Public finance
Final exam: CH 3-6, 8, 12, 14-16, 18, 20, 22
Chapter 3; Welfare economics
When markets don’t produce desirable results?
➔ Government action is needed.
When markets produce desirable results?
➔ Welfare economics.
Welfare economics: Basic concepts:
1. Efficiency: If we can improve welfare, it is not efficient.
Two types of efficiency:
▪ Technical efficiency: highest output with given input, or lowest input with given output.
(Does not concern us in welfare economics.
▪ Efficient allocation: who gets what? Optimal distribution of goods over persons.
Optimal = “Pareto efficiency”: An allocation of resources such that no person can be made better off
without making another person worse of.
2. Equity:
o Is it fair?
o What does fair mean?
Efficient allocation: how do we get that allocation?
➔ Edgeworth box.
Edgeworth box in exchange economy: (With fixed supplies, there is no production)
Which allocation is best?
• Adam and Eve have conventionally shaped indifference curves that represent their
preferences for apples and fig leaves.
• Indifferences curves with greater numbers represent higher levels of happiness (utitlity).
, ➔ Pareto improvement: a reallocation of resources that makes at least one person better off
without making anyone else worse of.
Contract curve: the locus of all the Pareto efficient points. (Denoted mm)
➔ It must be a point at which the indifference curves of Adam and Eve are barely touching. The
indifference curves are tangent, the slopes of the indifference curves are equal.
➔ Implicitly defines a relationship between the maximum amount of utility that Adam can
attain for each level of Eve’s utility.
MRS = Marginal rate of substitution.
MRS = absolute value of the slope of the indifference curve.
MRS = what are you willing to give up in order to get more of something else.
MRSaf = rate at which consumers are willing to trade apples for fig leaves.
MRS = 1/3 means: if Adam lost three extra apples, he would require only one fig leaf to maintain his
original utility level.
Pareto efficiency requires:
MRSafAdam = MRSafEve
Edgeworth box in production economy:
, • Productive inputs can be shift between the production of apples and fig leaves.
• Quantity can change.
• Supply is limited.
• If more apples are produced, then fig leaf production must necessarily fall and vice versa.
Production possibility curve (PPC): shows the maximum quantity of fig leaves that can be produced
along with any given quantity of apples.
• Depends on production technology.
MRT = marginal rate of transformation.
MRT = the absolute value of the slope with production possibilities frontier.
MRT = the rate at which the economy can transform one good into another good.
MRTaf = the rate at which apples can be transformed into fig leaves.
MRT = 2/3 means: two additional fig leaves could be produced by given up three apples.
It is useful to express the MRT in terms of MC.
MC = the incremental production cost of one more unit of output.
wy represents the incremental cost of producing apples, which we denote MCa.
xz is the incremental cost of producing fig leaves, MCf.
MRTaf = MCa / MCf
, Efficiency conditions with variable production:
➔ Necessary condition for Pareto efficiency.
MRTaf = MRSafAdam = MRSafEve
Substitute 2.3 into 3.3:
➔ A necessary condition for Pareto efficiency.
MCa / MCf = MRSafAdam = MRSafEve
The first fundamental theorem of welfare economics:
A competitive economy automatically allocates resource efficiently.
➔ No need for centralized direction. (Government action).
Policy implications; a competitive economy:
• Perfect competition.
o Equal prices.
o No market power.
• Market existence.
o A market exists for each and every commodity.
Necessary condition:
➔ (MRS equal to budget constraint)
MRSafAdam = Pa / Pf
MRSafEve = Pa / Pf
MRSafAdam = MRSafEve
Profit maximizing for competitive firms: Pa=MCa and Pf=MCf
MCa/MCf = Pa/Pf
MRTaf = Pa/Pf
MRTaf = MRSafAdam = MRSafEve
Pa / Pf = MCa / MCf
Final exam: CH 3-6, 8, 12, 14-16, 18, 20, 22
Chapter 3; Welfare economics
When markets don’t produce desirable results?
➔ Government action is needed.
When markets produce desirable results?
➔ Welfare economics.
Welfare economics: Basic concepts:
1. Efficiency: If we can improve welfare, it is not efficient.
Two types of efficiency:
▪ Technical efficiency: highest output with given input, or lowest input with given output.
(Does not concern us in welfare economics.
▪ Efficient allocation: who gets what? Optimal distribution of goods over persons.
Optimal = “Pareto efficiency”: An allocation of resources such that no person can be made better off
without making another person worse of.
2. Equity:
o Is it fair?
o What does fair mean?
Efficient allocation: how do we get that allocation?
➔ Edgeworth box.
Edgeworth box in exchange economy: (With fixed supplies, there is no production)
Which allocation is best?
• Adam and Eve have conventionally shaped indifference curves that represent their
preferences for apples and fig leaves.
• Indifferences curves with greater numbers represent higher levels of happiness (utitlity).
, ➔ Pareto improvement: a reallocation of resources that makes at least one person better off
without making anyone else worse of.
Contract curve: the locus of all the Pareto efficient points. (Denoted mm)
➔ It must be a point at which the indifference curves of Adam and Eve are barely touching. The
indifference curves are tangent, the slopes of the indifference curves are equal.
➔ Implicitly defines a relationship between the maximum amount of utility that Adam can
attain for each level of Eve’s utility.
MRS = Marginal rate of substitution.
MRS = absolute value of the slope of the indifference curve.
MRS = what are you willing to give up in order to get more of something else.
MRSaf = rate at which consumers are willing to trade apples for fig leaves.
MRS = 1/3 means: if Adam lost three extra apples, he would require only one fig leaf to maintain his
original utility level.
Pareto efficiency requires:
MRSafAdam = MRSafEve
Edgeworth box in production economy:
, • Productive inputs can be shift between the production of apples and fig leaves.
• Quantity can change.
• Supply is limited.
• If more apples are produced, then fig leaf production must necessarily fall and vice versa.
Production possibility curve (PPC): shows the maximum quantity of fig leaves that can be produced
along with any given quantity of apples.
• Depends on production technology.
MRT = marginal rate of transformation.
MRT = the absolute value of the slope with production possibilities frontier.
MRT = the rate at which the economy can transform one good into another good.
MRTaf = the rate at which apples can be transformed into fig leaves.
MRT = 2/3 means: two additional fig leaves could be produced by given up three apples.
It is useful to express the MRT in terms of MC.
MC = the incremental production cost of one more unit of output.
wy represents the incremental cost of producing apples, which we denote MCa.
xz is the incremental cost of producing fig leaves, MCf.
MRTaf = MCa / MCf
, Efficiency conditions with variable production:
➔ Necessary condition for Pareto efficiency.
MRTaf = MRSafAdam = MRSafEve
Substitute 2.3 into 3.3:
➔ A necessary condition for Pareto efficiency.
MCa / MCf = MRSafAdam = MRSafEve
The first fundamental theorem of welfare economics:
A competitive economy automatically allocates resource efficiently.
➔ No need for centralized direction. (Government action).
Policy implications; a competitive economy:
• Perfect competition.
o Equal prices.
o No market power.
• Market existence.
o A market exists for each and every commodity.
Necessary condition:
➔ (MRS equal to budget constraint)
MRSafAdam = Pa / Pf
MRSafEve = Pa / Pf
MRSafAdam = MRSafEve
Profit maximizing for competitive firms: Pa=MCa and Pf=MCf
MCa/MCf = Pa/Pf
MRTaf = Pa/Pf
MRTaf = MRSafAdam = MRSafEve
Pa / Pf = MCa / MCf
