1. Tools of normative analysis
Lecture 2
Public Finance - Introductory

2. Public Finance - Introductory
Welfare economics
Need of tools to evaluate desirability of alternative policies (“states of the world”)
WE helpful to understand when markets work or fail
Microeoconomic approach
Fundamental tool for government advisors
Public Finance - Introductory

3. Public Finance - Introductory
Pure exchange
Edgeworth box
2 goods (A and C), 2 individuals (groups), here Adam and Eve
Total goods quantities given, set equal to 1
What Adam does not have is owned by Eve
2 origins
Point v, endowment → distribution before exchange
Public Finance - Introductory

4. Edgeworth Box 2 person / 2 good economy
Eve r 0’ v w u
Fig leaves per year
Box and dimensions initially set
1st click – place point v
2nd click – draw horizontal line uw
3rd click – draw vertical line xy s
Adam
Apples per year
Public Finance - Introductory

5. Individual preference and Pareto-optimality
Individual preferences described by indifference curves (IC)
Begin with endowment point at intersection of IC
Lens is domain of exchange (Pareto set)
Pareto set denotes distributions that individuals may freely choose because
One is better off and none is worse off
Both are better off
Points within Pareto set are Pareto optimal
Public Finance - Introductory

6. Indifference curves in Edgeworth Box
Eve r A3 E1 0’ A2 E2 A1 E3
Fig leaves per year
Box and dimensions initially set
1st click – Adam’s indifference curves
2nd click – Eve’s indifference curves s
Adam
Apples per year
Public Finance - Introductory

7. Public Finance - Introductory
Pareto efficiency - 1
A Pareto efficient/optimal distribution: impossible to improve the situation of one individual without making another worse off (e.g. point p)
In Pareto efficient distributions individual ICs are tangent
Pareto improvement (Pareto superior move) → move from a situation where ICs are not tangent to one where they are tangent
Public Finance - Introductory

8. Beginning at Point g, how to make Adam better off without Eve becoming worse offAp r 0’ Ah g Ag Eg h
A Pareto Efficient Allocation
Fig leaves per year p
Box and dimensions initially set
1st click – “A Pareto efficient allocation” and arrow s
Adam
Apples per year
Public Finance - Introductory

9. Beginning at Point g, how to make Eve better off without Adam becoming worse off0’ Ag g Eg p
Fig leaves per year
Ep1
Box and dimensions initially set
1st click – “A Pareto efficient allocation” and arrow p1
A Pareto Efficient Allocation s
Adam
Apples per year
Public Finance - Introductory

10. Beginning at Point g how to make both Adam and Eve better off
Ap2 r 0’ g Ag Eg
Pareto efficient
Pareto improvement
Ep2 p
Fig leaves per year p2 p1
Box and dimensions initially set
1st click – Box with Pareto efficient and improvement within s
Adam
Apples per year
Public Finance - Introductory

11. Public Finance - Introductory
Pareto efficiency - 2
Point p not only optimal point
Conditional on original endowment
Contract curve is locus of all Pareto optimal points
Locus of tangency points
Slope of ICs identifies MRS
Pareto efficiency implies
Public Finance - Introductory

12. Starting from a different initial point: Point k
Eve
Ap2 0’ r g Ag Eg k p4
Ep2 p3
Fig leaves per year p p2
Box and dimensions initially set
1st click – p1 s
Adam
Apples per year
Public Finance - Introductory

13. Public Finance - Introductory
The Contract Curve
Eve
Ap2 r 0’ g Ag Eg
The contract curve –locus of all Pareto efficient points p4
Ep2 p3
Fig leaves per year p p2
Box and dimensions initially set
1st click – contract curve drawn from lower left to upper right and “The contract curve” and arrow appear p1 s
Adam
Apples per year
Public Finance - Introductory

14. Economics with production
Relax hypothesis of fixed quantities
Hypothesis: inputs (labour and capital) can be re-allocated between production of goods
If inputs are efficiently employed, producing more of good A shifts inputs from the production of good C
Production of C will decrease
‘Production possibility frontier’ (often cited by Hitler: Do you want more butter or more guns?) denotes the maximal quantity of good A that can be produced at any given quantity of good C
Public Finance - Introductory

15. Production Possibilities Curve
│Slope│ = marginal rate of transformation
Fig leaves per year w y
Axes and labels
1st click – PPC and labels
2nd click – lines x and w
3rd click – lines z and y C x z
Apples per year
Public Finance - Introductory

16. Marginal rate of transformation
To produce more C, from quantity 0x to 0z, one needs to produce less A, from 0w to 0y
Segment wy is marginal cost (MC) of producing xz more (opportunity cost)
MRT is ratio of wy to xz, so that
To produce wy → more inputs must be reallocated from production of A to production of C → producton of A reduced by xz
Public Finance - Introductory

