Upload
others
View
8
Download
0
Embed Size (px)
Citation preview
Economics 4315/7315: Public Economics
Saku Aura
Department of Economics - University of Missouri
1 / 28Economics 4315/7315: Public Economics
Normative (welfare) economics
Analysis of efficiency (and equity) in:
resource sharingproductionin any situation with one or more economic/social actors withwell-defined objectives
Not covered in detail in the textbookSupplementary reading: Pindyck and Rubinfeld, Chapter 16 (8thedition).
2 / 28Economics 4315/7315: Public Economics
Analysis of resource sharing
Pure Exchange EconomyTwo goods, two individualsOur running example:
Bob - AnneFood - Clothing
3 / 28Economics 4315/7315: Public Economics
Edgeworth box
Anne’s preferences
Food
Clothing
4 / 28Economics 4315/7315: Public Economics
Edgeworth box
Resource constraints
Food
Clothing
AvailableFood
AvailableClothing
A
Bob's clothingBob's origin
Anne'sorigin
Anne'sClothing
Anne'sFood
5 / 28Economics 4315/7315: Public Economics
Edgeworth box
Bob’s preferences
Food
Clothing
UtilityIncreases
6 / 28Economics 4315/7315: Public Economics
Edgeworth box
An allocation example
Food
Clothing
Bob'sIndifferenceCurve
Anne'sIndifferenceCurve A
7 / 28Economics 4315/7315: Public Economics
Pareto improvement
A Pareto Improvement is a situation where at least one person ismade better off without hurting anyone else.
Food
Clothing
Bob'sIndifferenceCurve
Anne'sIndifferenceCurve A
Allocationsbetter than A
8 / 28Economics 4315/7315: Public Economics
Pareto efficiency
An allocation is Pareto efficient (or ”efficient”, ”optimal” or ”Paretooptimal”) if
No Pareto improvements are possibleIn ”plain” English: It is impossible to rearrange the allocation andmake at least one person better off without hurting someone else
No free lunches: just trade offs
9 / 28Economics 4315/7315: Public Economics
Efficiency and tangency
Tangency (or non-crossing) of indifference curves required forefficiency (in an interior allocation)
Food
Clothing
12
3
4
B
1: Better for Anne, worse for Bob
2,3: Worse for both
4: Better for Bob, worse for Anne
10 / 28Economics 4315/7315: Public Economics
Boundary point
C is an efficient point
Food
Clothing
C Bob caresalmost solely aboutclothing in this example
11 / 28Economics 4315/7315: Public Economics
Formal proof of the tangency condition
Assign one of the individuals (say Bob) a fixed level of utilityub(fb, cb) = u.Maximize the utility of Anne subject to Bob’s utility constraint andthe total resource constraintsFor simplicity let there be 10 units of both food and clothing eachIn our 2 person, 2 good case there is only one degree of freedom
12 / 28Economics 4315/7315: Public Economics
Math of the tangency condition
max{fA,cA,fB,cB}
uA(fA, cA)
Subject touB(fB, cB) = u
fA + fB = 10
cA + cB = 10
13 / 28Economics 4315/7315: Public Economics
Math continued
Substituting in the resource constraint we have a LaGrangian:
max{fA,cA}
uA(fA, cA) + λ(
uB(10− fA, 10− cA)− u)
Taking the first-order conditions and rearranging gives:
uAf
uAc=
uBf
uBc
14 / 28Economics 4315/7315: Public Economics
Example
Ann: Perfect substitutes uA(f, c) = f + c.Bob: Cobb-Douglas UB(f, c) = log f + log c.
Efficiency: MRSA = MRSB ⇔ 1 = cB
fB ⇔ fB = cB
In this example, Bob should always consume equal amounts of foodand clothing
15 / 28Economics 4315/7315: Public Economics
Contract curveContract curve = the set of efficient pointsPareto optimality is satisfied by many pointsWithout altruism: Giving everything to one person is optimal
Food
Clothing
16 / 28Economics 4315/7315: Public Economics
Production economy: partial equilibriumReminders: consumer surplus, producer surplus, total surplusProducer Surplus=Variable ProfitsTotal Surplus= Producer Surplus+ Consumer Surplus
Price
Quantity
S
D
P*
Q*
Consumersurplus
Producersurplus
17 / 28Economics 4315/7315: Public Economics
Optimality of the market equilibrium
Price
Quantity
S
D
Q*Under production
Over production
Positivesurplus
Negativesurplus
18 / 28Economics 4315/7315: Public Economics
Optimality of the market equilibrium
With production, efficiency requires equality of demand and supplyUsing inverse demand and inverse supply curves:
Marginal Willingness to Pay = Marginal Cost
19 / 28Economics 4315/7315: Public Economics
First welfare theorem
Huge significance for the classical liberal (conservative) school ofthoughtGoes back to Adam SmithUnder certain conditions: markets deliver first-best(Pareto-Efficient) outcomes
20 / 28Economics 4315/7315: Public Economics
First welfare theorem intuition
In a market equilibrium prices decentralize the need for information:
All the relevant information about scarcity and production cost; andall the relevant information about consumer preferences and needs;
is in the prices
21 / 28Economics 4315/7315: Public Economics
Sketch of a ”proof” for the first welfaretheorem
Pareto Optimality Market EquilibriumConsumers Equality of the MRS between consumers Each consumer equates his/her MRS to the relative price (same for everyone) Partial equilibrium with production Demand=Supply Demand=Supply
22 / 28Economics 4315/7315: Public Economics
First welfare theorem requires no marketfailures
Market Failures (examples):1 Market power2 Externalities3 Public goods4 Informational problems:
Moral HazardAdverse Selection
Market failures are a potential reason for a government intervention
23 / 28Economics 4315/7315: Public Economics
Equity
Another reason for interventions
Food
Clothing
Bob's origin
Anne's origin
Potentialmarketoutcome
24 / 28Economics 4315/7315: Public Economics
Equity
Under very specialized conditions the ”Second Welfare Theorem”holdsThis says that the only intervention needed is costless redistributionof income/wealthNot relevant for practice: costless redistribution not possibleThe equity-efficiency trade off a key to understanding policy
25 / 28Economics 4315/7315: Public Economics
Utilitarianism and the social welfare function
In order to represent equity-efficiency trade offs mathematicallyeconomists often rely on a Social Welfare FunctionThe form usually used is the sum of individual utilities
Social WelfareW = uA + uB
One justification:
For policy analysis we need to be able to compare individual utilitiesProvides a reasonable presentation of the relevant equality-efficiencytrade offs for a particular (small) policy change
Can be justified through ”Veil of Ignorance” experiments (Rawls,Harsanyi)
26 / 28Economics 4315/7315: Public Economics
Utilitarianism: background
Historically an English-speaking school of moral philosphyPart of the consequentialist school of moral philosophy: ”the endresult is all that matters”Contrast with proceduralism: ”fair process is all that matters”
27 / 28Economics 4315/7315: Public Economics
Utilitarianism: some criticisms
Remember your micro: Utility is an ordinal concept. Here we are(through value judgements) forcing cardinalityChoice of welfare function is subjectiveArrow’s Impossibility Theorem limits the domain of applicabilityWithout other constraints can lead to paradoxical conclusions:
Mankiw/Hamermesh: height tax, beauty taxPopulation ethics: repugnant conclusions
Further (very optional reading): collected works of Amartya Sen, atextbook by Peter Lambert (”The Distribution and Redistribution ofIncome”)
28 / 28Economics 4315/7315: Public Economics