Public Finance 1

Public Finance in Theory and Practice

Durgesh C Pathak

M W F: 4; G 105; Tutorial: M 8; G 105 CCH: 12-1 pm on Class Days (M W F)

Public Finance is nothing else than a sophisticated discussion of the relationship between the individual and the state. There is no better school of training than public finance.

: Vaclav Klaus

Public Finance in Theory & Practice Durgesh C Pathak

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Community welfare

The goals of the Society are set by the government

Organic View of the Government

Individuals form a society

Society is a natural

organism

Government is the heart of the natural

organism

>> Individual welfare Example: “An activity of a citizen

is desirable only if it leads to a just society.” : The Republic


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Mechanistic View of the Government

Government is a contrivance created by individuals to better achieve their individual goals

“Government is a trust, and the officers of the government are trustees; and both the trust and the trustees are created for the benefit of the people.”

: Henry Clay (1829)


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Good of people! So

what is good?

Protection from violence

Protection from physical

coercion

“Creating and maintaining certain public works and certain public institutions, which it can never be the

interest of any individual, or small number of individuals, to erect and maintain.”

: Adam Smith

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Mechanistic View of

Government

Libertarians

Social Democrats

Believe in very limited role of government

Extremely skeptical ability of governments to improve social welfare. E.g.,” Sometimes it is said that man cannot be trusted with the government of himself. Can he, then be trusted with the government of others? Or have we found angels in the form of kings to govern him? Let history answer this question.” : Thomas Jefferson

Substantial government intervention is required for good of individuals.


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Modes of Analysis

Modes of Analysis

Positive Analysis

Normative Analysis

What are the responses of the public/private sector to various fiscal measures?

What are the social, political, and historical forces that have shaped the present fiscal institutions and which have determined the formulation of contemporary fiscal policy?

What criteria should be applied when one is judging the merit of various budget policies?


7

Tools of Positive analysis

The Role of

Theory

Effect of a tax on wage income on work hours

To generate testable hypotheses whose validity can be assessed through empirical work


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Causation versus Correlation

Conditions necessary for establishing cause and effect: o The Cause (X) must precede the Effect (Y) o X and Y (i.e., the cause and the effect) must be correlated o Other possible explanations (say factor Z) for any observed correlation

must be eliminated. This is called ‘Third Variable Problem’.


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Experimental Study

Treatment Group

Control Group Or

Counterfactual

Observational Study

Use of Regression

Types of Data

Cross-Sectional data

Time-Series data

Panel data


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Tools of Normative Analysis

Pure Exchange Economy: o Two People o Two Goods in fixed supplies The Economic Problem: Distribution of the two goods between the two people

Tool used: Edgeworth Box Diagram Edgeworth Box Diagram shows allocation of two goods between two people.


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Fig

Leav

es

Fig

Leav

es

Apples

Apples

V U

R

Y

X O

O’

Adam

Eve

Figure 1: Edgeworth Box diagram of Distribution of Apples and Fig Leaves between Adam & Eve

At point V, Adam has: 0X of Apples & 0U of Fig Leaves;

At point V, Eve has 0’Y of Apples & O’W of Fig Leaves

W


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Fig

Leav

es

Fig

Leav

es

Apples

Apples

R

O

O’

Adam

Eve

A1 A2

E3

E2 E1

Figure 2: Indifference Curves in an Edgeworth Box


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Fig

Leav

es

Fig

Leav

es

Apples

Apples

R

O

O’

Adam

Eve

A1 A2

E3

A3

P

Pareto Efficient Point

G

H

Figure 3: Pareto Efficient Allocation of Resources/Goods

An allocation point at which the only way to make a person better off is to make another person worse off is called a Pareto Efficient Point. E.g., Point P in Fig. 3


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Pareto Improvement: a reallocation of resources/goods that makes one person better off without making anyone worse off. Example: a movement from point H to point P in Fig. 3

One can find innumerable number of Pareto Efficient Points in an Edgeworth Box

Fig

Leav

es

Fig

Leav

es

Apples

Apples

R

O

O’

Adam

Eve

P

H

G

Q

Contract Curve

Figure 4: The Contract Curve


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Contract Curve: The locus of all Pareto Efficient Points in an Edgeworth Box

