Public Finance
Question #1
Warrenia has two regions. In Oliviland, the marginal benefit associated with pollution cleanup is MB=300 –
10Q, while in Linneland, the marginal benefit associated with pollution cleanup is MB=200 – 4Q. Suppose
that the marginal cost of cleanup is constant at $12 per unit. What is the optimal level of pollution cleanup
in each of the two regions?
Answer:
The optimal level of cleanup will occur when the marginal benefit just equals the marginal cost. In
Oliviland, the marginal benefit is 300 – 10 Q; marginal cost is 12. Therefore, the equation to solve for
Oliviland is 300 – 10 Q = 12, or 288 = 10 Q. The optimal level in Oliviland is equal to 28.8. For Linneland,
the marginal benefit is 200– 4 Q. Setting the benefit equal to 12 yields 200 – 4 Q = 12, or 188 = 4 Q. The
optimal level in Linneland is equal to 47.
Question #2
The private marginal benefit associated with a product’s consumption is PMB=360 – 4Q and the private
marginal cost associated with its production is PMC=6P. Furthermore, the marginal external damage
associated with this good’s production is MD=2P. To correct the externality, the government decides to
impose a tax of T per unit sold. What tax T should it set to achieve the social optimum?
Answer:
Find the social optimum by setting PMB= PMC + MD (= SMC): 360 – 4Q = 8Q, or Q* = 30. Setting a tax of
T effectively increases the PMC by T per unit sold. The new equilibrium quantity solves 360 – 4 Q = 6 Q +
T. Setting Q = 30 and solving for T gives T = 60. A tax of T = 60 will achieve the social optimum.
Question #3
When the state of Virginia imposed stricter regulations on air pollution in 2003, it also authorized an
auction of pollution permits, allowing some plants to emit larger amounts of ozone-depleting chemicals
than would otherwise be allowed, and some to emit less. Theory predicts that this auction led to a socially
efficient allocation of pollution. Describe how this outcome would occur.
Answer:
Assuming that the given level of pollution permits was set correctly, an auction would lead to a socially
efficient allocation of permits across firms. Firms that would benefit the most from having the right to
pollute—say, because it would be very costly for them to produce without polluting—would be the most
willing to pay for the right. Therefore, those firms would bid more at the auction and would receive the
permits. Firms that find it easy to adopt less-polluting technologies in their production process would be
less willing to pay for the right to pollute and therefore would not bid as much at the auction and would not
receive as many permits. This means that the permits would be allocated to the firms that cannot easily
reduce pollution, while the firms that could most easily reduce emissions would do so instead of buying
permits and continuing to pollute. This is the socially efficient outcome: pollution would be reduced, and it
would be reduced most by firms that could most cheaply reduce it.
Question #4
Question #1
Warrenia has two regions. In Oliviland, the marginal benefit associated with pollution cleanup is MB=300 –
10Q, while in Linneland, the marginal benefit associated with pollution cleanup is MB=200 – 4Q. Suppose
that the marginal cost of cleanup is constant at $12 per unit. What is the optimal level of pollution cleanup
in each of the two regions?
Answer:
The optimal level of cleanup will occur when the marginal benefit just equals the marginal cost. In
Oliviland, the marginal benefit is 300 – 10 Q; marginal cost is 12. Therefore, the equation to solve for
Oliviland is 300 – 10 Q = 12, or 288 = 10 Q. The optimal level in Oliviland is equal to 28.8. For Linneland,
the marginal benefit is 200– 4 Q. Setting the benefit equal to 12 yields 200 – 4 Q = 12, or 188 = 4 Q. The
optimal level in Linneland is equal to 47.
Question #2
The private marginal benefit associated with a product’s consumption is PMB=360 – 4Q and the private
marginal cost associated with its production is PMC=6P. Furthermore, the marginal external damage
associated with this good’s production is MD=2P. To correct the externality, the government decides to
impose a tax of T per unit sold. What tax T should it set to achieve the social optimum?
Answer:
Find the social optimum by setting PMB= PMC + MD (= SMC): 360 – 4Q = 8Q, or Q* = 30. Setting a tax of
T effectively increases the PMC by T per unit sold. The new equilibrium quantity solves 360 – 4 Q = 6 Q +
T. Setting Q = 30 and solving for T gives T = 60. A tax of T = 60 will achieve the social optimum.
Question #3
When the state of Virginia imposed stricter regulations on air pollution in 2003, it also authorized an
auction of pollution permits, allowing some plants to emit larger amounts of ozone-depleting chemicals
than would otherwise be allowed, and some to emit less. Theory predicts that this auction led to a socially
efficient allocation of pollution. Describe how this outcome would occur.
Answer:
Assuming that the given level of pollution permits was set correctly, an auction would lead to a socially
efficient allocation of permits across firms. Firms that would benefit the most from having the right to
pollute—say, because it would be very costly for them to produce without polluting—would be the most
willing to pay for the right. Therefore, those firms would bid more at the auction and would receive the
permits. Firms that find it easy to adopt less-polluting technologies in their production process would be
less willing to pay for the right to pollute and therefore would not bid as much at the auction and would not
receive as many permits. This means that the permits would be allocated to the firms that cannot easily
reduce pollution, while the firms that could most easily reduce emissions would do so instead of buying
permits and continuing to pollute. This is the socially efficient outcome: pollution would be reduced, and it
would be reduced most by firms that could most cheaply reduce it.
Question #4
