Chapter 2 Theoretical Tools of Public Finance Jonathan

Chapter 2 Theoretical Tools of Public Finance Jonathan Gruber Public Finance and Public Policy Aaron S. Yelowitz - Copyright 2005 © Worth Publishers

Introduction Theoretical Tools of Public Finance n Theoretical tools are a set of tools used to understand economic decision making. They are primarily graphical and mathematical. n Empirical tools allow you to examine theory with data.

CONSTRAINED UTILITY MAXIMIZATION n Constrained utility maximization means that all decisions are made in order to maximize the well-being of the individual, subject to his available resources. n Utility maximization involves preferences and a budget constraint. n One of the key assumptions about preferences is non-satiation–that “more is preferred to less. ”

Constrained Utility Maximization Preferences and indifference curves n Figure 1 illustrates some preferences over movies (on the x-axis) and CDs (on the y-axis). n Because of non-satiation, bundles A and B are both inferior to bundle C.

Bundle“C” “C”gives 2 CDs higher utility 2 movies than Bundle “A” gives 2 and either “A” or “B” CDs and 1 movie QCD (quantity of CDs) A 2 C B 1 0 Figure 1 Bundle “B” gives 1 CD and 2 movies 1 2 Different Bundles of Goods QM (quantity of movies)

Constrained Utility Maximization: Preferences and indifference curves n A utility function is a 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, n And f( • ) is some mathematical function. n

Constrained Utility Maximization: Preferences and indifference curves n One formulation of a utility function is U(QM, QC) = QMQC, where QM = quantity of movies and QC = quantity of CDs. n The combinations {1, 2} (bundle A) and {2, 1} (bundle B) both give 2 “utils. ” n The combination {2, 2} (bundle C) gives 4 “utils. ” n With these preferences, indifferent to A or B. n Figure 2 illustrates this.

QCD (quantity of CDs) Bundle“C” “C”gives 4 Higher utility as “A” and “B” Bundle both “utils” utility is than on a move toward give 2 “utils”higher and higher either indifference “A” or “B” northeast in the lie on the same quadrant. indifference curve A 2 C B 1 IC 2 IC 1 0 Figure 2 1 2 Utility From Different Bundles QM (quantity of movies)

Constrained Utility Maximization: Utility mapping of preferences n How are indifference curves derived? n Set utility equal to a constant level and figure out the bundles of goods that get that utility level. n For U = QMQC, how would we find the bundles for the indifference curve associated with 25 utils? Set 25 = QMQC, n Yields QC = 25/QM, n Or bundles like {1, 25}, {1. 25, 20}, {5, 5}, etc. n

Constrained Utility Maximization: Marginal utility n Marginal utility is the additional increment to utility from consuming an additional unit of a good. n Diminishing marginal utility means each additional unit makes the individual less happy than the previous unit.

l Constrained Utility Maximization: a c ni h c Marginal utility Te n With the utility function given before, U = QMQC, the marginal utility is: n Take the partial derivative of the utility function with respect to QM to get the marginal utility of movies.

Constrained Utility Maximization: Marginal utility n Evaluating the utility function U = (QMQC)1/2, at QC = 2 allows us to plot a relationship between marginal utility and movies consumed. n Figure 3 illustrates this.

Marginal utility of movies First movie gives 1. 41 additional utils Second movie gives 0. 59 Third movie gives additional utils Analysis holds CD 0. 45 additional consumption utils constant at 2 CDs 1. 41 0. 59 0. 45 MU (QCD=2) 0 Figure 3 1 2 3 Declining Marginal Utility From Movies QM (quantity of movies)

Constrained Utility Maximization: Marginal utility n Why does diminishing marginal utility make sense? n Most consumers order consumption of the goods with the highest utility first.

Constrained Utility Maximization: Marginal rate of substitution n Marginal rate of substitution—slope of the indifference curve is called the MRS, and is the rate at which consumer is willing to trade off the two goods. n Returning to the (CDs, movies) example. n Figure 4 illustrates this.

