41-310 Assignment 2 Due on Nov. 16 (Monday), 2:30pm. (Please turn it
in at the beginning of the class.)
1.
Player 2
Left Right
Player 1 Top 4,4 0,6
Bottom 6,0 1,1
For the game as shown above,
a. which strategy is the dominant strategy for P1?
b. Write down the dominant strategy equilibrium.
c. The dominant strategy equilibrium payoffs (1,1) are not optimal. Is
it possible to change the game with a transfer (or penalty) between the two
players so that the dominant strategy equilibrium of the new game becomes
efficient? Find the transfer and represent the new game after the transfer.
2. (GHG) There are 40 identical countries in the world. Facing a decision
making problem of maintaining a steady economic growth and reducing
GHGs, each has two choices: Reduce GHGs (R) and Not to reduce
GHGs(NR). If a country chooses NR, then the economy grows faster, and
the faster growth generates an additional estimated economic value of 20
billion dollars. But it increases the level of GHGs in the atmosphere, and its
negative impact imposes the cost of $1 billion on each and every country
in the world. If a country selects R, then its economy grows slower, the
slower growth generates an additional estimated economic value of only 5
billion dollars. In this case, there is no increase in GHGs in the atmosphere,
and hence no negative impact.
(a) Show that R is dominated by NR for a country.
(b) Find the total (social) maximum surplus and the minimum surplus
(or maximum loss).
(c) Explain the reason why the minimum surplus, not the total maximum
surplus, is likely to be the outcome these countries collectively select.
3. Two countries, country 1 and country 2, select either Abate or Pollute.
Each country has two types of individuals, Ninenine and Topone. Individuals
receive two types of gains(or losses); economic gain and non-economic gain.
Assume that Ninenines only receive non-economic gain and Topones only
receive economic gain.
If there are no Topones and only Ninenines in both countries, then the
game is represented as shown below.
1
Country 2
Abate Pollute
Country 1 Abate 0.5, 0.5 0.4, 0
Pollute 0, 0.4 -0.1,-0.1
If there are only Topones without Ninenines in both countries, then the
game is represented as shown below.
Country 2
Abate Pollute
Country 1 Abate -8, -8 -9, 12
Pollute 12, -9 10, 10
a. Suppose that there are 50 Ninenines and 1 Topone. Find or represent
the game that the two countries are playing. And find the dominant strategy
equilibrium of the game.
b. If the non-economic gains are ignored in each country, what will be
the expected choices made by the countries? Explain why it is suboptimal.
c. Is the prisoners’ dilemma game an appropriate game that describes
the problem faced by the two countries here? Explain.
4. Individuals A and B both enjoy flowers (public good). The MWTP curves
of flowers are given by MW T P(A) = 60-x for A and MW T P(B) = 120-2x
for B where x is the level of flowers. Suppose individual A is the only one
who produces good x (Only A knows how to garden.) The marginal cost
(MC) of producing the good is given by MC = x.
1. Find the level of flowers that maximizes A’s welfare.
2. Find the socially efficient level of flower
3. Discuss why the inefficient allocation obtained in 1 is a likely outcome
and how a subsidy to A may leads the economy to a socially optimal
allocation.
5. Suppose that there are two countries in the world, C1 and C2, whose
marginal benefit curves are given as follows. MB1 = 100 – G1 and MB2 =
60-2G2 where G1 and G2 are the levels of emission by C1 and C2 respectively.
Both countries agreed on putting a cap on the level of CO2 emission, 50
million (mega) tons each and 100 total.
(1) Find the efficient distribution of 100 units of the total emission.
(2) Suppose that the international market price for carbon is given by
$10 per unit, i.e., an unlimited amount of carbon credits is bought and sold
at price $10. How many units of carbon credits will C1 buy or sell and how
many units of carbon credits will C2 buy or sell?
2
(3) Suppose there is a demand from individuals who purchase the permits
to reduce GHGs.The demand is given by D(or G3) = 20 –
1
2
p. Find the
equilibrium market price, and the distribution of permits, G1, G2 and G3 at
the equilibrium price.
