资源简介

(共51张PPT)
2.1 Constrained Utility Maximization
2.2 Putting the Tools to Work: TANF and Labor Supply Among Single Mothers
2.3 Equilibrium and Social Welfare
2.4 Welfare Implications of Benefit Reductions: The TANF Example Continued
2.5 Conclusion
Theoretical Tools of Public Finance 2
2
This chapter covers the theoretical tools of public finance.
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.
Theoretical Tools of Public Finance
2
We can illustrate how consumers are presumed to make choices in four steps:
First, we discuss how to model preferences graphically.
Then, we show how to take this graphical model of preferences and represent it mathematically with a utility function.
Next, we model the budget constraints that individuals face.
Finally, we show how individuals maximize their utility (make themselves as well off as possible) given their budget constraints.
Introduction: How Consumers Make Choices
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.
Constrained Utility Maximization
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 key properties:
1. Consumers prefer higher indifference curves.
2. Indifference curves are always downward sloping.
2.1
Preferences and Indifference Curves
2.1
Preferences and Indifference Curves
Consumer is indifferent between A and B.
C is preferred to A or B.
Preferences and Indifference Curves
Consumer is indifferent between A and B.
C is preferred to A or B.
2.1
Utility Mapping of Preferences
2.1
Underlying the indifference curves is an individual’s utility function.
A utility function is some mathematical representation,
and so on are the quantities of the goods consumed.
is some mathematical function that describes how consumption of each good translates to utility.
Utility Mapping of Preferences: Example
2.1
Example utility function: Andrea’s utility for CDs () and Movies () is:
Andrea is indifferent between 4 CDs and 1 movie, or 1 CD and 4 movies.
Andrea prefers 3 CDs and 3 movies to either bundle.
2.1
Marginal Utility
How much do consumers like a good
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 the individual less happy than the consumption of the previous one.
Many utility functions exhibit diminish marginal utility, including
The first bite of pizza is often the tastiest.
Marginal Utility: Graphical Representation
2.1
With each additional movie consumed, utility increases but by ever smaller amounts.
2.1
Marginal rate of substitution (MRS): The rate at which a consumer is willing to trade one good for another.
Moving along an indifference curve keeps a consumer equally well off, so
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.
Marginal Rate of Substitution
Marginal Rate of Substitution
2.1
As Andrea moves down the indifference curve, getting more movies and fewer cakes, the marginal utility of cakes rises, and the marginal utility of movies falls, lowering the MRS.
Budget Constraints
2.1
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.
Quick hint: 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.
Budget Constraints
2.1
The slope of the budget constraint is the rate at which she can trade cakes for movies in the marketplace, PM/PC = –8 16 = –1 2.
2.1
The slope of the budget constraint says how much of one good you can buy if you give up one unit of the other, .
The marginal rate of substitution says how much you like trading one good for another.
If , you get more utility buying fewer CDs and more movies.
If , you get more utility buying more CDs and fewer movies.
Putting It All Together: Constrained Choice
2.1
To maximize utility, therefore:
Or, find tangency between indifference curves and budget constraint.
Putting It All Together: Constrained Choice
2.1
Putting It All Together: Constrained Choice
Whenever a consumer is at a point where the indifference curve and the budget constraint are not tangent, she can make herself better off by moving to a point of tangency.
2.1
Maximizing utility tells us how many goods a person buys at a given price.
What happens when we change the prices
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.
The Effects of Price Changes: Substitution and Income Effects
The Effects of Price Changes: Substitution and Income Effects
2.1
The substitution effect holds utility constant but changes the income while reflecting the change in relative prices.
2.1
How do changes in income affect demand
Normal goods: Goods for which demand increases as income rises.
Inferior goods: Goods for which demand falls as income rises.
The Effects of Price Changes: Substitution and Income Effects
2.1
The TANF program was created in 1996 and provides a monthly support check to families with incomes below a threshold level that is set by each state.
Suppose that Joelle is a single mother who spends all of her earnings and TANF benefits on food for herself and her children.
By working more hours, she can earn more money for food, but she has less time at home with her children and for leisure.
She would prefer time at home to time at work (leisure is a normal good). With these preferences, more work makes Joelle worse off, but it allows her to buy more food.
How does Joelle decide on the optimal amount of labor to supply
Putting the Tools to Work: TANF and Labor Supply Among Single Mothers
2.1
Putting the Tools to Work: TANF and Labor Supply Among Single Mothers: Identifying the Budget Constraint
If she takes no leisure, she can have consumption of $20,000 per year; but if she takes 2,000 hours of leisure, her consumption falls to 0. This is represented by the budget constraint with a slope of –10, the relative price of leisure in terms of food consumption.
2.1
Putting the Tools to Work: TANF and Labor Supply Among Single Mothers: Identifying the Budget Constraint
Point D marks the end of the new budget constraint and provides a new option: she can have 2,000 hours of leisure and $5,000 in food consumption because of the $5,000 TANF benefit guarantee.
Putting the Tools to Work: TANF and Labor Supply Among Single Mothers: Effects of Changes in Benefit Guarantee
2.1
Food consumption (dollars)
$20,000
2,000
Leisure (hours)
A
B
C
Slope = 10
Slope = 5
10,000
5,000
1,000
D
F
E
6,000
3,000
1,400
If the guarantee falls to $3,000, the budget constraint (AEF) doesn’t flatten until she takes more than 1,400 hours of leisure; now, with 2,000 hours of leisure, her consumption is only $3,000 at point F.
2.1
Food consumption (dollars)
$20,000
2,000
Leisure (hours)
10,000
5,000
1,000
6,000
3,000
1,400
How Large Will the Labor Supply Response Be
A
B
(1,910 hours,
$5,450)
(1,655 hours,
$4,725)
The substitution effect holds utility constant but changes relative prices.
2.1
The size of the response depends on:
How much was earned before the benefit change.
