Theme 1 – The Foundation
of Public Economics
11F251 Financial Theory,
Policy and Institutions
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From: Rosen, Gayer: Public Finance, 10th ed., 2013:
Defining the Field of Study:
Public Finance – Field of economics that analyzes
government taxation and spending activities.
Public Sector Economics or Public Economics:
Terms that better capture the fundamental issues
of this field of economics - government’s role in
the allocation of real resources - that includes, but
is not limited to, government’s financial behavior.
Focus on microeconomic functions of government.
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Welfare economics
(Chapter 3 in TRESCH, R W. Public sector economics.
Basingstoke: Palgrave Macmillan, 2008. ISBN 978-0-230-522237)
• Need systematic framework to assess the desirability of
various government actions.
• Welfare economics is concerned with the social
desirability of alternative economic states.
– Distinguishes cases when private markets work well from
cases where government intervention may be warranted.
• Relies heavily on basic microeconomic tools, particularly
indifference curves.
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Pure exchange economy
• Economy with
– 2 people (Adam & Eve)
– 2 commodities (Apples & Figs)
– Fixed supply of commodities (e.g., on a desert island)
• An Edgeworth Box depicts the distribution of goods
between the two people.
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BL
- Budget Line
I1 – indiference curve
good Y
I1
Y1
BL
MRS X ,Y
PX

PY
X1
good X
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Figure 1.1
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Pure exchange economy
• Each point in the box in Figure 1.1 represents an allocation
between Adam and Eve.
– Each point in the box fully exhausts the resources on the
island. Adam consumes what Eve doesn’t.
– Adam’s consumption of apples and figs increases as we
move toward the northeast in the box.
– Eve’s consumption of apples and figs increases as we move
toward the southwest in the box.
• At point v in the figure, Adam’s allocation of apples is Ox,
and of figs is Ou. Eve consumes O’v of apples, and O’w of
figs.
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Pure exchange economy
• Assume that Adam and Eve each have conventionally
shaped indifference curves.
• Adam’s happiness increases as he consumes more;
therefore his utility is higher for bundles toward the
northeast in the Edgeworth Box.
– We can therefore draw “standard” indifference curves for
Adam in this picture. Adam would get even higher utility by
moving further to the northeast, outside of the Edgeworth Box,
but he is constrained by the resources on the island.
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Pure exchange economy
• Similarly, Eve’s happiness increases as she consumes
more; therefore her utility is higher for bundles toward the
southwest in the Edgeworth Box.
– Eve’s indifference curves therefore are “flipped around.” Her
utility is higher on E3 compared E2 or E1.
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Figure 1.2
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Pure exchange economy
• Suppose some arbitrary point in the Edgeworth Box is
selected, for example point g in Figure 1.3.
• This provides an initial allocation of goods to Adam and Eve,
and thus some initial level of utility.
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Figure 1.3
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Pure exchange economy
• We can now pose the following question: Is it possible to
reallocate apples and figs between Adam and Eve to make
Adam better off, while Eve is made no worse off?
• Allocation h in Figure 1.3 is one possibility. We are “moving
along” Eve’s indifference curve, so her utility remains
unchanged. Adam’s utility clearly increases.
• Clearly, other allocations achieve this same goal, such as
allocation p.
• Once we reach allocation p, we cannot raise Adam’s utility
any more, while keeping Eve’s utility unchanged.
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Pure exchange economy
• An allocation is Pareto efficient if the only way to make
one person better off is to make another person worse off.
– Often used as the standard for evaluating desirability of an
allocation of resources.
– Pareto inefficient allocations are wasteful.
• A Pareto improvement is a reallocation of resources that
makes one person better off without making anyone else
worse off.
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Figure 1.4
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Pure exchange economy
• Many allocations are Pareto efficient. Figure 1.5 illustrates
three of them -- allocations p, p1 and p2.
– Among these Pareto efficient allocations, some provide Adam
with higher utility than others, and the opposite ones provide
Eve with higher utility.
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Figure 1.5
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Pure exchange economy
• In fact, there are a whole set of Pareto efficient points in the
Edgeworth Box.
• The locus of all the set of Pareto efficient points is called
the contract curve.
• Figure 1.6 illustrates the contract curve.
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Figure 1.6
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Edgeworth box
XE
F
.
YE
.
E
YA
E
IA
IE
A
XA
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Pure exchange economy
• Figure 1.6 shows that each of the Pareto efficient points is
where an indifference curve of Adam is tangent to an
indifference curve of Eve.
• Mathematically, the slopes of Adam’s and Eve’s
indifference curves are equal.
• The (absolute value of) slope of the indifference curve
indicates the rate at which the individual is willing to trade
one good for another, know as the marginal rate of
substitution (MRS).
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Pure exchange economy
• Pareto efficiency requires:
MRS
Adam
af
 MRS
Eve
af
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Production economy
• In pure exchange economy, assumed supplies of
commodities were fixed.
• Now consider scenario where quantities can change.
• The production possibilities curve shows the maximum
quantity of figs that can produced with any given quantity of
apples.