QCD (quantity of CDs) A 2 MRS Marginal rate of at bundle C appears substitution at bundleto. A be is larger than B but smaller than A. its slope MRS at bundle B is C smaller in absolute terms than at A. B 1 IC 2 IC 1 0 Figure 4 1 2 QM (quantity of movies) Marginal Rate of Substitution At Different Bundles

Constrained Utility Maximization: Marginal rate of substitution n MRS is diminishing (in absolute terms) as we move along an indifference curve. n This means that Andrea is willing to give up fewer CD’s to get more movies when she has more movies (bundle B) than when she has less movies (bundle A). n Figure 5 illustrates this.

QCD (quantity of CDs) Willing to give up a lot of CDs for another movie … Not willing to give up very many CDs for another Even less willing to give movie up additional CDs A 2 B 1 D IC 1 0 Figure 5 1 2 3 Marginal Rate of Substitution is Diminishing QM (quantity of movies)

Constrained Utility Maximization Marginal rate of substitution n Direct relationship between MRS and marginal utility. n MRS shows how the relative marginal utilities evolve over the indifference curve. n Straightforward to derive this relationship graphically, as well. n Consider the movement from bundle A to bundle B. Figure 6 illustrates this.

QCD (quantity of CDs) A 2 Moving from A to B does Must Simply have rearrange MU ΔQthe=MU equation MΔQM not change utility. C C Loss Movement utility fromonless isthe to because getin the relationship we down are between same Gain Movement in utility across from more is change CDs isin. MU CDs, ΔQ. Cutilities. . MRS indifference and marginal curve. CΔQ C change movies inismovies, MUMΔQ ΔQ M. M. B 1 IC 1 0 Figure 6 1 2 3 Relationship Between Marginal Utility and MRS QM (quantity of movies)

Constrained Utility Maximization: Budget constraints n The budget constraint is a mathematical representation of the combination of goods the consumer can afford to buy with a given income. n Assume there is no saving or borrowing. n In the example, denote: Y = Income level n PM = Price of one movie n PC = Price of one CD n

Constrained Utility Maximization: Budget constraints n The expenditure on movies is: n While the expenditure on CDs is:

Constrained Utility Maximization: Budget constraints n Thus, the total amount spent is: n This must equal income, because of no saving or borrowing.

Constrained Utility Maximization: Budget constraints n This budget constraint is illustrated in the next figure. n Figure 7 illustrates this.

QCD (quantity of CDs) 3 Her If Andrea budget spent constraint all her consists income of allon combinations CDs, she could on the buyred this line. amount. Andrea would never choose the interior of the budget set because of nonsatiation. 2 If Andrea spent all her income on movies, she could buy this amount. 1 0 Figure 7 1 The Budget Constraint 2 3 QM (quantity of movies)

Constrained Utility Maximization: Budget constraints n The slope of the budget constraint is: n It is thought that government actions can change a consumer’s budget constraint, but that a consumer’s preferences are fixed.

Constrained Utility Maximization: Putting it together: Constrained choice n What is the highest indifference curve that an individual can reach, given a budget constraint? n Preferences tells us what a consumer wants, and the budget constraint tells us what a consumer can actually purchase. n This leads to utility maximization, shown graphically, in Figure 8. 8

QCD (quantity of CDs) 3 This bundle of goods This gives indifference the curve gives much highest utility, subject higher to the budget utility, but is not attainable. constraint. This indifference curve is not utilitymaximizing, because there are bundles that give higher utility. 2 1 0 Figure 8 1 Utility Maximization 2 3 QM (quantity of movies)

Constrained Utility Maximization: Putting it together: Constrained choice n In this figure, the utility maximizing choice occurs where the indifference curve is tangent to the budget constraint. n This implies that the slope of the indifference curve equals the slope of the budget constraint.

