Summary Week 1, 2, & 3 of Public Finance, 10th ed., by Rosen & Gayer.
Week 1: Chapter 3 and 4
Chapter 3
The necessity of government intervention: Government action becomes necessary when markets fail to
produce desirable outcomes. Welfare economics, which assesses the social desirability of economic
states, helps distinguish situations where markets perform well from those where they fail. The key
factors considered in welfare economics are efficiency (overall welfare) and equity (fairness).
Efficiency involves optimal allocation of goods in society, characterized by Pareto efficiency, where no
one can be made better off without making someone else worse off. In order to explain how efficiency
and equity are distributed over societies, let’s consider a simple economy where there are two people
who consume two commodities supplied at a fixed amount.
Example: There are 2 individuals: Adam & Eve, and 2 goods: Apples (food) & Fig leaves (clothing).
In the graph, point (a) represents specific amounts of apples and fig leaves for both Adam and Eve.
Adam prefers fig leaves, while Eve prefers apples. The Edgeworth Box with indifference curves
illustrates their preferences and willingness to trade. Adam is indifferent between points (a) and (b) on
indifference curve A3, while Eve prefers point (b), as it improves total welfare on indifference curves
E1 to E2. The contract curve (b, d, c) reflects Pareto efficiency.
Figure 1: Edgeworth box.
The marginal rate of substitution (MRS) is crucial, representing the rate at which individuals trade one
good for another. Pareto efficiency requires MRSAdam = MRSEve, ensuring equal rates. An efficient
allocation is one where improving someone's well-being is impossible without worsening someone
else's. Transitioning to a production economy, where commodities (apples and fig leaves) vary, the
production possibilities curve (PPC) depicts the maximum fig leaves that can be produced with any
quantity of apples in this economy.
Figure 2: Edgeworth Box: Indifference curve.
Efficient allocation occurs when it is impossible to improve one individual's well-being without
simultaneously diminishing another's. Shifting from the previous analysis of an exchange economy,
which lacked production and had fixed commodity supplies, we now examine a production economy
where the quantities of apples and fig leaves can vary. In this scenario, the production possibilities curve
(PPC) illustrates the maximum quantity of fig leaves that can be produced for any given quantity of
apples.
1
, Figure 3: Production Possibilities Curve.
The production possibilities curve (PPC) illustrates possible combinations of apples and fig leaves.
Points (a), (b), and (c) fall within the PPC limits, while point (d) does not. The marginal rate of
transformation (MRT), representing the curve's slope, indicates the rate at which the economy can
switch between producing apples and fig leaves. Expressing MRT in terms of marginal cost (MC),
which is the cost of producing an additional unit, the slope of the PPC equates to the ratio of MC of
apples (MCa) to MC of figs (MCf):
MCf (x/y) = MRTaf = MCa / MCf
Figure 4: Production Possibilities Curve: Pareto Efficiency.
As previously mentioned, a Pareto efficiency allocation occurs when MRT = MRSAdam = MRSEve.
In Figure 4, point (a) demonstrates MRS ≠ MRT, while point (b) shows MRS = MRT. Moving from
the analysis of achieving Pareto efficiency to the debate on how to attain it, two theorems of welfare
economics are explored.
The First Fundamental Theorem of Welfare Economics asserts that, under the assumption of perfect
competition where all producers and consumers are perfect competitors, and there is no monopoly, a
competitive economy automatically achieves Pareto efficiency. This implies that resources are
efficiently allocated. Perfect competition ensures everyone faces the same prices, with consumers and
producers having no influence on prices. Therefore, a Pareto-efficient allocation results if perfect
competition exists and markets are comprehensive, allowing everything to be traded. In this context,
the government's role is to ensure the existence of competitive markets. However, the emphasis on
fairness, along with efficiency, is crucial, aligning with efficiency and equity.
To maximize social welfare, both efficiency and fairness are crucial. In Figure 5, points (a) and (c) are
Pareto-efficient, while point (b) is not. However, point (c) is preferable as it combines efficiency and
fairness. The debate between equity and efficiency is straightforward when assessing resource
allocation. However, understanding society's diverse preferences is more challenging. If society
prioritizes an equal income distribution over efficiency, a non-Pareto-efficient situation may be favored,
as seen in Figure 5 where point (b) is preferred over point (a). In such cases, government intervention
2
Week 1: Chapter 3 and 4
Chapter 3
The necessity of government intervention: Government action becomes necessary when markets fail to
produce desirable outcomes. Welfare economics, which assesses the social desirability of economic
states, helps distinguish situations where markets perform well from those where they fail. The key
factors considered in welfare economics are efficiency (overall welfare) and equity (fairness).
