Theoretical Tools of Public...
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Theoretical Tools of Public Economics
Part-2
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Previous Lecture
• Definitions and Properties
– Utility functions
• Marginal utility: positive (negative) if x is a ‘good’(‘bad’)
• Diminishing marginal utility
– Indifferences curves
• Downward sloping
• Consumers prefer higher indifference curves
• Do not intersect
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Previous Lecture
• Definitions and Properties
– Optimization with constraints
• Utility maximization subject to a budget constraint
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Application in Public Economics(TANF Example-Chapter 2.2)
– Temporary Assistance to Needy Families: provides a monthly support check to families with incomes below a threshold level that varies by state.
– Largely targeted to single-female-headed households with children.
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Application in Public Economics(TANF Example-Chapter 2.2)
– Suppose Joelle is a single mother who spends all of her earnings and TANF benefits on food for her and her children (consumption denoted by C)
– The cost of working more is spending less time with her family (time worked denoted by W or leisure-time denoted by L)
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Application in Public Economics(TANF Example-Chapter 2.2)
– Can use
1. Consumption (C) and time-worked (W): one good and one bad
2. Consumption (C) and leisure-time (L): two goods
– We will use the second approach and then calculate the time-worked by subtracting the leisure-time from the total work hours.
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Application in Public Economics(TANF Example-Chapter 2.2)
– Assume that Joelle can work a maximum of 2000 hours per year at $10/hour.
– Assume further that a unit of food costs $1.
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Application in Public Economics(TANF Example-Chapter 2.2)
• Budget constraint without TANF
– With the first approach (using C and W)
WC 10≤
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Application in Public Economics(TANF Example-Chapter 2.2)
• Budget constraint without TANF
– With the second approach (using C and L)
– In other words, the price of leisure is $10/hour.
( )LC −≤ 200010
2000010 ≤+ LC
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Application in Public Economics(TANF Example-Chapter 2.2)
• The budget constraint without TANF
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Application in Public Economics(TANF Example-Chapter 2.2)
• The budget constraint under TANF
– Scenario-1: Guarantee of $5000 and 50% reduction rate
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Application in Public Economics(TANF Example-Chapter 2.2)
• Budget constraints under TANF (Scenario-1)
If or 1000≤W 20001000 ≤< L
( )WWC 105.0105000 −+≤
( )LC −+≤ 200055000
150005 ≤+ LC
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Application in Public Economics(TANF Example-Chapter 2.2)
• Budget constraints under TANF (Scenario-1)
If or 1000>W 10000 ≤< L
WC 10≤
2000010 ≤+ LC
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Application in Public Economics(TANF Example-Chapter 2.2)
• The budget constraint under TANF
– Scenario-2: Guarantee of $3000 and 50% reduction rate
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Application in Public Economics(TANF Example-Chapter 2.2)
• Budget constraints under TANF (Scenario-2)
If or 1400≤W 20001400 ≤< L
( )WWC 105.0103000 −+≤
( )LC −+≤ 200053000
130005 ≤+ LC
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Application in Public Economics(TANF Example-Chapter 2.2)
• Budget constraints under TANF (Scenario-2)
If or 600>W 6000 ≤< L
WC 10≤
2000010 ≤+ LC
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Application in Public Economics(TANF Example-Chapter 2.2)
• What if we switch from Scenario-1 to Scenario-2?
– Substitution effects
– Income effects
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Application in Public Economics(TANF Example-Chapter 2.2)
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Application in Public Economics(TANF Example-Chapter 2.2)
• How do we calculate the magnitude of the impact of the switch from Scenario-1 to Scenario-2?
• Assume that Joelle’s utility function takes the following forms
– Case 1:
– Case 2:
– Case 3:
( ) ( ) ( )LCLCU ln175ln100, +=
( ) ( ) ( )LCLCU ln300ln75, +=
( ) ( ) ( )LCLCU ln75ln300, +=
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Application in Public Economics(TANF Example-Chapter 2.2)
• Case-1
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Application in Public Economics(TANF Example-Chapter 2.2)
• Case-2
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Equilibrium and Social Welfare (Chapter 2.3)
• Now that we examined the individual level, what happens at the aggregate level?