3

41-310 Assignment 2 Due on Nov. 16 (Monday), 2:30pm. (Please turn it
in at the beginning of the class.)
1.
Player 2
Left Right
Player 1 Top 4,4 0,6
Bottom 6,0 1,1
For the game as shown above,
a. which strategy is the dominant strategy for P1?
b. Write down the dominant strategy equilibrium.
c. The dominant strategy equilibrium payoffs (1,1) are not optimal. Is
it possible to change the game with a transfer (or penalty) between the two
players so that the dominant strategy equilibrium of the new game becomes
efficient? Find the transfer and represent the new game after the transfer.
2. (GHG) There are 40 identical countries in the world. Facing a decision
making problem of maintaining a steady economic growth and reducing
GHGs, each has two choices: Reduce GHGs (R) and Not to reduce
GHGs(NR). If a country chooses NR, then the economy grows faster, and
the faster growth generates an additional estimated economic value of 20
billion dollars. But it increases the level of GHGs in the atmosphere, and its
negative impact imposes the cost of $1 billion on each and every country
in the world. If a country selects R, then its economy grows slower, the
slower growth generates an additional estimated economic value of only 5
billion dollars. In this case, there is no increase in GHGs in the atmosphere,
and hence no negative impact.
(a) Show that R is dominated by NR for a country.
(b) Find the total (social) maximum surplus and the minimum surplus
(or maximum loss).
(c) Explain the reason why the minimum surplus, not the total maximum
surplus, is likely to be the outcome these countries collectively select.
3. Two countries, country 1 and country 2, select either Abate or Pollute.
Each country has two types of individuals, Ninenine and Topone. Individuals
receive two types of gains(or losses); economic gain and non-economic gain.
Assume that Ninenines only receive non-economic gain and Topones only
receive economic gain.
If there are no Topones and only Ninenines in both countries, then the
game is represented as shown below.
1
Country 2
Abate Pollute
Country 1 Abate 0.5, 0.5 0.4, 0
Pollute 0, 0.4 -0.1,-0.1
If there are only Topones without Ninenines in both countries, then the
game is represented as shown below.
Country 2
Abate Pollute
Country 1 Abate -8, -8 -9, 12
Pollute 12, -9 10, 10
a. Suppose that there are 50 Ninenines and 1 Topone. Find or represent
the game that the two countries are playing. And find the dominant strategy
equilibrium of the game.
b. If the non-economic gains are ignored in each country, what will be
the expected choices made by the countries? Explain why it is suboptimal.
c. Is the prisoners’ dilemma game an appropriate game that describes
the problem faced by the two countries here? Explain.
4. Individuals A and B both enjoy flowers (public good). The MWTP curves
of flowers are given by MW T P(A) = 60-x for A and MW T P(B) = 120-2x
for B where x is the level of flowers. Suppose individual A is the only one
who produces good x (Only A knows how to garden.) The marginal cost
(MC) of producing the good is given by MC = x.
1. Find the level of flowers that maximizes A’s welfare.
2. Find the socially efficient level of flower
3. Discuss why the inefficient allocation obtained in 1 is a likely outcome
and how a subsidy to A may leads the economy to a socially optimal
allocation.
5. Suppose that there are two countries in the world, C1 and C2, whose
marginal benefit curves are given as follows. MB1 = 100 – G1 and MB2 =
60-2G2 where G1 and G2 are the levels of emission by C1 and C2 respectively.
Both countries agreed on putting a cap on the level of CO2 emission, 50
million (mega) tons each and 100 total.
(1) Find the efficient distribution of 100 units of the total emission.
(2) Suppose that the international market price for carbon is given by
$10 per unit, i.e., an unlimited amount of carbon credits is bought and sold
at price $10. How many units of carbon credits will C1 buy or sell and how
many units of carbon credits will C2 buy or sell?
2
(3) Suppose there is a demand from individuals who purchase the permits
to reduce GHGs.The demand is given by D(or G3) = 20 –
1
2
p. Find the
equilibrium market price, and the distribution of permits, G1, G2 and G3 at
the equilibrium price.
3