the provision of a real public good, like the date of the midterm, it is still of
interest to run through a numerical example, such as the one given in the book.
92 Chapter Highlights
Chapter 37 93
Public Goods
A. Public goods involve a particular kind of externality — where the same
amountofthegoodhastobeavailabletoeveryone.
B. Examples: national defense, street lights, roads, etc. — same amount must
be provided to all.
C. But people can value the public good in different ways.
D. Private goods
E. Public goods
1. each person consumes the same amount, but values it differently.
F. Two questions about public goods
G. Example: a TV for two roommates. Roommate iwill contribute gi≥0
towards the purchase. TV will be purchased if g1+g2≥C.
1. consider the reservation prices r1and r2. These measure maximum
willingness-to-pay for TV by each person.
2. suppose that we can find (g1,g
2) such that r1≥g1,r2≥g2and g1+g2≥C.
3. then clearly it is a good idea to provide the TV.
H. Example of divisible good
1. two people each contributes gito a TV. Person igets utility ui(g1+g2)−gi.
2. efficient alloction maximizes sum of utilities:
4. this determines the optimal amount of the public good: G∗=g∗
1+g∗
2.
94 Chapter Highlights
I. Consider various social institutions to provide the public good.
1. voluntary contributions
a) person 1 will contribute until u
1(g1+g2)=1.
2. majority voting
a) assume that there are n>2 people.
b) suppose that each person pays 1/n of the public good if it is provided.
e) if a majority of the people vote for an increase in the public good, then
we get a small increase.
f) so the amount of the public good is determined by the condition that
the median voter is happy with the current amount.
1) median voter means half the voters want more, half the voters want
less.
3. Clarke-Groves tax
a) in order to get an efficient amount of the public good, each person must
Chapter 37 93
Public Goods
A. Public goods involve a particular kind of externality — where the same
amountofthegoodhastobeavailabletoeveryone.
B. Examples: national defense, street lights, roads, etc. — same amount must
be provided to all.
C. But people can value the public good in different ways.
D. Private goods
E. Public goods
1. each person consumes the same amount, but values it differently.
F. Two questions about public goods
G. Example: a TV for two roommates. Roommate iwill contribute gi≥0
towards the purchase. TV will be purchased if g1+g2≥C.
1. consider the reservation prices r1and r2. These measure maximum
willingness-to-pay for TV by each person.
2. suppose that we can find (g1,g
2) such that r1≥g1,r2≥g2and g1+g2≥C.
3. then clearly it is a good idea to provide the TV.
H. Example of divisible good
1. two people each contributes gito a TV. Person igets utility ui(g1+g2)−gi.
2. efficient alloction maximizes sum of utilities:
4. this determines the optimal amount of the public good: G∗=g∗
1+g∗
2.
94 Chapter Highlights
I. Consider various social institutions to provide the public good.
1. voluntary contributions
a) person 1 will contribute until u
1(g1+g2)=1.
2. majority voting
a) assume that there are n>2 people.
b) suppose that each person pays 1/n of the public good if it is provided.
e) if a majority of the people vote for an increase in the public good, then
we get a small increase.
f) so the amount of the public good is determined by the condition that
the median voter is happy with the current amount.
1) median voter means half the voters want more, half the voters want
less.
3. Clarke-Groves tax
a) in order to get an efficient amount of the public good, each person must