Public Economics

Question 1

Organic view of government

Answer 1

Society is a natural organism
Government is the heart
Individuals are parts of the organism that have significance only as part of the community, which is stressed above the individual
The goals of the society are set by the state, which attempts to lead society towards their realisation.
However, it is not clear how to select societal goals.

Question 2

Mechanistic view of government

Answer 2

Government is not an organic part of society, It is created by individuals for individuals.
The individual is at centre stage.
Libertarians vs. Social Democrats: role of government

Question 3

Merit good

Answer 3

A good that is under consumed because it is not realised by the public.

Question 4

Welfare economics

Answer 4

Concerned with the social desirability of alternative economy states.

Question 5

Pareto Efficiency

Answer 5

An allocation of resources such that no person can be made better off without making another person worse off.

Question 6

Pareto Improvement

Answer 6

A reallocation of resources that makes at least one person better off without making anyone worse off.

Question 7

Individual budget line graph

Answer 7

Prices: p1,p2 > 0 (strictly positive)
Initial endowmnet omega = w1, w2
Available Income Y = p1w1 + p2w2 = p1x1 + p2x2

Hence the individual budget constraint is
Y = p1w1 + p2w2 = p1x1 + p2x2 –> x2 = (p1w1 + p2w2)/p2 - (p1/p2)x1

Intercepts are telling us how much of good 1 you can purchase given the amount of endowment.

If there are more endowment there are more available goods to be purchased - parallel shift in the budget line shown in the individual budget line (2).

If the price of good 1 decreases to p’1 < p1 there is a change in the budget line which gets flatter and passes through the endowment line.

Question 8

Marginal rate of subsitution

Answer 8

• 𝑀𝑅𝑆12(𝒙): minus the ratio of marginal utilities, it corresponds to the rate at which a consumer is willing to substitute one good with the other while leaving utility unchanged.
• Quantity of good 2 that the consumer is willing to give up in exchange for an additional unit of good 1 to keep the same utility. It corresponds to the slope of indifference curves.

Δ𝑈 = 𝑀𝑈1Δ𝑥1 + 𝑀𝑈2Δ𝑥2.

On the same indifference curve Δ𝑈 = 0, so

Δ𝑥2 Δ𝑥1 = − 𝑀𝑈1 𝑀𝑈2 = 𝑀𝑅𝑆12 𝒙

Question 9

Optimal Individual choice

Answer 9

The optimal consumption bundle 
𝑥 ∗ = (𝑥1 ∗ , 𝑥2 ∗ ) is such that: 
• 𝑥 ∗ lies on the budget constraint. 
• 𝑀𝑅𝑆12 𝑥 ∗ = 𝑝1 𝑝2 . 
• Net demands are given by 𝑥1 − 𝜔1 > 0 (net demander) and 𝑥2 − 𝜔2 < 0 (net supplier).

Question 10

The contract curve (Edgeworth box)

Answer 10

It is the locus of all pareto efficient points. (Very different allocations).

Question 11

Pareto efficiency in consumption

Answer 11

MRS adam = MRS eve
Where MRS af:
Is the rate at which an indiviudal is willing to trade fig leaves for apples at constant utility.
Is the absolute value of the slope of an indifference curve.

Question 12

Production economy (analysis of 2 goods)

Answer 12

Production economy (2)
• Production Economy: Analysis when supplies of 2 goods (apples and fig leaves) are variable rather than fixed.

Question 13

Production possibilities curve

Answer 13

• Graph to model production economy.
• Maximum quantity of one output that can be produced given the amount of the other output.

Production Possibilities curve (1)

Amount of fig leaves for amount of apple.
Because of the law of diminishing margin of productivity.
Slope = marginal rate of transformation

l Slope l = MRT = MCa/MCf = w-y/x-z

Question 14

Pareto efficiency conditions with variable production

Answer 14

Now pareto efficiency requires both economic agents MRS be equal to the MRT.
Example support that at a given allocation

This cannot be an efficient allocation of resources:

2 figleaves can be produced by giving up 3 apples
Adam is willing to give up three apples for 1 additional fig leaf.

Hence it it clearly optimal.

Question 15

First fundamental theorem of welfare economics

Answer 15

Given:

All producers and consumers are perfect competitors
A market exists for every commodity

Then a Pareto efficient allocation of resources emerges.
Every market equilibrium allocation is pareto efficient.
A competitive economy allocates resources efficiently without any need for centralized direction.
• In the words of Adam Smith (1776): “It is not from the benevolence of the butcher, the brewer, or the baker, that we can expect our dinner, but from their regard to their own interest.”
• The “invisible hand” guides the decentralized market to an efficient allocation.

Question 16

Production side

Answer 16

A profit-maximising firm produces output up to the point in which price equals marginal cost.

Question 17

Market equilibrium and private information

Answer 17

• All the private information relevant for achieving market efficiency is embedded in the market prices.
• The general equilibrium (Pareto efficient) arises naturally without any ex-ante acquisition of private information by a public planner.
• Even if consumers and firms do not explicitly reveal their preferences and costs, in equilibrium an efficient allocation will emerge out of a decentralized market.

Question 18

Utility possibility curves

Answer 18

Maximum amount of one person’s utility given each level of another person’s utility.

All points on the contract curves are on the utility possibilities curve
Allocation q is feasible but no pareto efficient ie.e it lives below the curve.

Question 19

Utilitarianism

Answer 19

Utilitarianism: Social welfare function based on the theories of utilitarian philosophers of the XIX century.

Social welfare function is simply the sum of individual utilities:

W = U1 + U2 + … + Un

IF the object is to maximize W, the government may obtain this result simply increasing the endowment of any of the individuals in the society (not necessarily the poorest one).

For this reason the utilitarian social welfare function is neutral from an equity/distributive perspective.

An alternative social welfare function is the Rawlsian one:
W = min(U1,U2, … , Un)

In this case the social welfare depends ONLY on the utility of the individual who is worse off.

Question 20

Maximizing Social welfare

Answer 20

If society values a more equitable distribution of goods - embodied in social indifference curves, fairness and efficiency are possible (iii)

Society might have a problem for which one is better if there are two equal maximizing points on the graph (two lines tangents).