Public Economics

LECTURE 1 - Introduction

Public economics

Study of government’s intervention in the economy. (HOW does it intervene)

Why is public economics relevant

• Affects all individuals (Ex: Taxes)

• Improves life of all citizens (Ex: Pensions)

• Asks if there is a “good” government (Depends on the pov)

2 questions of this class

1. How do governments affect the economy? Which decisions are taken? - POSITIVE APPROACH (objective)

2. What policy decisions should the government make and how should policies be designed? - NORMATIVE APPROACH (ALWAYS with a specific goal, that’s why it is normative) (Subjective)

Positive analysis

Why is there a public sector? Where government objectives emerge? How are policies chosen? What are the observed observed effects?

Assumption: There is a limited set of available policies (information, compliance, administrative costs are constraints)

Ex: Taxe revenues decrease by 10% → List the impact of this reduction in government resources.N

Normative analysis

What are the best policies? Optimal policy is the one that meets gov goals.

Assumption:

• Government has a specified set of objectives (including the policy of laissez-faire)

• Aggregate social welfare can be measured and welfare levels of differnt individuals can be compared.

Ex: Goal is to have optimal taxation to ensure everyone is better off, or not too much worse off -> Policy is decided to reach this goal.

Government interventions

• Public revenues

• Public expenditures

• Prices: Taxes, welfare, social insurance, public goods

• Regulations: Labour market, product market, environment

• Employer

Global trend of the wieght of the public sector

19th C: Minimal state, public spendig is around 10% of GDP, no social spending

20th C: Growth, especially between 1960-1980

High level today: About 45% of the GDP but hetegeneitya cross OECD countries.

Social expenditure

• Health

• Education

• Pensions

Social spending in public spending

Social insurance explains an important part of public spending and the differences across countries.

Ex: Bismarck’s social insurance in Germany, Beveidge National insurance in UK…

Different models of welfare state

• Continental

• Nordic

• South

• Anglo-saxon

What will cause increase in social spendings in the future

Increase in the elderly population around the world → Increase in retired persons → Increase in the number of pensions → Increase in social spendings.

Types of taxations

• Direct taxes

• Indirect taxes

• Contributions

(Direct and indirect taxes got o general revenues of the state, WHEREAS contributions go to fund a specific program).

Types of taxation: direct taxes

• Labor income

• Capital income

• Corporate

• Wealth (property, estate, inheritence)

Types of taxation: indirect taxes

• Consumption (VAT, sales tax, excise tax)

• Production

  • Trade (import tariffs)

Types of taxes: Contributions

Directed to the funding of a specific welfare program, such as soc ial sescurity, health care or unemplotyment benefits.

Regressive taxation

A system where the tax rate or burden takes a larger percentage of income from low-income earners than from high-income earners.

Ex: VAT takes a higher proportion of income of low income than large incomes.

Solution → Different VAT rates depending on the good.

Justifications for the public sector

• Minimal state: An economy requires at least

  • Property rights

  • Contract laws (to enforce rules)

• Market failures

  • Government must intervene to correct them

• Redistribution

  • Government redistribute resources to reduce inequality.

Growth of the public sector

• Development models: As you develop, there is a larger government

• Wagner’s law: Public expenditure increases with economic growth (as a proportion of income) as public goods have a high elasticity (education, healthcare)

• Baumol’s law: Tech of the public sector is labor intensive and cannot subsittute capital for labor (contrairement au private sector) → Thus public sector expenditure have to increase to maintain a constant level of public sector output for the increased productivity in the private sector.

• Political economy: Democratization increases the power of the poor → Making the median voter poorer → Voters requiring redistribution and public goods.

• Ratchet effect: If expenditure increase, the level of expenditure does not fall back: debts, people get used, electoral promises.

Leviathan theory - Excessive govenrment

The government is controlled by self-interest bureaucrats who max their private utility (not idealism). They try to increase the size of the bureau, → public sector increases.

LECTURE 2 - Welfare economics and public choice

Two fundamental criterion of a policy

• Efficiency

• Equity

Ex: Increasing revenues might lead to a reduction in equity because the distribution might not be changed as well.

Efficiency

How well resources are allocated, the total amount.

