WEEK 2 Public Finance

Week 2: Theoretical Tools of Public Finance

• Theoretical tools are used to understand the mechanics behind economic decision-making.
• Empirical tools are used to analyze data and answer questions raised by theoretical analysis.

Constrained Utility Maximization

• Constrained utility maximization is the process of maximizing the well-being (utility) of an individual, subject to her resources (budget constraint).

Utility Function

• A mathematical function representing an individual's set of preferences.
• It translates her well-being from different consumption bundles into units that can be compared to determine choice.

Models

• Mathematical or graphical representations of reality.

Preferences and Indifference Curves

• Indifference curves are a graphical representation of all bundles of goods that make an individual equally well off.
• An individual is indifferent as to which bundle he consumes because these bundles have equal utility.
• Indifference curves have two essential properties, both of which follow naturally from the more-is-better assumption.
• Consumers prefer higher indifference curves.
• Indifference curves are always downward sloping.

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.
• "f" is some mathematical function that describes how the consumption of those goods translates to utility.

Marginal Utility

• The additional increment to utility obtained by consuming an additional unit of a good.
• Diminishing marginal utility: the consumption of each additional unit of a good makes an individual less happy than the consumption of the previous unit.

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.
• It describes the rate at which the consumer will trade the good on the vertical axis for the good on the horizontal axis.

Budget Constraints

• Budget constraint is a mathematical representation of all the combinations of goods an individual can afford to buy if she spends her entire income.
• Opportunity cost is the next best alternative use of the money, or the forgone opportunity.

The Effects of Price Changes: Substitution and Income Effects

• A relative rise in the price of a good will always cause an individual to choose less of that good, by holding utility constant (Substitution 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 (Income Effect).
• Normal goods are Goods for which demand increases as income rises.
• Inferior goods are Goods for which demand falls as income rises.

Putting the Tools to Work: TANF and Labor Supply Among Single Mothers

• Joelle has a choice of taking more leisure and consuming less, or taking less leisure (working harder) and consuming more.
• With a TANF guarantee of $5,000 and a benefit reduction rate of 50%, the budget constraint becomes ABD.
• Once she has taken more than 1,000 hours of leisure, the budget constraint flattens, and she now can enjoy $5,000 of consumption even with 2,000 hours of leisure at point D.
• Utility Maximization for Sarah: When the TANF guarantee is $5,000, the optimal choice for Sarah is to take 1,910 hours of leisure and consume $5,450 at point A.
• When the guarantee falls to $3,000, she reduces her leisure to 1,655 hours, and her consumption falls to $4,275 at point B.
• Utility Maximization for Naomi: Because Naomi values leisure more highly relative to consumption than Sarah, she chooses 2,000 hours of leisure regardless of the TANF guarantee.
• The reduction in guarantee therefore lowers Naomi's consumption from $5,000 to $3,000.

Equilibrium and Social Welfare

• Welfare economics is the study of the determinants of well-being, or welfare, in society.

Demand Curves

• Demand curve is the quantity of a good demanded by individuals at each price.
• Changes in the price of movies shift the budget constraint, changing the number of movies demanded by individuals.

Elasticity of Demand

• The percentage change in the quantity demanded of a good caused by each 1% change in the price of that good.
• Elasticities of demand are typically negative, since quantity demanded typically falls as price rises, and 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 the cross-price elasticity is zero.

Supply Curves

• Supply curve is the quantity of a good that firms are willing to supply at each price.
• Marginal productivity is the impact of a one unit change in any input, holding other inputs constant, on the firm's output.
• The incremental cost to a firm of producing one more unit of a good (Marginal cost).
• The difference between a firm's revenues and costs (Profits) maximized when marginal revenues equal marginal costs.

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.

Social Efficiency

• Social efficiency represents the net gains to society from all trades that are made in a particular market.
• It is composed of consumer and producer surplus.
• Consumer surplus is the benefit that consumers derive from consuming a good, above and beyond the price they paid for the good.

Producer Surplus

• The benefit that producers derive from selling a good, above and beyond the cost of producing that good.

Social Surplus

• Total social surplus (social efficiency) is the sum of consumer surplus and producer surplus.

Competitive Equilibrium Maximizes Social Efficiency

• Deadweight loss: The reduction in social efficiency from denying trades for which benefits exceed costs.
• First Fundamental Theorem of Welfare Economics: The competitive equilibrium, where supply equals demand, maximizes social efficiency.

From Social Efficiency to Social Welfare: The Role of Equity

• Social welfare is 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.

Equity-Efficiency Trade-off

• Society must make a choice 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.

Utilitarian SWF

• Society's goal is to maximize the sum of individual utilities with a utilitarian social welfare function.
• SWF = U1 + U₂ + . . . + UN, and the utilities of all individuals are given equal weight, and summed to get total social welfare.

Rawlsian Social Welfare Function

• 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).
• 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.

Equity Criterion

• Commodity egalitarianism: society should ensure that individuals meet a set of basic needs, but that beyond that point income distribution is irrelevant.
• Equality of opportunity: society should ensure that all individuals have equal opportunities for success, but not focus on the outcomes of choices made.

Welfare Implications of Benefit Reductions: The TANF (Temporary Assistance for Needy Families)

• Labor market's efficiency has implications because, without TANF, the labor market is in competitive equilibrium at point X.
• There's an efficiency implication when introducing TANF, because labor supply falls to S2 and creating a deadweight loss of A+B+C+D+ Ε.
• When TANF benefits are reduced, supply increases to S3, and social efficiency rises by A + B + C.
• There's also equity to be considered and 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.

Conclusion

• This chapter has shown both the power and the limitations of the theoretical tools of economics.
• By making relatively straightforward assumptions about how individuals and firms behave, complicated questions such as how TANF benefits affect the labor supply of single mothers, and the implications of that response for social welfare can be addressed.
• The changes are imprecise about the potential size of the changes that occur in response to changes in TANF benefits.