economics 4315/7315: public economics

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).


Analysis of resource sharing

Pure Exchange EconomyTwo goods, two individualsOur running example:

Bob - AnneFood - Clothing


Edgeworth box

Anne’s preferences

Food

Clothing


Edgeworth box

Resource constraints

Food

Clothing

AvailableFood

AvailableClothing

A

Bob's clothingBob's origin

Anne'sorigin

Anne'sClothing

Anne'sFood


Edgeworth box

Bob’s preferences

Food

Clothing

UtilityIncreases


Edgeworth box

An allocation example

Food

Clothing

Bob'sIndifferenceCurve

Anne'sIndifferenceCurve A


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


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


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


Boundary point

C is an efficient point

Food

Clothing

C Bob caresalmost solely aboutclothing in this example


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


Math of the tangency condition

max{fA,cA,fB,cB}

uA(fA, cA)

Subject touB(fB, cB) = u

fA + fB = 10

cA + cB = 10


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


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


Contract curveContract curve = the set of efficient pointsPareto optimality is satisfied by many pointsWithout altruism: Giving everything to one person is optimal

Food

Clothing


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


Optimality of the market equilibrium

Price

Quantity

S

D

Q*Under production

Over production

Positivesurplus

Negativesurplus


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


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


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


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


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


Equity

Another reason for interventions

Food

Clothing

Bob's origin

Anne's origin

Potentialmarketoutcome


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


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)


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”


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”)


economics 4315/7315: public economics

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