Graph: Efficiency is reached when we are ON the curve.

Equity

how resources are distributed among individuals.

Graph: Improve distirbution by moving ALONG the curve.

2 roles of the government

• Efficiency: efficient private market allocation (competitive equilibrium)

• Equity: Improve distribution

invisible hand of adam Smith

Individually motivated decisions produce a socially efficient outcome through the prices → coordination of demand and supply leads to an efficient equilibrium.

Positive POV: Market works well + allocation of resources is efficient.

Negative POV: There are failures, which is why we need the government to intervene to correct these failures.

Competitive economies/competitive equilibrium model

Assumptions (without them, the market fails, so they are MANDATORY):

• Prices are given for consumers’ and firms’ choices

  • prices adjust to adequate demand and supply

• All agents have access to the same information (symmetric)

2 forms of this model

• Exchange economies WITHOUT production

• Exchange economies WITH production

Exchange economy ( without production) model

• 2 consumers (h = 1, 2), 2 goods (i = 1, 2). No production — people only trade what they already own.

  Key assumptions:

  • Prices p₁ and p₂ are set by the market

  • Each consumer is a price-taker (cannot influence prices)

  • Initial endowment of consumer h: w^h = (wh1, wh2)

  • Each consumer maximizes utility U^h(xh1, xh2) subject to their budget constraint

• Each consumer chooses a consumption plan x^h = (xh1, xh2) where the budget constraint is satisfied → LAST FORMULA IS THE BUDGET CONSTRAINT for individual h. It predicts exchanges on the market because it matches the prices and the utility of each goods of every individual.

Edgeworth box

A box that contains ALL goods in the economy and shows ALL feasible allocations.

A feasible allocation satisfies: x1i + x2i = w1i + w2i (total consumption = total endowment, for each good)

 To remember:

• The total amount of goods is fixed, extra cannot be produced

• Budget constraints

• Individuals want to maximize their utility (Utility function is important and it is represented by the indifference curves)

Reading the graph:

• Individual 1 reads from bottom-left

• Individual 2 reads from top-right

• Point w = initial endowment point (starting position of the economy)

• Total supply of each good is fixed (no production)

AS A RESULT, the point w on the graph is the stage at which the economy is INITIALLY. But it can be changed to be x, y, z if the allocation changes through exchanges.

Budget constraint

spending (What you want to consume multiplied by the price…) = income (what you have multiplied by the price) (valued at market prices)

p₁·xh1 + p₂·xh2 = p₁·wh1 + p₂·wh2

It is an individual equation for both, but the visual representation is common since the total amount of goods is shared, the same for the prices.

• Slope = −p₁/p₂ (same for both consumers, same prices)

• Must pass through w (both can always afford their endowment)

• Since both conditions are identical → one single line in the box, shared by both

How to read it in the box

• Individual 1 reads from bottom-left → everything below-left of the BC is affordable for him

• Individual 2 reads from top-right → everything above-right of the BC is affordable for him

Indifference curves

A curve showing all combinations of good 1 and good 2 giving the same utility to one individual.

• Red curves = Individual 1 | Green curves = Individual 2

• Moving higher/right = higher utility for Individual 1

• Curves never shift, they reflect preferences, not prices

• Optimal choice = highest indifference curve tangent to the BC (Makes the price and the preference match) → BUT IT IS NOT THE EQUILIBRIUM BECAUSE THERE MIGHT BE EXCESS DEMAND OR SUPPLY FOR GOODS.

• Tangency condition: MRS₁,₂ = p₁/p₂

Marginal Rate of Substitution (MRS)

MRS₁,₂ = how many units of good 2 you're willing to give up for one more unit of good 1, staying equally happy.

= the slope of the indifference curve at a given point

Why MRS = p₁/p₂ at optimum?

	Meaning
MRS	Your personal trade rate
p₁/p₂	The market's trade rate

If they differ → you can do better by trading. Optimum is where they match.

Disequilibrium

Each consumer finds their own optimal point (tangent to BC) → but they land on different points.

This means: excess demand for good 1, excess supply for good 2 → markets don't clear → not an equilibrium because the market clearing condition might not be satisfied.