Constrained Utility Maximization: Putting it together: Constrained choice n Thus, the marginal rate of substitution equals the ratio of prices: n At the optimum, the ratio of the marginal utilities equals the ratio of prices. But this is not the only condition for utility maximization. n Figure 9 illustrates this.

QCD (quantity of CDs) 3 The MRS equals the price ratio at this bundle, but is unaffordable. The MRS equals the price ratio at this bundle, but it wastes resources. 2 1 0 Figure 9 1 2 3 MRS Equal to Price Ratio is Insufficient QM (quantity of movies)

Constrained Utility Maximization: Putting it together: Constrained choice n Thus, the secondition is that all of the consumer’s money is spent: n These two conditions are used for utility maximization.

The Effects of Price Changes: Substitution and income effects n Consider a typical price change in our framework: n Increase the price of movies, PM. n This rotates the budget constraint inward along the x-axis. n Figure 10 illustrates this.

QCD (quantity of CDs) 3 Andrea Increase is worse in PM rotates off, andthe consumes budget constraint lessinward movies. on x-axis. 2 1 0 Figure 10 1 2 Increase in the Price of Movies 3 QM (quantity of movies)

The Effects of Price Changes: Substitution and income effects n A change in price consists of two effects: n Substitution effect–change in consumption due to change in relative prices, holding utility constant. n Income effect–change in consumption due to feeling “poorer” after price increase. n Figure 11 illustrates this.

QCD (quantity of CDs) 3 Movement from one indifference curve to the other is the income effect. Movement along the indifference curve is the substitution effect 2 1 Decline in QMindue QMtodue income to substitution effect 0 Figure 11 1 2 3 QM (quantity of movies) Illustration of Income and Substitution Effects

PUTTING THE TOOLS TO WORK TANF and labor supply among single mothers n TANF is “Temporary Assistance for Needy Families. ” n Cash welfare for poor families, mainly single mothers. n For example, in New Mexico, family of three receives $389 per month. n Assume the two “goods” in utility maximization problem are leisure and food consumption. n Whatever time is not devoted to leisure is spent working and earning money.

PUTTING THE TOOLS TO WORK Identifying the budget constraint n What does the budget constraint look like? n Assume the person can work up to 2000 hours per year, at a wage rate of $10 per hour, and that TANF is not yet in place. n Price of food is $1 per unit.

PUTTING THE TOOLS TO WORK Identifying the budget constraint n The “price” of one hour of leisure is the hourly wage rate. n Creates a direct tradeoff between leisure and food: each hour of work brings her 10 units of food. n Figure 12 illustrates this.

Food consumption (QF) 20, 000 Food is a more “typical” good. 500 hours of leisure, 15, 000 units of Thus, there are various food combinations of (L, F) consumed … The This slope leads ofto the budget kind of constraint budget 1, 000 hours ofthe leisure, 10, 000 units constraint iswe –w/P have , or seen -10. previously. of. Ffood 15, 000 1, 500 hours ofisleisure, 5, 000 Leisure a “good” justunits as movies food is preferred to less. were …ofmore 10, 000 5, 000 0 Figure 12 500 1000 1500 2000 Leisure is a “good” and labor is a “bad. ” Leisure (hours)

PUTTING THE TOOLS TO WORK The effect of TANF on the budget constraint n Now, let’s introduce TANF into the framework. TANF has two key features: n n Benefit guarantee, G – amount that a recipient with $0 earnings gets. Benefit reduction rate, J – rate at which benefit guarantee falls as earnings increases.

PUTTING THE TOOLS TO WORK The effect of TANF on the budget constraint n Assume that benefit guarantee, G, is $5, 000 per year. n Assume the benefit reduction rate, J, is 50%. n Figure 13 illustrates this.