17. Efficiency with variable production
Condition of Pareto efficiency becomes
(1)
Suppose MRSAdam=1/3 and MRT=2/3.
Adam wants 1 of bread in exchange of 3 croissants, but if he produces 3 croissants can obtain 2 of bread
Adam can be better off without anyone being worse off → always possible when MRS≠MRT
When MRS=MRT utility level cannot be changed
Rearranging (1)
Public Finance - Introductory

18. First Theorem of Welfare Economics - 1
First Theorem of Welfare Economics: if producers and consumers are perfectly competitive (price takers) under certain conditions (to be explained later) they will always reach a PE distribution of resources (→ laissez faire)
FTWE shows that competitive markets authomatically allocate resources in the most efficient way, without need of government intervention (Adam Smith’s “invisible hand”)
Public Finance - Introductory

19. First Theorem of Welfare Economics - 2
Competition implies that all individuals face same prices
Under utility maximization, price ratio must be equal to individuals’ MRSs
On the production side, firm produces till P=MC. Setting prices equal to marginal costs
Price ratio is hence equal to MRT
This equation is equivalent to efficiency condition → perfect competition determines efficient allocation of resources
Public Finance - Introductory

20. Public Finance - Introductory
Role of equity - 1
If markets produce efficient use of resources, government has no economic role
Efficiency not the only criterion to evaluate the employ of resources
In the diagram p3 is efficient and q is not, but q is characterized by a more equal distribution of resources
Public Finance - Introductory

21. Public Finance - Introductory
The role of equity - 2
On the contract curve UAdam and UEve are in trade off → the higher the utility of Adam, the lower that of Eve
Utility possibilities frontier
Locus of maximal utility levels on the contact curve
Which is the ‘best point’?
Social welfare function: equivalent for society of an individual IC
iii is optimum of optima
Public Finance - Introductory

22. Efficiency versus Equity
Eve
Does society have to choose between p3 & q? r 0’ p3
Fig leaves per year
Box and dimensions initially set
1st click – contract curve drawn from lower left to upper right and “The contract curve” and arrow appear q p5 s
Adam
Apples per year
Public Finance - Introductory

23. Public Finance - Introductory
Utility Possibilities Curve Maximum amount of one person’s utility given each level of another person’s utility
Adam’s utility U p3
Axes and labels
1st click – Utility possibilities curve, p3 and p5
2nd click - q p5 q U
Eve’s utility
Public Finance - Introductory

24. Public Finance - Introductory
Social Indifference Curve Society’s willingness to trade off one person’s utility for another’s
W = F(UAdam, UEve)
Adam’s utility
Increasing social welfare
Axes and labels
1st click – the arrow (speed: medium) and “Increasing social welfare”
Eve’s utility
Public Finance - Introductory

25. Maximizing Social Welfare
If society values a more equitable distribution of goods - embodied in Social Indifference Curves, fairness and efficiency are possible (iii)
Adam’s utility i
iii
Axes, labels, and social indifference curves
1st click – utility possibilities curve and points ii
Eve’s utility
Public Finance - Introductory

26. Public Finance - Introductory
Role of equity - 3
SWF is “seducing” side of WE – no scientific underpinnings!
Heavily influenced by value judgements
Slope of SWF is MRS between individual utilities
How to assess that one individual is more important of another (Egalité, etc…)?
Problem of ethics (but an unsolved/unsolvable one)
Efficiency has empirical dimensions and can be evalated with tools of economic analysis
Public Finance - Introductory

27. Public Finance - Introductory
Violations of FTWE - 1
Market power or non-existing markets
P>MC: market economy produces inefficient results → violation of FTWE
Asymmetric information
Market does not emerge (Akerlof’s ‘market for lemons’) → government may intervene
Externalities
Activity of one individual affects the utility of others without going through price system (market) → government may intervene
Public good
Good whose consumption is non rival → individual has no incentive to reveal her MU → MU≠P
Public Finance - Introductory

28. Public Finance - Introductory
Violations of FTWE - 2
The fact that markets fail to produce efficient allocations does not mean that governments can do better
It’s a possibility, which depends on many issues
There are also government failures
One of the subject matters of Public Choice
FTWE helps thinking rigorously about merits of government intervention
Are distributive consequences desirable?
Are there efficiency improvements?
Are costs reasonable?
When the answer to any of these questions is no → better to opt for market alternative
Government intervention might be demanded for reasons of general interest (e.g. equity) but become in fact a special advantage (lobbies, bureaucracy)
Public Finance - Introductory