Market clearing condition

total demand = total endowment, for each good (the formula just below is for one good, it must be true for both so there is as such formulas to calculate as the number of oods.)

x¹(p₁,p₂) + x²(p₁,p₂) = w¹ + w²

• x¹(p₁,p₂) = what individual 1 wants to consume at those prices

• x²(p₁,p₂) = what individual 2 wants to consume at those prices

• w¹ + w² = total amount of each good that exists in the economy

→ Nobody can consume more than what exists. If this equation holds for both goods, markets clear and we have equilibrium.

Price Adjustment → Equilibrium

Because of excess demand for good 1: p₁ ↑, p₂ ↓ → BC becomes steeper (BUT IT COULD BE THE OTHER WAY AROUND, it depends on which good is in excess demand).

. A new tangency point emerges.

Equilibrium is reached when:

• Both indifference curves are tangent to the BC at the same point

• Markets clear: total demand = total endowment for both goods

→ NOW, the two indifference curves are tangent on the same point along the budget curve -> EQUILIBRIUM

First-best outcome

Achieved when when BOTH:

• production technology

• Limited endowments (=resources)

are the ONLY things restricting the choice of the decision-market.

Second-best outcome

Achieved whenever constraints OTHER than technology and resources are placed on what the planner can do (limits on income redistribution, inability to remove monopoly power, lack of information).

Equilibrium is efficient when

More cannot be achieved.

Ex: If there is a singe consumer, their preferences are the social preferences.

Pareto efficiency/optimality

A feasible consumption allocation x^ (x = y + w) is Pareto efficient if there is no alternative feasible allocation a- that satisfies BOTH:

• Allocation a- gives all consumers at least as much utility as x^

• Allocation a- gives one consumer more utility than x^

TRANSLATION: you cannot make someone better off without making someone else worse off.

Is Pareto-efficiency/optimality always relevant?

No because if someone has everything, and the rest has nothing, it is a pareto optimum, even though redistribution could make a lot of people better off. Because the one who has everything would be worse off…

→ so not always relevant.

First welfare theorem

A competitive equilibrium (i.e. the allocation achieved by the market) is Pareto efficient if it satisfies some conditions:

• No externalities or public goods

• Perfect information

• Perfect competition

→ Else, the first welfare theorem fails → justifies the governemnt intervention.

Why is the first welfare theorem relevant

The assumptions made for it to hold are crazy → So it fails almost automatically without them (in real life) → So need for government intervention.

Externalities

Actions of one party makes another party worse OR better off, and the first party either bears the costs nor receives benefits from doing so.

Negative externalities: Pollution

Positive externalities: Oil exploration

What can the government do to include externalities

• Taxes

• Subsidies

Imperfect/asymetric informaiton

Not all parties have the same information/level of information.

Ex: Adverse selection on the insurance mrket → high risk individuals go for insurance bc they hope to make it worth it. Imperfect info bc the insurance company doesn’t know the risk of everyone. → MARKET FAILS → Solution: Mandatory insurance so the pool of insurance is larger to divide the risk.

Second welfare theorem

Any pareto-efficient allocation can be achieved as a competitive equilibrium, under the same conditions of the first welfare theorem, + the lump-sum tax/transfers (redistribution of initial resources)

Ex: Economy starts at w, we want to reach e’ since it is the pareto-efficiency point. → Need to redistribute endowment because the market only acts along the budget constraint line, else no exchange… → Then from w’ to “‘, exchanges make you reach this point bc it is the pareto efficient point and equlibilurm.equilibrium

→ FAILURE of the 2nd welfare theorem since lump-sum taxes are not in the real world.

Lump sum tax/transfer

Change in the allocation BUT it doesn’t affect the behavior, it is just a change in basic endowment.

Contract curve

Set of all pareto efficient allocations in exchange economy.

Utility possibility frontier

A graph in economics that shows the maximum possible combinations of satisfaction (utility) that two or more people can achieve from a given set of resources and technology

Relationship between the edgeworth box and utility possibility fruntier

The utility possibility frontier is the contract curve but with utilities on the axes.

GRAPH: The two graphs are related. Individual 1 has a low level of utility at point a on the contract curve. (remember red for the individual 1). But it represents high level of utility for individual 2.

B, high level of utility for individual 1, and low level of utility for individual 2.