Food consumption (QF) 20, 000 Slope on this section of the budget constraint is -10. At 1, 000 hours of work, TANF benefits The benefit reduction rate of 50% fall to zero. Slope onthe thisguarantee section ofas theearnings budget reduces constraint isrepresents -5. that a new increase. Green area $5000 guarantee means recipient bundles from TANF. could now consume (2000, 5000). 15, 000 10, 000 5, 000 0 Figure 13 500 1, 000 1, 500 2, 000 Leisure (hours) Introduce Temporary Assistance to Needy Families

PUTTING THE TOOLS TO WORK The effect of changes in the benefit guarantee n One possible “policy experiment” is reducing the benefit guarantee level G. n What happens when G falls from $5, 000 to $3, 000, holding all other parameters constant? n Figure 14 illustrates this.

Food consumption (QF) 20, 000 The earnings level where TANF ends falls from $10, 000 Lowering the guarantee to $6, 000. reduces the initial non-working bundle to (2000, 3000). 15, 000 10, 000 6, 000 5, 000 3, 000 0 Figure 14 500 1, 000 1, 400 1, 500 Lower the Benefit Guarantee 2, 000 Leisure (hours)

PUTTING THE TOOLS TO WORK How large will the labor supply response be? n What is the expected labor supply response to such a policy change? n It depends on where the single mother initially was on the budget constraint. n If she initially earned less than $6, 000 per year, the policy change involves only an income effect, not a substitution effect. n Figure 15 illustrates this.

Food consumption (QF) 20, 000 The effective rate does If leisurewage is a normal good, the not change foreffect this person. income would reduce leisure (increase work). 15, 000 10, 000 6, 000 5, 000 3, 000 0 Figure 15 500 1, 000 1, 400 2, 000 Policy Change Generates Income Effect Only Leisure (hours)

PUTTING THE TOOLS TO WORK How large will the labor supply response be? n If she initially earned between $6, 000 and $10, 000 per year, the policy change involves both an income and substitution effect. n The substitution and income effects go in the same direction. n Figure 16 illustrates this.

Food consumption (QF) 20, 000 The change effectiveinwage The laborrate supply changes thisincome person. involvesfor both and substitution effects. 15, 000 10, 000 6, 000 5, 000 3, 000 0 Figure 16 500 1, 000 1, 400 2, 000 Leisure (hours) Both Income and Substitution Effects From Policy

PUTTING THE TOOLS TO WORK How large will the labor supply response be? n Economic theory clearly suggests that such a benefit reduction will increase labor supply, but does not speak to the magnitude of the response. n For example, some welfare recipients who were not initially working continue to choose not to work. n Figure 17 illustrates this.

Food consumption (QF) 20, 000 15, 000 This person was initially out of the labortoforce. She continues stay out of the labor force, even with the benefits reduction. 10, 000 6, 000 5, 000 3, 000 0 Figure 17 500 1, 000 1, 400 2, 000 No Labor Supply Response To Policy Change Leisure (hours)

PUTTING THE TOOLS TO WORK How large will the labor supply response be? n The actual magnitude of the labor supply response therefore depends on the preferences of various welfare recipients. n To the extent the preferences are more like the first two cases, the larger the labor supply response. n Thus, theory alone cannot say whether this policy change will increase labor supply, or by how much. n Must analyze available data on single mothers to figure out the magnitude.

EQUILIBRIUM AND SOCIAL WELFARE n Welfare economics is the study of the determinants of well-being, or welfare, in society. It depends on: n Determinants of social efficiency, or size of the economic “pie. ” n Redistribution.

EQUILIBRIUM AND SOCIAL WELFARE Demand curves n Demand curve is the relationship between the price of a good and the quantity demanded. n Derive demand curve from utility maximization problem, as shown in Figure 18. 18

QCD (quantity of CDs) Raising P more gives another M even Initial utility-maximizing point gives (PM, QM)Raising combination with even less another (PM, QM) M gives one. P(P M, QM) combination. movies with demanded. combination fewer movies demanded. QM, 3 QM, 2 QM, 1 Figure 18 Increase in the Price of Movies QM (quantity of movies)

EQUILIBRIUM AND SOCIAL WELFARE Demand curves n This gives various (PM, QM) combinations that can be mapped into price/quantity space. n This gives us the demand curve for movies. n Figure 19 illustrates this.

