Welfare economics

Lecture note 5

Warning

• Much of what follows if not in the course textbook

• Some of it comes from the far more advances Mas-Collel, Whinston & Green textbook

• Some of it comes from too many dispersed sources

• So come to class!

Goals

• Want to make normative statements• First, without any cardinality assumptions

– Pareto efficiency– Welfare theorems

• Next, with cardinality assumptions– Consumer surplus

– Social welfare functions– Social choice functions

Basic question

• In GE framework– Allocation:

• Consumption/production vector

– Feasible allocation

• How do we compare feasible allocations?– Which one do we pick?

Edgeworth box and utility possibility frontier

No interpersonal comparisons

• Originally, utility fn only ordinal– Building blocks

• Implications for interpersonal comparisons– Are tradeoffs possible?

Pareto efficiency

• Can still eliminate subset of feasible allocations

• Definition of Pareto efficient allocation

Diagram on UPF

Diagram on Edgeworth box

Pareto superiority

• Definition of superiority

• Pareto efficiency does not imply superiority

– Major stumbling block for potential policies• E.g., lobbying

Other problems

• Information requirements

• Still doesn’t yield unique prescription

• Silent on distribution

• So need something else

Competitive markets

• Despite problems, still desirable property

• However given info problems, how to implement it?

FFTWE

• Statement

• Assumptions– Price-taking

– Perfect information– No externalities/complete markets

FFTWE – sketch proof

• Consumers– Relative prices = MRS

• = desirability of switching

• Producers– Relative prices = TRS

• = ability to switch

• Breakdowns

FFTWE diagram

• Edgeworth box– Note previous diagram

• Exchange economy: MRS equalised

FFTWE

• Implication– Can trust market

• However– Equity?– Doesn’t always Pareto dominate alternative

• Also– Assumptions

Need interpersonal comparisons

• Even under ideal conditions, FFTWE is silent on distribution– Need refinement

• Social welfare fn– Definition

• Domain

• Range

Social welfare fns

• Under ordinal utility, extent of preference did not exist

• For non-degenerate social welfare fn to exist

– need cardinal utility

Social welfare fns

• Examples– Rawlsian

– Convex

– Utilitarian• Equal weights

• Different weights

Social welfare fns

• Typical features– Increasing

– Symmetric

– Convex

First-best planner problem

• Statement

• Q: how does Pareto efficiency relate to the solution?

– Which properties define link?

Standard procedure in micro

• Previously (positive economics)1. Make assumptions

• Action space• Payoff functions

2. Solve for behaviour3. Derive testable predictions4. Empirically evaluate model

• Now add one step (normative economics)– Solve planner problem

• Check if system is efficient• Make prescriptions

Problems with social choice theory

• Arrow critique– Impossibility theorem

• Sen critique– Questions Pareto efficiency

• Operationalisability critique

Application: cost-benefit analysis

• Easiest social welfare fn is pure utilitarian

• Need to cardinalise utility– Q: what’s the easiest unit?

Monetising utility

• How to get from utility to money?• Easiest way

– Have a base and an alternative allocation• Typically status quo and potential policy alternative

– E.g., a price change

CV & EV

• Compensating variation

• Equivalent variation

CV diagram

EV diagram

CV vs. EV

• Cause of difference

• Which is preferred?

Measurement

• Direct survey

• Revealed preference method

• Q: pros and cons?

Consumer surplus

• One alternative is consumer surplus– Definition

– Intuition on definition

Consumer surplus diagram

CS vs EV vs CV

• How are they related

• When are they all the same

Why use CS?

• Main advantage is potential additional method of quantification

Producers surplus

• Definition:

• Intuition:

• Less complicated than CS because:

PS diagram

Recap on CS and PS

• CS and PS allows us to measure welfare effects of price changes– Allow interpersonal comparison

• Also allow winner/loser breakdown

Example: imposing a tax

Example: price ceiling