Social optimality

allocation of resources that maximizes total net benefit or economic welfare for society as a whole.

→ IT IS THE ROLE OF THE GOVERNMENT

How to choose the social optimality point?

WHICH POINT TO CHOSE ALONG THE UTILITY POSSIBILITY FRUNTIER?:

• c is inefficient

• a and b are efficient but they don’t lead to the same utility for everyone… → which one should be chose?

→ REQUIRES TO MAKE AN ASSUMPTION ABOUT GOVERNMENT’S GOAL

Welfare function

Formula that combine the individual utility levels (well-being or satisfaction) of everyone in a society into a single overall measure of collective welfare.

• Used by the government to choose the policies.

• government wants to maximize this function

• BUT what to consider to calculate this function? Different ways to aggregate individual preferences

Social indifference curve

A combination of the 2 consumers’ utilities that gives a constant level of social welfare. Along a social indifference curve, the government is indifferent.

3 types of social indifference curve

The social indifference curve depends on how you calcualte the welfare:

• Utilitarian welfare function: W = U1 + U2 - The sum of both utilities.

• Intermediate: rounded curve

• Rawlsian welfare function: W = min(U1, U2) - The lowest utility is the social utility, meaning that to maximize it, you need to focus on the lowest utilities. (Socialooossss)

→ Choosing the social welfare formula is philosophical..

Socially optimal allocation

Highest social indifference curve on the utility possibility fruntier.

How to reach the socially optimal allocation?

Tax and transfers (2nd welfare theorem)

Arrow’s impossibility theorem

No democratic mechanism in which people can express their preferences can satisfy these 4 properties:

1. Rationality (Aggregate preferences are complete and transitive)

2. Unrestricted domain (on individual preferences): works for any possible individual preferences, not just special cases

3. Weak pareto optimality: if everyone prefers A over B, society prefers A over B

4. Independence (from irrelevant alternatives): the social ranking of A vs B depends only on individual rankings of A vs B, not on some third option C

Solution to the Arrow’s impossibility theorem in political economics

Drop the unrestricted domain on indiviudual preferences (2)

OR dictatorship lol

3 voting systems and their problems

Key takeaway: same preferences, different system → different winner

This means that aggreagting the prefernces of everyone is hard/impossible in a democratic system.

Bliss point

each voter's most preferred policy (maximizes their utility)

Single-peaked preferences

the further from your bliss point, the worse → only one peak on the utility curve

Condorcet winner

policy that beats every other option in pairwise voting.

Pairwise voting = comparing two options at a time, head-to-head.

Instead of voting on A, B, C, D all at once → you vote:

• A vs B → winner goes against C → winner goes against D

The Condorcet winner is the option that wins every single pairwise vote against all others.

So which option you compare first defines the outcome → a chier.

Median voter

voter whose bliss point divides the population exactly in half

Single-peaked VS not single peaked

Single-peaked → utility goes up then down → one clear hill → Median Voter Theorem applies

Not single-peaked → utility goes up, down, up → multiple peaks → no clear winner, voting can cycle Ex: 6 and 7.

What is the solution to the Arrow’s impossibility problem?

Median voter theorem: MVT avoids Arrow's by dropping unrestricted domain (2nd condition).

CONDITIONS:

• it only works when preferences are single-peaked, which is a restriction on the domain.

→ It doesn't fully solve Arrow's, it sidesteps one condition.

Median voter theorem

If preferences are single-peaked along a one-dimensional economic policy, the median voter’s bliss point represents the equilibrium outcome of the majoritatian voting game (qm), i.e. a Condorcet winner.

'“The median voter's bliss point is the Condorcet winner”

→ Useful: tells who decides of the outcome of the democratic process → helps predict which policy will be implemented. + It sidesteps the Arrows’ problem.

Median voter always wins a majority voting election.

LECTURE 3 (1 Galasso) - The Architecture of Pension systems

Pension

Stream of money received by an individual as long as they are alive.