Efficiency involves optimal allocation of goods in society, characterized by Pareto efficiency, where no
one can be made better off without making someone else worse off. In order to explain how efficiency
and equity are distributed over societies, let’s consider a simple economy where there are two people
who consume two commodities supplied at a fixed amount.
Example: There are 2 individuals: Adam & Eve, and 2 goods: Apples (food) & Fig leaves (clothing).
In the graph, point (a) represents specific amounts of apples and fig leaves for both Adam and Eve.
Adam prefers fig leaves, while Eve prefers apples. The Edgeworth Box with indifference curves
illustrates their preferences and willingness to trade. Adam is indifferent between points (a) and (b) on
indifference curve A3, while Eve prefers point (b), as it improves total welfare on indifference curves
E1 to E2. The contract curve (b, d, c) reflects Pareto efficiency.
Figure 1: Edgeworth box.
The marginal rate of substitution (MRS) is crucial, representing the rate at which individuals trade one
good for another. Pareto efficiency requires MRSAdam = MRSEve, ensuring equal rates. An efficient
allocation is one where improving someone's well-being is impossible without worsening someone
else's. Transitioning to a production economy, where commodities (apples and fig leaves) vary, the
production possibilities curve (PPC) depicts the maximum fig leaves that can be produced with any
quantity of apples in this economy.
Figure 2: Edgeworth Box: Indifference curve.
Efficient allocation occurs when it is impossible to improve one individual's well-being without
simultaneously diminishing another's. Shifting from the previous analysis of an exchange economy,
which lacked production and had fixed commodity supplies, we now examine a production economy
where the quantities of apples and fig leaves can vary. In this scenario, the production possibilities curve
(PPC) illustrates the maximum quantity of fig leaves that can be produced for any given quantity of
apples.
1
, Figure 3: Production Possibilities Curve.
The production possibilities curve (PPC) illustrates possible combinations of apples and fig leaves.
Points (a), (b), and (c) fall within the PPC limits, while point (d) does not. The marginal rate of
transformation (MRT), representing the curve's slope, indicates the rate at which the economy can
switch between producing apples and fig leaves. Expressing MRT in terms of marginal cost (MC),
which is the cost of producing an additional unit, the slope of the PPC equates to the ratio of MC of
apples (MCa) to MC of figs (MCf):
MCf (x/y) = MRTaf = MCa / MCf
Figure 4: Production Possibilities Curve: Pareto Efficiency.
As previously mentioned, a Pareto efficiency allocation occurs when MRT = MRSAdam = MRSEve.
In Figure 4, point (a) demonstrates MRS ≠ MRT, while point (b) shows MRS = MRT. Moving from
the analysis of achieving Pareto efficiency to the debate on how to attain it, two theorems of welfare
economics are explored.
The First Fundamental Theorem of Welfare Economics asserts that, under the assumption of perfect
competition where all producers and consumers are perfect competitors, and there is no monopoly, a
competitive economy automatically achieves Pareto efficiency. This implies that resources are
efficiently allocated. Perfect competition ensures everyone faces the same prices, with consumers and
producers having no influence on prices. Therefore, a Pareto-efficient allocation results if perfect
competition exists and markets are comprehensive, allowing everything to be traded. In this context,
the government's role is to ensure the existence of competitive markets. However, the emphasis on
fairness, along with efficiency, is crucial, aligning with efficiency and equity.
To maximize social welfare, both efficiency and fairness are crucial. In Figure 5, points (a) and (c) are
Pareto-efficient, while point (b) is not. However, point (c) is preferable as it combines efficiency and
fairness. The debate between equity and efficiency is straightforward when assessing resource
allocation. However, understanding society's diverse preferences is more challenging. If society
prioritizes an equal income distribution over efficiency, a non-Pareto-efficient situation may be favored,
as seen in Figure 5 where point (b) is preferred over point (a). In such cases, government intervention
2