∵ 𝑆𝑙𝑜𝑝𝑒 𝑜𝑓 𝑖𝑛𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝐶𝑢𝑟𝑣𝑒 𝑜𝑓 𝐴𝑑𝑎𝑚 = 𝑀𝑅𝑆𝑎𝑓𝐴𝑑𝑎𝑚

and,

∵ 𝑆𝑙𝑜𝑝𝑒 𝑜𝑓 𝑖𝑛𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝐶𝑢𝑟𝑣𝑒 𝑜𝑓 𝐸𝑣𝑒 = 𝑀𝑅𝑆𝑎𝑓𝐸𝑣𝑒

∴ 𝑎𝑡 𝑡𝑎𝑛𝑔𝑒𝑛𝑐𝑦 𝑝𝑜𝑖𝑛𝑡 𝑃,

𝑀𝑅𝑆𝑎𝑓𝐴𝑑𝑎𝑚 = 𝑀𝑅𝑆𝑎𝑓

𝐸𝑣𝑒………………………eq. 1

Therefore, o Pareto Efficiency requires that MRS is equal for all consumers and, o The Contract curve is the Locus of Points of equal MRS

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The Production Economy

Lets relax the assumption of Fixed supplies of the commodities.

If the productive inputs can shift between production of the two goods, we face a trade off.

Apples per year

Fig

leav

es p

er y

ear

c

d

w

y

x z 0

𝑆𝑙𝑜𝑝𝑒 = 𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑅𝑎𝑡𝑒 𝑜𝑓 𝑇𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛

Figure 5

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𝑴𝑹𝑻𝒂𝒇 is rate at which economy can transform apples into fig leaves

Try to think of 𝑀𝑅𝑇𝑎𝑓in terms of Marginal Costs

∵ In Figure 5, the incremental cost of producing WY of Fig leaves is XZ of Apples ∴ 𝑀𝐶𝑓 = 𝑥𝑧

Similarily, ∵ In Figure 5, the incremental cost of producing XZ of Apples is WY of Fig leaves ∴ 𝑀𝐶𝑎 = 𝑤𝑦

But 𝑀𝐶𝑎

𝑀𝐶𝑓= 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑃𝑃𝐹 = 𝑀𝑅𝑇𝑎𝑓 ……………………………………𝑒𝑞. 2

Thus, 𝑴𝑹𝑻𝒂𝒇 is the marginal cost of producing one more unit of fig leaves or

one more unit of apple.

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Efficiency Conditions with Variable Production

Pareto Efficiency Condition in a Fixed Supply Economy:


𝐸𝑣𝑒 …………… . 𝑓𝑟𝑜𝑚 𝑒𝑞. 1

We need to extend the Pareto Efficiency Condition in case of Variable supplies of Apples and Fig Leaves. Since Supply is variable, 𝑀𝑅𝑇𝑎𝑓 comes into picture.

𝑀𝑅𝑇𝑎𝑓 = 𝑀𝑅𝑆𝑎𝑓𝐴𝑑𝑎𝑚 = 𝑀𝑅𝑆𝑎𝑓

𝐸𝑣𝑒 ………………………………𝑒𝑞. 3

⇒ The rate at which apples can be transformed into fig leaves 𝑴𝑹𝑻𝒂𝒇 must equal the rate at

which the consumers are willing to trade apples for fig leaves 𝑴𝑹𝑺𝒂𝒇 .

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Since 𝑀𝑅𝑇𝑎𝑓 =𝑀𝐶𝑎

𝑀𝐶𝑓 𝑓𝑟𝑜𝑚 𝑒𝑞. 2

Therefore, 𝑀𝐶𝑎

𝑀𝐶𝑓= 𝑀𝑅𝑆𝑎𝑓

𝐴𝑑𝑎𝑚 = 𝑀𝑅𝑆𝑎𝑓𝐸𝑣𝑒 ………………………………𝑒𝑞. 4

Eq. 4 is the necessary condition for Pareto Efficiency in an economy with variable Supplies of commodities.

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The First Fundamental Theorem of Welfare Economics

Answers the question “whether a given economy will achieve the Pareto Efficient State

Yes, if following Conditions/assumption are met: o All producers and consumers act as perfect competitors o A market exists for every commodity

If the above two assumptions are met, a Pareto Efficient allocation of resources emerges.