– How does the aggregate labor supply change with TANF among low income families?
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Equilibrium and Social Welfare (Chapter 2.3)
• Welfare economics: the study of determinants of well-being, or welfare, in society.
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Equilibrium and Social Welfare (Chapter 2.3)
• How do we determine social welfare?
– First we define the determinants of social efficiency (the size of the economic pie),
• Demand curves
• Supply curves
• Equilibrium
– Then we discuss how to introduce equality (how to distribute the pie)
• Social welfare function
• How to choose the social welfare function?
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Equilibrium and Social WelfareDemand Curves
• Demand curve: A curve showing the aggregate quantity of a good demanded by individuals at each price.
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Equilibrium and Social WelfareDemand Curves
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Equilibrium and Social WelfareDemand Curves
• Elasticity of demand: The percentage change in the quantity demanded of a good caused by each 1% change in the price of that good.
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Equilibrium and Social WelfareDemand Curves
• Elasticity of demand:– They are typically negative, since quantity demanded typically
falls as price rises.
– 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.
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Equilibrium and Social WelfareSupply Curves
• Supply curve: A curve showing the quantity of a good that firms are willing to supply at each price.
– Analogous to the utility maximization problem
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Equilibrium and Social WelfareSupply Curves
• Analogous to utility maximization
– Utility functions � Profit functions
• Profit function:
– Total revenue (p*q(K,L)) – Total cost (C(q(K,L))
– Price*Production function – Cost function
– Maximize with respect to goods � Maximize with respect to inputs and outputs
• q: output, K (capital) and L (labor) input
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Equilibrium and Social WelfareSupply Curves
• Analogous to utility maximization
– Marginal utility � Marginal productivity
• Marginal productivity of K: Keeping all other inputs, the change in output as a result of a unit change in capital
– Diminishing marginal utility � Diminishing marginal productivity
( )LKqK
MPK ,∂
∂=
0<∂
∂KMP
K
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Equilibrium and Social WelfareSupply Curves
• The optimum quantity of output is achieved at the point where marginal revenue equals marginal cost.
– Marginal cost: The incremental cost to a firm of producing one more unit of a good.
• (In a competitive market), All firms with initial marginal costs lower than the market price will produce until their marginal costs equal the market price.
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Equilibrium and Social WelfareMarket 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 between the supply and demand curves.
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Equilibrium and Social WelfareMarket Equilibrium
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Equilibrium and Social WelfareSocial Efficiency
• Consumer surplus: the gain to consumers from trades in a market for consumer goods.
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Equilibrium and Social WelfareSocial Efficiency
• Produces surplus: the benefit that producers derive from selling a good, above and beyond the cost of producing that good.
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Equilibrium and Social WelfareSocial Efficiency
• Social surplus: the sum of consumer surplus and producer surplus
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Equilibrium and Social WelfareSocial Efficiency
• First Fundamental Theorem of Welfare Economics: the competitive equilibrium, where supply equals demand, maximizes social surplus (social efficiency).
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Equilibrium and Social WelfareSocial Welfare
• Social welfare: the level of social well-being in society; determined both by social efficiency (the size of the economic pie) and the equitable distribution of society’s resources (the distribution of the pie)
• Second Fundamental Theorem of Welfare Economics: Society can attain any socially efficient outcome by suitably redistributing resources among individuals and then allowing them to trade freely.
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Equilibrium and Social WelfareSocial Welfare
• Equity-efficiency trade-off: The choice society must make between the total size of the economic pie and its distribution among individuals.
• How to measure this trade-off?
– Social welfare functions
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Equilibrium and Social WelfareSocial Welfare Functions
• SWF maps the set of individual utilities in society into an overall society utility function.
• Examples:
– Utilitarian SWF:
– Rawlsian SWF:
NUUUSWF +++= ...21
( )NUUUSWF ,...,,min 21=
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Equilibrium and Social WelfareSocial Welfare
• How to choose a SWF?
– Two different approaches
• 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.
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Equilibrium and Social WelfareTANF Example