PM PM, 3 Various of At a high combinations price for pointsdemanded like these create movies, QM, 3 the demand curve. At a somewhat lower price for movies, demanded QM, 2 At an even lower price for movies, demanded QM, 1 PM, 2 PM, 1 Demand curve for movies QM, 3 Figure 19 QM, 2 QM, 1 Deriving the Demand Curve for Movies QM

EQUILIBRIUM AND SOCIAL WELFARE Elasticity of demand n A key feature of demand analysis is the elasticity of demand. It is defined as: n That is, the percent change in quantity demanded divided by the percent change in price.

EQUILIBRIUM AND SOCIAL WELFARE Elasticity of demand n For example, an increase in the price of movies from $8 to $12 is a 50% rise in price. n If the number of movies purchased fell from 6 to 4, there is an associated 33% reduction in quantity demanded. n The demand elasticity is therefore -0. 67. n Demand elasticities features: n Typically negative number. n Not constant along the demand curve (for a linear demand curve).

EQUILIBRIUM AND SOCIAL WELFARE Elasticity of demand n For a vertical demand curve n Elasticity of demand is zero—quantity does not change as price goes up or down. n Perfectly inelastic n For a horizontal demand curve n Elasticity of demand is negative infinity—quantity changes infinitely for even a small change in price. n Perfectly elastic n Figure 20 illustrates this.

PM PM, 3 With this inelastic demand Inelastic demand curve, choose QM, 2 curve for With movies this elastic demand of the price. regardless curve, choose any quantity at price PM, 2 Elastic demand curve for movies PM, 1 QM, 3 Figure 20 QM, 2 QM, 1 Perfectly Elastic and Perfectly Inelastic Demand QM

EQUILIBRIUM AND SOCIAL WELFARE Elasticity of demand n More generally, an elasticity divides the percent change in a dependent variable by the percent change in an independent variable: n For example, Y is often the quantity demanded or supplied, while X might be own-price, cross-price, or income.

EQUILIBRIUM AND SOCIAL WELFARE Supply curves n Supply curve is the relationship between the price of a good and the quantity supplied. n Derive supply curve from profit maximization problem. n The firm’s production function measures the impact of a firm’s input use on output levels.

EQUILIBRIUM AND SOCIAL WELFARE Supply curves n Assume two inputs, labor (L) and capital (K). Firm’s production function for movies is, in general: n That is, the quantity of movies produced is related to the amount of labor and capital devoted to movie production. n Similarly, there would be a production function for CDs.

EQUILIBRIUM AND SOCIAL WELFARE Supply curves n One specific production function is: n From a production function like this, we can figure out the marginal productivity of an input by taking the derivative with respect to it.

l a c i Equilibrium and Social Welfare: n ch e Supply curves T n For example, the marginal productivity of labor is: n This is the partial derivative of Q with respect to L. The marginal product is positive.

l Equilibrium and Social Welfare: a c ni h c e Supply curves T n Taking the second derivative yields: n This second derivative is negative, meaning that the production function features diminishing marginal productivity.

EQUILIBRIUM AND SOCIAL WELFARE Supply curves n Diminishing marginal productivity means that holding all other inputs constant, increasing the level of one input (such as labor) yields less and less additional output.

EQUILIBRIUM AND SOCIAL WELFARE Supply curves n The total costs of production are given by: n In this case, r and w are the input prices of capital and labor, respectively.