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Figure 1.7
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Production economy
• For apple production to be increased, fig production must
necessarily fall.
• The marginal rate of transformation (MRT) of apples for
figs (MRTaf) shows the rate at which the economy can
transform apples to fig leafs.
– It is the absolute value of the slope of the production
possibilities curve.
• The marginal rate of transformation can be written in terms
of marginal costs:
MCa
MRTaf 
MC f
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Efficiency with variable
production
• With variable production, efficiency requires:
MRTaf  MRSafAdam  MRSafEve
• If this were not the case, it is possible to make one person
better off with an adjustment production. Rewriting in terms of
marginal costs, we then have:
MCa
Adam
Eve
 MRSaf  MRSaf
MC f
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Y
P
X
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First fundamental theorem of
welfare economics
• Assume that
– All producers and consumers act as perfect competitors (e.g.,
no market power)
– A market exists for each and every commodity
• Under these assumptions, the first fundamental theorem
of welfare economics states that a Pareto efficient
allocation will emerge.
• Implication: Competitive economy automatically allocates
resources efficiently, without central planning.
• Conclusion: Free enterprise systems are amazingly
productive.
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Second fundamental theorem of
welfare economics
• Note that Pareto efficiency (and the first fundamental
welfare theorem) does not fairness.
– Either the northeast or southwest corner of the Edgeworth
Box is Pareto efficient, but very unequal distribution.
• Society may care about more than Pareto efficiency.
• From the contract curve in the Edgeworth Box, could map
the derive the relationship between Adam’s and Eve’s
utilities, on the utilities possibilities curve.
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Figure 1.8
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Second fundamental theorem of
welfare economics
•
The frontier of the utilities possibilities curve is, by definition,
attainable. Similar to a budget constraint.
•
Could postulate a social welfare function, which embodies
society’s views on the relative well-being of Adam and Eve:
W  F (U Adam , U Eve )
•
Could then maximize society’s preferences, or demonstrate that
some Pareto-inefficient bundles are preferred to some Paretoefficient ones.
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Figure 1.9
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Second fundamental theorem of
welfare economics
• The second fundamental theorem of welfare economics
states that society can attain any Pareto-efficient allocation
of resources by making a suitable assignment of initial
endowments and then allowing free trade.
• No adjustments to prices.
• Issues of efficiency and distributional fairness can be
separated.
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The Market Assumptions
Best market structure → Perfect competition
(1) Many, many consumers and firms
(2) Homogenous product
(3) Perfect information for buyers and sellers
(4) Free entry and exit in Long-run
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Market failures
Theory suggests potential power of markets, but … do
markets always function well? Theorems will be violated
when there are market failures:
Distribution branch
Addresses failures to achieve end-results or process
equity
Allocation branch
Addresses failures to achieve Pareto Optimal outcomes
Stabilization branch
Addresses failures in macroeconomic policy
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The Distribution Branch
- How to compare C and D?
- Both are Pareto Optimal
- Allocation Branch is satisfied
- What about distribution?
- D is more equitable
- C is less equitable
- Economy must decide
which it prefers
- How can economy move from
C to D?
- Tax 2 and redistribute to 1
- Will Market ever do this on its own?
- No. It must be done by government (issue of end-results
equity)
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Violations of the Market Assumptions I.
There are several potential reasons that markets
fail in allocation …
Externalities
Consumption by individual or production by firm that affects
utility function or production function of at least one other
individual or firm
Can be positive (utility increasing) or negative (cost
increasing)
Examples: Positive - education, urban renewal, public
health, R&D, etc; Negative - air pollution, noise pollution,
etc.
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Violations of the Market Assumptions II
Nonexclusive (Public) goods
A good for which, once someone buys, it everyone is able
to enjoy the full amount of the services provided by the
good
Examples: national defense, highways, parks, pools, golf
clubs, etc.
Problem: If you can consume a good whether you pay for
it or not, you have no incentive to contribute to production
(the free-rider problem) which results in under-production
Solution: Government provides more efficient level of
production which is financed through collection of taxes
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Violations of the Market Assumptions III.
1. Property Rights and Enforceable Contracts
- Problem: If property rights are not protected (i.e. I can steal what
you produce) there is no incentive to undertake economic activity
- Solution: Government regulation and enforcement
2. Decreasing Costs/Economies of Scale
- Goods for which the average cost of production decreases as
quantity produced increases over a large scale
- Example: Public utilities, public transportation, telecomms, etc.
- Problem: Efficient production results with one (or few) large firms.
- Such a market has incentive to act as monopoly which
results in under-production
- Solution: Government grants monopoly and regulates production
to get more efficient outcome
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Violations of the Market Assumptions IV.
3. Private/Asymmetric Information:
- One party in a two-party transaction possesses more
information than the other
- Firms may possess more information
- Example: Product quality, drug safety/effectiveness,
etc.
- Individuals may possess more information
- Example: Individual health, personal risk-avoidance,
etc.
- Problem: Party possessing more information can take
advantage of other party which results in inefficient outcome
- Solution: Government creates oversight bodies that regulate
functioning of such markets to create more efficient outcome
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