The size of the income and substitution effects on her leisure/labor decision.
Let’s consider two individuals: Individual 2 values leisure more highly relative to consumption than Individual 1 does.
TANF and Labor Supply Among Single Mothers: How Large Will the Labor Supply Response Be
2.1
When the TANF guarantee is $5,000, the optimal choice 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 $4,725 (at point B).
How Large Will the Labor Supply Response Be
2.2
Food consumption (dollars)
$20,000
2,000
Leisure (hours)
10,000
5,000
1,000
6,000
3,000
1,400
How Large Will the Labor Supply Response Be
B
A
(2,000 hours,
$5,000)
(2,000 hours,
$3,000)
Because leisure is valued more highly relative to consumption for this individual, she chooses 2,000 hours of leisure regardless of the TANF guarantee. The reduction in guarantee therefore lowers her consumption from $5,000 (at point A) to $3,000 (at point B).
2.3
How do markets determine what gets produced Do they produce the right amount
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.
Welfare economics: The study of the determinants of well-being, or welfare, in society.
Equilibrium and Social Welfare
2.3
How much of a good do people want to buy at the market price
Demand curve: A curve showing the quantity of a good demanded by individuals at each price.
Obtained by finding the utility-maximizing bundle at each price.
Demand Curves
2.3
Demand Curves
The relationship between the price and utility maximizing choices can be used to trace out the demand curve for movies, DM.
2.3
Elasticity of demand: The percentage change in the quantity demanded of a good caused by each 1% change in the price of that good.
Mathematically:
Elasticity of Demand
Elasticities of demand:
Elasticities of demand are often negative: Quantity demanded falls as price rises.
Elasticities of demand are typically not constant along a demand curve.
Typically, a change in the price of one good will affect demand for other goods as well.
The effect of one good’s prices on the demand for another good is the cross-price elasticity.
2.3
Elasticity of Demand
Perfectly inelastic and perfectly elastic demand:
When the elasticity of demand is zero, the demand curve is perfectly inelastic, in which case
the demand curve is vertical, and quantity demand does not change when price rises.
When the elasticity of demand is infinite, the demand curve is perfectly elastic, in which case
the demand curve is horizontal, and quantity demanded changes infinitely for even a very small change in price.
2.3
Elasticity of Demand
2.3
How much do firms want to sell or produce at each price
Supply curve: A curve showing the quantity of a good that firms are willing to produce (supply) at each price.
Supply curves are the outcome of profit maximization by firms.
Firms produce output using a production, such as .
Supply Curves
Profit Maximization
2.3
How do firms decide how much to produce
Marginal productivity: The impact of a 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.
Firms choose quantities to maximize profits, the difference between revenues and costs.
Profit is maximized when market price equals marginal cost.
Equilibrium
2.3
To undertake welfare analysis we need to analyze at the market level:
The demands of each individual who is demanding goods in this market is added to obtain market demand.
The supplies of each firm that is supplying goods in the market is added to get market supply.
The market-level supply and demand curves interact to determine the market equilibrium.
Social efficiency is maximized at the competitive equilibrium.
Equilibrium: Graphical Representation
2.3
Equilibrium is the price and quantity pair that will satisfy both demand and supply.
Social Efficiency
Social efficiency represents the net gains to society from all trades that are made in a market, and it consists of the sum of two components: consumer and producer surplus. Also called total social surplus.
Consumer surplus: 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.
2.3
Consumer Surplus: Graphical Representation
2.3
Consumer surplus is the area under the demand curve and above equilibrium price. Demand = willingness to pay.
Producer Surplus: Graphical Representation
2.3
Producer surplus is the area above the supply curve and below equilibrium price. Supply = marginal cost.
Social Surplus: Graphical Representation
2.3
Social surplus for this market is the sum of the shaded areas A + B + C + D + E.
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.
Quick hint: Deadweight loss is a triangle that points toward the equilibrium price and grows away from it.
2.3
From Social Efficiency to Social Welfare: The Role of Equity
2.3
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.
Difficult in practice to redistribute like this.
Social welfare: The level of well-being in society.
Determined by both how much gets produced and how it is distributed.
Equity–efficiency trade-off: The choice society must make between the total size of the economic pie and its distribution among individuals.
Social Welfare Functions
2.3
Social Welfare Function (SWF): A function that combines the utility functions of all individuals into an overall social utility function.
The utilitarian social welfare function maximizes the sum of individual utility:
The Rawlsian social welfare function maximizes the utility of the worst-off member of society:
Choosing an Equity Criterion
2.3
Social welfare functions reflect different possible equity criteria, including:
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.
Welfare Implications of Benefit Reductions: The TANF Example Continued: Efficiency
2.4
Effects on efficiency:
Without TANF, the labor market is in competitive.
When TANF is introduced, labor supply falls, which creates a deadweight loss.
When TANF benefits are reduced, supply increases and social efficiency rises.
Welfare Implications of Benefit Reductions: The TANF Example Continued: Efficiency
2.4
When TANF benefits are reduced, supply increases to S3, and social efficiency rises by A + B + C.
Increasing TANF benefits reduces efficiency. Is this a good thing
Governments have programs such as TANF because their citizens care not only about efficiency, but also about equity.
While reducing TANF benefits may increase social efficiency, it need not increase social welfare.
Overall conclusion depends on social welfare function.
2.4
Welfare Implications of Benefit Reductions: The TANF Example Continued: Equity
This chapter has shown both the power and the limitations of the theoretical tools of economics.
Using theoretical tools, 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, we have been very imprecise about the potential size of the changes that occur in response to changes in TANF benefits.
2.5
Conclusions

展开更多......

收起↑