EQUILIBRIUM AND SOCIAL WELFARE Supply curves n If we assume capital is fixed in the short-run, the cost function becomes: n Thus, only labor can be varied in the short run. The marginal cost is the incremental cost of producing one more unit of Q, or the product of the wage rate and amount of labor used to produce that unit.

EQUILIBRIUM AND SOCIAL WELFARE Supply curves n Diminishing marginal productivity implies rising marginal costs. n Since each additional unit, Q, means calling forth less and less productive labor at the same wage rate, costs of production rise.

EQUILIBRIUM AND SOCIAL WELFARE Supply curves n Profit maximization means maximizing the difference between total revenue and total costs. n This occurs at the quantity where marginal revenue equals marginal costs.

EQUILIBRIUM AND SOCIAL WELFARE Equilibrium n In a perfectly competitive market, the marginal revenue is the market price. Thus, the firm produces until: n P = MC. n Thus, the MC curve is the supply curve.

EQUILIBRIUM AND SOCIAL WELFARE Equilibrium n In equilibrium, we horizontally sum individual demand curves to get aggregate demand. n We also horizontally sum individual supply curves to get aggregate supply. n Competitive equilibrium represents the point at which both consumers and suppliers are satisfied with the price/quantity combination. n Figure 21 illustrates this.

PM Intersection of supply and demand is equilibrium. Supply curve of movies PM, 3 PM, 2 PM, 1 Demand curve for movies QM, 3 Figure 21 QM, 2 QM, 1 Equilibrium with Supply and Demand QM

EQUILIBRIUM AND SOCIAL WELFARE Social efficiency n Measuring social efficiency is computing the potential size of the economic pie. It represents the net gain from trade to consumers and producers.

EQUILIBRIUM AND SOCIAL WELFARE Social efficiency n Consumer surplus is the benefit that consumers derive from a good, beyond what they paid for it. n Each point on the demand curve represents a “willingness-to-pay” for that quantity. n Figure 22 illustrates this.

PM The Yet The consumer’s the willingness-to-pay actual “surplus” price paid from for is Supply the first unit much unit is this lower. is very trapezoid. high. curve of There willingness is stilltosurplus, pay for the movies The consumer’s “surplus” from because second unit the is price a bitislower. the next unit is this trapezoid. The consumer total consumer surplus at Q* is is the area between this triangle. the demand curve and market price. P* Demand curve for movies 0 Figure 22 1 2 Q* Deriving Consumer Surplus QM

EQUILIBRIUM AND SOCIAL WELFARE Social efficiency n Consumer surplus is determined by market price and the elasticity of demand: With inelastic demand, demand curve is more vertical, so surplus is higher. n With elastic demand, surplus is lower. n n Figure 23 illustrates this.

PM Supply curve of movies Consumer surplus is larger when demand curve is more inelastic. P* Demand curve for movies 0 Figure 23 1 2 Q* Consumer Surplus and Inelastic Demand QM

EQUILIBRIUM AND SOCIAL WELFARE Social efficiency n Producer surplus is the benefit derived by producers from the sale of a unit above and beyond their cost of producing it. n Each point on the supply curve represents the marginal cost of producing it. n Figure 24 illustrates this.

PM Supply curve of movies The producers total producer’s surplus at Q* is the area between this triangle. the demand curve and market price. P* There The marginal is producer costsurplus, for from the The producer’s “surplus” because second unit the price a bit ishigher. the next unit is is this trapezoid. The producer’s The. Yet marginal the actual “surplus” costprice forfrom the first received first unit isisthis ismuch very trapezoid. higher. low. 0 Figure 24 1 2 Producer Surplus Q* Demand curve for movies QM

EQUILIBRIUM AND SOCIAL WELFARE Social efficiency n 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. n With elastic supply, producer surplus is lower. n

EQUILIBRIUM AND SOCIAL WELFARE Social efficiency n The total social surplus, also known as “social efficiency, ” is the sum of the consumer’s and producer’s surplus. n Figure 25 illustrates this.