Why pensions matter in public economics

• Large component of the welfare state (16% of GDP in Italy)

• Redistribute across age, income groups, cohorts

• Affect labor supply, retirement, saving, taxation (Employers pay taxes for retirements, affecting negatively employement)

• Create long-term fiscal commitments that are politically hard to change

• Combine insurance, redistribution and intergenerational contracts

3 elements

• Financial sustainability of the system (can it be viable now and in the future)

• Pension adequacy (do pension systems transfer enough resources? → usually yes but it gets more and more costly)

• System fairness

2 types of fairness

• Sustainability fairness

• Intergeneration fairness

Sustainability fairness

Do you get out a fair share of what you did put in (=as an investment did you get as much?)

Intergenerational fairness

Is the system fair cohort to cohort (usually it is not → causes problems).

Ex: someone retiring in the 80s got higher pensions, contributed less, and retired at an earlier age.

Pension system characteristics

1. Coverage: who is protected?

2. Financing: who pays?

3. Formula: how are benefits calculated?

4. Risk: who bears demographic, wage, political, or financial risk?

5. Objective: Insurance, redistribution, adequacy or actuarial fairness?

Risks in the pension system

• Demographic risk: aging

• Wage risk: no economic growth

• Financial risk: funded pension → risk of getting less

• Political risk: reform

→ Who bears them?

Types of pension benefits

Contributory pensions (=income replacement, funded by contributions that hence give you a right to pension):

• Old-age or early-retirement pensions: workers who satisfy age and/or contribution requirements.

• Disability pensions: workers who become unable to work. Once you reach the retirement age you switch to old-age pension.

• Survivor pensions: spouses and children of deceased workers

Non-contributory pensions (=poverty relief, funded by the general taxation):

• social pensions or minimum-income schemes: usually for elderly individuals with low income.

Ex: RSA in France.

2. How are pension benefits financed

• Social security contribution: Paid by workers, employers, or both. Linked to earnings.

• General taxation: Used for social pensions that are without contribution, credits or benefits.

• Accumulated assets: Funded systems → accumulation of contributions invested and later converted into retirement income.

What is impacted by the financing system chosen

• Labor costs

• Redistribution

• Political exposure

Pensions systems

• Pay as you go (PAYG)

• Fully funded

Pay-as-you-go (PAYG)

Current workers pay the pensions of current retirees.

• Intergenerational transfer: every generation pays for the past one, hoping to benefit as well later.

• Depends on the number of workers, wages, contribution rates, and benefit rules.

Who benefited the most of PAYG

1st generation of PAYG because they:

• Contributed at low rates or not at all if they were already old

• Got generous pensions

• Retired earlier than current generations

PAYG: main return

• Demographic → Employment

• Economic growth → Amount of contributions

→ High demographic and economic growth ensures there is a lot of contributions.

PAYG: main risks

• Demography

• Productivity

• Politics

PAYG: Political exposure

• Eligibility

• Indexation

• Retirement age

PAYG: Transition problem

Implicit pension debt

Fully funded

Contributions are accumulated in assets

• Worker contributes ot a fund made of

  • Assets

  • Financial returns

• Benefit of annuity or drawdown once they retire.

Advantages of Fully funded

• Diversifies demographic risks

• Less reform risk

Disadvantages of fully funded

• Financial market risk

• Annuity risk

• PENSIONS ARE NOMINAL (not indexed on inflation, contrary to what is done in the PAYG)

Fully funded: main return

Market performance/how it is invested.

Fully funded main risks

• Asset prices

• Inflation: what you have is NOMINAL once you retire

• Annuity markets

Fully funded: Political exposure

• Regulation: Ex: government can impose a class of assets.

• Tax incentives

• Guarantees

Fully funded: Transition problem

Double payment if replacing PAYG

What is the impact of a pension reform

Changes WHO bears the risk. Rarely eliminates it.

3. Types of benefit formulas

• Defined Benefit (DB)

• Defined Contribution (DC)

• Notional DC (NDC)

A pension formula is a distributional rule.

Types of benefit formulas: Defined Benefit (DB)

• Benefit formula is defined in advance

• contributions or public transfers must finance it.

Types of benefit formulas: Defined Contribution (DC)

• Contributions are defined in advance

• Benefits depend on accumulated assets and returns

Types of benefit formulas: Notional Account (NDC)

• contributions are recorded in a notional account

• Benefits depend on notional wealth and life expectancy.

Table of benefit/Finance