the guarantee reduces the initial non-working bundle to (2000,000). How large will the labor supply response be? What is the expected labor supply response to such a policy change? It depends on where the single mother initially was on the budget constraint. () If she initially earned less than $6,000 and more than $5000 per year, the policy change involves only an income effect, not a substitution effect. Figure 5 illustrates this. Figure 4 Lower the Benefit Guarantee Food 6,000,000 The effective wage rate does not change for this person. If leisure is a normal good, the income effect would reduce leisure (increase work). How large will the labor supply response be? (2) If she initially earned between $6,000 and $ per year, the policy change involves both an income and substitution effect. The substitution and income effects go in the same direction. Figure 6 illustrates this ,000,400 Figure 5 Policy Change Generates Income Effect Only Food 6,000,000 The effective wage rate changes for this person. The change in labor supply involves both income and substitution effects. How large will the labor supply response be? Economic theory clearly suggests that such a benefit reduction will increase labor supply, but does not speak to the magnitude of the response. () For example, some welfare recipients who were not initially working continue to choose not to work. Figure 7 illustrates this ,000,400 Figure 6 Both Income and Substitution Effects From Policy 4

5 Food 6,000, ,000,400 This person was initially out of the labor force. She continues to stay out of the labor force, even with the benefits reduction. How large will the labor supply response be? The actual magnitude of the labor supply response therefore depends on the preferences of various welfare recipients. To the extent the preferences are more like the first two cases, the larger the labor supply response. Thus, theory alone cannot say whether this policy change will increase labor supply, or by how much. Must analyze available data on single mothers to figure out the magnitude. Figure 7 No Labor Response To Policy Change Welfare economics is the study of the determinants of well-being, or welfare, in society. This involves a normative question: Does the policy change make society as a whole better off or not? This depends on: Determinants of social efficiency, or size of the economic pie. Redistribution. Equilibrium In equilibrium, we horizontally sum individual demand curves to get aggregate demand. We also horizontally sum individual supply curves to get aggregate supply. Competitive equilibrium represents the point at which both consumers and suppliers are satisfied with the price/quantity combination. Figure 2 illustrates this. Intersection of supply and demand is equilibrium.,,2 Measuring social efficiency is computing the potential size of the economic pie. It represents the net gain from trade to consumers and producers.,,,2, Figure 2 Equilibrium with and 5

6 Consumer surplus is the benefit that consumers derive from a good, beyond what they paid for it. Each point on the demand curve represents a willingness-to-pay for that quantity. Figure 22 illustrates this. The consumer total consumer surplus surplus at is the area between this triangle. the demand curve and market price. 0 2 Figure 22 Deriving Consumer Surplus Consumer surplus is determined by market price and the elasticity of demand: With inelastic demand, demand curve is more vertical, so surplus is higher. With elastic demand, surplus is lower. Figure 2 illustrates this. Consumer surplus is larger when demand curve is more inelastic. 0 2 Figure 2 Consumer Surplus and Inelastic Producer surplus is the benefit derived by producers from the sale of a unit above and beyond their cost of producing it. Each point on the supply curve represents the marginal cost of producing it. Figure 24 illustrates this. The producers total producer s surplus surplus at is the area between this triangle. the demand curve and market price. 0 2 Figure 24 Producer Surplus 6

7 Similar to consumer surplus, producer surplus is determined by market price and the elasticity of supply: With inelastic supply, supply curve is more vertical, so producer surplus is higher. With elastic supply, producer surplus is lower. The total social surplus, also known as social efficiency, is the sum of the consumer s and producer s surplus. Figure 25 illustrates this. Providing the first unit gives a great deal of surplus to society. Competitive equilibrium maximizes social efficiency 0 This area represents the social surplus from producing the first unit. Social The area efficiency between is maximized the supply at and Q demand *, is curves the sum from of the zero to consumer Q* represents and producer the surplus. The First Fundamental Theorem of Welfare Economics states that the competitive equilibrium, where supply equals demand, maximizes social efficiency. Any quantity other than reduces social efficiency, or the size of the economic pie. Consider restricting the price of the good to P <. Figure 26 illustrates this. Figure 25 Social Surplus The social surplus from Q is P this area, consisting of a larger consumer and smaller producer surplus. Figure 26 Q This triangle represents lost surplus to society, known as deadweight loss. Deadweight Loss from a Price Floor With such a price restriction, the quantity falls to Q, and there is excess demand. Competitive equilibrium maximizes social efficiency A policy like price controls creates deadweight loss, the reduction in social efficiency by restricting quantity below the competitive equilibrium. 7

8 Societies usually care not only about how much surplus there is, but also about how it is distributed among the population. Social welfare is determined by both criteria. The Second Fundamental Theorem of Welfare Economics states that society can attain any efficient outcome by a suitable redistribution of resources and free trade. In reality, society often faces an equity-efficiency tradeoff. Society s tradeoffs of equity and efficiency are models with a Social Welfare Function. This maps individual utilities into an overall social utility function. The utilitarian social welfare function is: SWF = i U i The utilities of all individuals are given equal weight. Implies that government should transfer from person to person 2 as long as person 2 s gain is bigger than person s loss in utility. Utilitarian SWF is defined in terms of utility, not dollars. Society not indifferent between giving $ of income to rich and poor; rather indifferent between one util to rich and one util to poor. Utilitarian SWF is maximized when the marginal utilities of everyone are equal: MU = MU 2 =... = MU i Thus, society should redistribute from rich to poor if the marginal utility of the next dollar is higher to the poor person than to the rich person. The Rawlsian social welfare function is: ( ) SWF = min U, U 2,..., U N Societal welfare is maximized by maximizing the well-being of the worst-off person in society. Generally suggests more redistribution than the utilitarian SWF. 8

9 WELFARE IMPLICATIONS OF BENEFIT REDUCTIONS: TANF continued Efficiency and equity considerations in introducing or cutting TANF benefits. In a typical labor supply/labor demand framework, these changes shift the labor supply single parents. Figure 27 illustrates this. Wage w w 2 w Equilibrium Inefficient, with but generous entails substantial TANF redistribution. benefit. Labor supply Labor supply Equilibrium with no government intervention, no deadweight loss. Labor demand Labor supply H H 2 H Hours worked Figure 27 Market Equilibrium with Labor and WELFARE IMPLICATIONS OF BENEFIT REDUCTIONS: TANF continued Different policies involve different deadweight loss triangles, but also different levels of redistribution for the poor. SWF helps determine the right policy for society. 9