PM The Providing surplus the from first theunit next Supply gives unit isathe great difference deal of curve of between surplusthe to demand “society. ”and movies supply curves. Social The area efficiency between is maximized the supplyat *, and iscurves and Q demand the sum from of the zero to consumer Q* represents and producer the surplus. P* This area represents the social surplus from producing the first unit. 0 Figure 25 1 Social Surplus Q* Demand curve for movies QM

EQUILIBRIUM AND SOCIAL WELFARE Competitive equilibrium maximizes social efficiency n The First Fundamental Theorem of Welfare Economics states that the competitive equilibrium, where supply equals demand, maximizes social efficiency. n Any quantity other than Q* reduces social efficiency, or the size of the “economic pie. ” n Consider restricting the price of the good to P´<P*. n Figure 26 illustrates this.

PM This triangle represents lost surplus to society, known as “deadweight loss. ” The With socialsuch surplus a price from Q’ is restriction, this area, consisting the quantity of a ´, and there falls larger to Q consumer andis smaller excess producer demand. surplus. P* P´ Demand curve for movies Q´ Figure 26 Supply curve of movies Q* Deadweight Loss from a Price Floor QM

EQUILIBRIUM AND SOCIAL WELFARE Competitive equilibrium maximizes social efficiency n A policy like price controls creates deadweight loss, the reduction in social efficiency by restricting quantity below the competitive equilibrium.

EQUILIBRIUM AND SOCIAL WELFARE The role of equity n Societies usually care not only about how much surplus there is, but also about how it is distributed among the population. n Social welfare is determined by both criteria. n The Second Fundamental Theorem of Welfare Economics states that society can attain any efficient outcome by a suitable redistribution of resources and free trade. n In reality, society often faces an equity-efficiency tradeoff.

EQUILIBRIUM AND SOCIAL WELFARE The role of equity n Society’s tradeoffs of equity and efficiency are models with a Social Welfare Function. n This maps individual utilities into an overall social utility function.

EQUILIBRIUM AND SOCIAL WELFARE The role of equity n The utilitarian social welfare function is: n The utilities of all individuals are given equal weight. n Implies that government should transfer from person 1 to person 2 as long as person 2’s gain is bigger than person 1’s loss in utility.

EQUILIBRIUM AND SOCIAL WELFARE The role of equity n Utilitarian SWF is defined in terms of utility, not dollars. n Society not indifferent between giving $1 of income to rich and poor; rather indifferent between one util to rich and one util to poor.

EQUILIBRIUM AND SOCIAL WELFARE The role of equity n Utilitarian SWF is maximized when the marginal utilities of everyone are equal: n 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.

EQUILIBRIUM AND SOCIAL WELFARE The role of equity n The Rawlsian social welfare function is: n Societal welfare is maximized by maximizing the well-being of the worst-off person in society. n Generally suggests more redistribution than the utilitarian SWF.

WELFARE IMPLICATIONS OF BENEFIT REDUCTIONS: TANF continued n Efficiency and equity considerations in introducing or cutting TANF benefits. n In a typical labor supply/labor demand framework, these changes shift the labor supply curve for single parents. n Figure 27 illustrates this.

Wage w 3 Equilibrium Inefficient, with butgenerous entails substantial TANF redistribution. benefit. Entails Equilibrium some redistribution with TANF Labor supply and some benefit inefficiency. cut. Equilibrium with no government intervention, no deadweight loss. Labor supply w 2 w 1 Labor demand H 3 Figure 27 H 2 H 1 Hours worked Market Equilibrium with Labor Supply and Demand

WELFARE IMPLICATIONS OF BENEFIT REDUCTIONS: TANF continued n Different policies involve different deadweight loss triangles, but also different levels of redistribution for the poor. n SWF helps determine the right policy for society.

Recap of Theoretical Tools n Utility maximization n Labor supply example n Efficiency n Social welfare functions