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Since it is a perfect market, both Adam and Eve should pay same prices for apples and fig leaves

Further, for Utility maximization, a necessary condition is that

𝑀𝑅𝑆𝑎𝑓𝐴𝑑𝑎𝑚 =

𝑃𝑎𝑃𝑓

……………… . . 𝐸𝑞. 5

Similarly for Eve

𝑀𝑅𝑆𝑎𝑓𝐸𝑣𝑒 =

𝑃𝑎𝑃𝑓

……………… . . 𝐸𝑞. 6

From eq. 5 & eq. 6,


𝐸𝑣𝑒

Which is nothing but eq. 1 (necessary condition for Pareto Efficiency)

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Now consider the production side as well.

A profit maximizing firm would produce up to a point where MC is equal to Price

𝑀𝐶𝑎

𝑀𝐶𝑓=

𝑃𝑎𝑃𝑓

………………… . 𝑒𝑞. 7

But since 𝑀𝐶𝑎

𝑀𝐶𝑓 is the MRT between apples and fig leaves. So,

𝑀𝑅𝑇𝑎𝑓 =𝑃𝑎𝑃𝑓

…………………… . . 𝑒𝑞. 8

From eq. 5, 6, and 8, we get

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𝐸𝑣𝑒 = 𝑀𝑅𝑇𝑎𝑓

Which is the necessary condition for Pareto Efficiency


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Can we re-write the conditions for Pareto Efficiency in terms of Marginal Cost? Yes, why not.

Substituting eq. 5 or 6 into eq. 4, we get

𝑃𝑎𝑃𝑓

=𝑀𝐶𝑎

𝑀𝐶𝑓…………𝑒𝑞. 9

⇒ For Pareto Efficiency, Prices must be in the same ratio as the Marginal Costs. ⇒ Efficiency requires the additional cost of each commodity is reflected in its price.


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Fairness and the Second Fundamental Theorem of Welfare Economics

o Why do we need a government? o Is Pareto Efficiency desirable?

Fig

Leav

es

Fig

Leav

es

Apples

Apples

R

O

O’

Adam

Eve

P

H

G

Q

Contract Curve

Figure 6: Efficiency Versus Equity

Z


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What should be the allocation of resources: o Point P? o Point Q? o Point Z?

Case for Point P: o Is Pareto Efficient o Favours Eve!

Case for Point Q: o Is Pareto Efficient o Favours Adam!

Case for Point Z: o Not Pareto Efficient o Favours everyone almost equally, i.e., favours more equal distribution of resources

Now, we have to make a value judgment about which of these is a FAIR distribution


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We can derive a Utility Possibilities Curve from the Contract Curve!

𝑃

𝑄 𝑍

Adam’s Utility

Eve’

s U

tilit

y

U

U

Utility Possibility Curve: A graph showing the maximum amount of one person’s utility given each level of utility attained by the other person.

Figure 7: Utility Possibility Curve


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o All points on the Curve UU are Pareto Efficient o These points differ in the allocation of resources they implicitly indicate o Which point is the BEST?

The answer lies in the Social Welfare Function

A statement of how the society’s well-being relates to the well-being of its members Social

Welfare Function

Society’s view on relative deservedness of Adam and Eve

𝑊 = 𝐹 𝑈𝐴𝑑𝑎𝑚 , 𝑈𝐸𝑣𝑒 ………………𝑒𝑞. 10

Social Welfare (W) is some function (F) of each individuals utility


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Try to think in terms of Utility:

Adam’s Utility

Eve’

s U

tilit

y

Social Indifference Curves show how society is willing to trade off one individual’s utility for the other’s

𝑈1

𝑈2

𝑈3

Social Welfare is Increasing as we move to a higher curve

Figure 8: Maximizing Social Welfare

U

U

𝑖

𝑖𝑖

𝑖𝑖𝑖

o Point 𝑖: Pareto Efficient but Not fair! o Point 𝑖𝑖: Not Pareto Efficient but fair! o Point 𝑖𝑖𝑖: Pareto Efficient and fair!


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⇒ Even if an economy generates a Pareto Efficient Allocation of resources, government intervention may be necessary to achieve a “fair” distribution of utility and thus to maximize the social welfare.

When the conditions required for the First Welfare Theorem to work are not met in the real world, it is possible that the free-market allocation of resources may be inefficient and unfair. Government intervention becomes desirable in such circumstances.

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Public Finance 1

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