Reminder on the basics

Question 1

Welfare theorems : 1st theorem :

Answer 1

Any competitive equilibrium is Pareto-efficient (or

Pareto-optimal)

Question 2

Welfare theorems : 2nd theorem:

Answer 2

There exists a set of prices and transfers such that

any Pareto-efficient allocation can be supported in a competitive equilibrium

Question 3

These theorems are true under assumptions :

Answer 3

• Perfect markets (no transaction cost, perfect information)
• Agents are price takers
• Non-satiation of preferences

Question 4

These theorems do not hold when :

Answer 4

there are externalities, public goods, market power

Question 5

Externalities : def in words

Answer 5

when there is an interaction between two agents that does not occur through a market. Can be production or consumption externalities, positive or negative

Question 6

Externalities : def in math

Answer 6

Two agents i and j. Agent j’s payoffs is uj .
hi is an action taken by agent i. Externality when
∂uj/∂hi is not = 0

Question 7

Externalities : properties

Answer 7

with externalities, the competitive equilibrium is not

Pareto-optimal

Question 8

Externalities : intuition

Answer 8

individuals do not internalize their externality on the
other(s). At the equilibrium, too much externality if negative (too little if positive) relative to the Pareto-efficient allocation

Question 9

Decentralized equilibrium : Program of firm:

Answer 9

minimize production costs to reach a level of
production y ; min y ;h C(y; h)
And h∗ = ̄h, the maximum level of pollution

Question 10

Decentralized equilibrium : Intuition:

Answer 10

Reducing pollution increases the firm’s cost so the firm does not make any effort to reduce pollution and pollutes as much as it can
As a consequence, equality of the sum of marginal disutilities and marginal cost of depollution is not satisfied

Question 11

Decentralized equilibrium : Traditional solutions:

Answer 11

• Impose a cap on the level of pollution
• Impose a tax for pollution
• Create a market of pollution permits

Question 12

Public goods and the tragedy of commons : definition

Answer 12

i) non-rivality: consumption by one does not prevent another agent from consuming
(ii) non-exclusion: cannot exclude someone from consuming when he/she does not pay

Question 13

Tragedy of the commons : definition

Answer 13

Everyone likes public goods but no one

wants to pay for them

Question 14

Problem of free-riding :

Answer 14

if we ask agents to contribute for a public good, they have incentive to lie about their tastes for public good and avoid to subscribe because they cannot be excluded.
This leads to under-provision of the public good.

Question 15

Categories of public goods : Pure public good if:

Answer 15

(i) impossibility to exclude someone
(ii) agents are forced to consume
(iii) No degradation of quality with the number of users
Examples: lighthouse, air, pollution, army, water sanitation…

Question 16

Mixed public goods :

Answer 16

Two types :
(i) Common resources: when there is congestion, i.e. utility of someone depends on the number of users
Examples: roads, fish, park
(ii) Club goods: non-rivality but possibility to exclude
Examples: local goods (street light), school, sewer services, telecommunications

Question 17

Pareto-efficient allocation with public good :

Answer 17

This is Bowen, Lindahl, Samuelson equation (BLS): the Pareto-efficient allocation is such that the sum of marginal rates of substitution (MRS) between private and public goods must be equal to the marginal cost of production of the public good

Question 18

Equilibrium with private subscription : What is the decentralized allocation ?

Answer 18

Individuals subscribe and pay what they decide

Public good is produced according to the total subscriptions

Question 19

So the individual maximizes its utility ( In Equilibrium with private subscription) when :

Answer 19

Between private and public good is equal to the marginal cost of production

Question 20

Under-provision of public good because …

Answer 20

… individuals do not internalize the effect of their subscription on others’ utilities

Question 21

By contributing to the public good, an individual…

Answer 21

…not only increases its utility but also the utility of the other individuals

Question 22

The private return to the subscription is…

Answer 22

…lower than the total return of the subscription, leading to the inefficiency of the decentralized equilibrium

Question 23

This is Bowen, Lindahl, Samuelson equation (BLS) :

Answer 23

the Pareto-efficient allocation is such that the sum of marginal rates of substitution (MRS) between private and public goods must be equal to the marginal cost of production of the public good.

Question 24

Lindahl equilibrium :

Answer 24

Principle = each agent is offered a price pi for the public good, and they choose which quantity to buy. Total quantity of the public good determined by the sum of individual quantities