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K4020 Problem Set 2 Due in class on 10/13/2016 Please submit your response in groups.

 

1. A public health department is considering five alternative programs to encourage parents to have their

 

preschool children vaccinated against a communicable disease. At most one program will be adopted.

 

The following table shows the cost and number of vaccinations predicted for each program.

 

Program Program Cost Vaccinations

 

A

 

$24, 000

 

2, 000

 

B

 

$33, 000

 

3, 000

 

C

 

$72, 000

 

7, 500

 

D

 

$110, 000

 

11, 000

 

E

 

$200, 000

 

18, 000

 

(a) Compute the average cost per vaccination for each program.

 

(b) Ignoring issues of scale, which program is most cost-effective?

 

(c) Assuming the public health department wishes to vaccinate at least 10,000 children, which program

 

is most cost-effective?

 

(d) If the health department believes that each vaccination delivers social benefits of $15, which program

 

should it adopt? (HINT: Compute net aggregate benefits for each program)

 

2. A person?s demand for organic cotton shirts is given by the following equation:

 

q = 4 ? 0.25p + 0.0002I

 

where, q is the quantity demanded per year at price p when the person?s annual income is I. Assume

 

initially that the person?s income is $60,000.

 

(a) At what price will demand fall to zero? (This is sometimes called the choke price because it is the

 

price that chokes off demand.)

 

(b) If the market price for the shirts is $24, how many will be demanded?

 

(c) At a price of $24, what is the price elasticity of demand for organic cotton shirts?

 

(d) At a price of $24, what is the consumer surplus?

 

(e) If price falls to $20, how much consumer surplus is gained?

 

(f) If income were $90,000, what would be the consumer surplus gain from a price drop from $24 to

 

$20?

 

(g) Does your answer to part (f) above suggest that willingness to pay depends on income? If so, how

 

does willingness to pay depend on income? If not, why does it not depend on income?

 

3. A country imports 1.5 billion barrels of crude oil per year and domestically produces another 4.5 billion

 

barrels of crude oil per year. The world price of crude oil is $93 per barrel. Assuming linear demand

 

and supply curves, economists estimate the price elasticity of domestic supply to be 0.25 and the price

 

elasticity of domestic demand to be 0.10 at the current equilibrium.

 

(a) Consider the changes in social surplus that would result from imposition of a $30 per barrel import

 

fee on crude oil that would involve annual administrative costs of $600 million. Assume that the

 

world price will not change as a result of the country imposing the import fee, but that the domestic

 

price will increase by $30 per barrel. Also assume that only producers, consumers, and taxpayers

 

within the country have standing. Determine the quantity consumed, the quantity produced domestically, and the quantity imported after the imposition of the import fee. Then estimate the

 

annual social net benefits of the import fee.

 

(b) Economists have estimated that the marginal excess burden of taxation in the country is 0.25.

 

Re-estimate the social net benefits assuming that 20 percent of the increase in producer surplus

 

is realized as tax revenue under the existing tax system. In answering this question, assume that

 

increases in tax revenues less the cost of administrating the import fee are used to reduce domestic

 

taxes. 4. Suppose you have been asked to advise the Energy Ministry of Mexico on their reform of the electricity

 

sector. The Ministry wants to impose a tax per unit of electricity generated by heavy fuel oil (HFO)

 

generation plants. The amount of the tax is meant to offset the damage incurred by the Mexican

 

population from respiratory health diseases and decreased crop yields resulting from SO2 emissions

 

which are a by-product of HFO power plants.

 

Suppose demand (in MWh) is given by Qd = 140 ? P where P is the price in pesos per MWh and Qd is

 

the quantity demanded. The supply of electricity (in MWh) from HFO plants is given by Qs = 4P ? 200

 

where P is the price in pesos per MWh and Qs is the quantity supplied. Suppose further that the damage

 

caused by the SO2 emissions is given by 0.125Q2 pesos where Q is electricity generated in MWh.

 

(a) (7 points) In the absence of a tax for SO2 emissions, what will be the equilibrium price and quantity

 

of HFO-generated electricity in the market?

 

(b) (6 points) What is the socially optimal amount of electricity production from HFO power plants,

 

taking into account the SO2 emissions damage? (Ignore damage from other emissions such as NOx,

 

particulate matter, carbon etc. Note that the marginal damage from the SO2 emissions is given by

 

the derivative of 0.125Q2 with respect to electricty generated, i.e. 0.25Q.)

 

(c) (4 points) Suppose the Ministry is considering a tax of $T per MWh generated by HFO plants.

 

Find the level of the tax, T , that ensures that the socially optimal amount of HFO-generated power

 

will be produced in competitive equilibrium.

 

(d) (4 points) Compute the deadweight loss which is eliminated by imposition of the tax.

 

(e) (4 points) In general, do all taxes eliminate deadweight losses? If yes, state why. If not, state why

 

not.

 

5. The Department of Transportation plans to build a temporary bridge to reduce travel time during the

 

three years it will take to renovate the Pulaski Skyway, an important bridge for commuters. The temporary bridge can be put up in a few weeks at a cost of $48 million. At the end of three years, the bridge

 

would be decommissioned and the steel would be sold for scrap. The real net cost of decommissioning

 

would be $3 million, after accounting for scrap sales. Based on estimated time savings and wage rates,

 

fuel savings, and reductions in risks of accidents, department analysts predict that the benefits in real

 

dollars would be $15,900,000 during the first year, $18,900,000 during the second year, and $19,000,000

 

during the third year. Departmental regulations require use of a real discount rate of 4 percent.

 

(a) Calculate the net present value of the temporary bridge assuming that the benefits are realized at

 

the end of each of the three years.

 

(b) Calculate the net present value of the temporary bridge assuming that the benefits are realized at

 

the beginning of each of the three years.

 

(c) Calculate the net present value of the temporary bridge assuming that the benefits are realized in

 

the middle of each of the three years.

 

(d) Does it make sense for the Department of Transportation to build the temporary bridge?

 

6. The environmental protection agency of a county would like to preserve a piece of land as a wilderness

 

area. The current owner has offered to lease the land to the county for 30 years in return for a lump-sum

 

payment of $1.75 million, which would be paid at the beginning of the 30-year period. The agency

 

has estimated that the land would generate $102,000 per year in benefits to hunters, bird watchers,

 

and hikers. Assume that the lease price represents the social opportunity cost of the land and that the

 

appropriate real discount rate is 5 percent.

 

(a) Assuming that the yearly benefits, which are measured in real dollars, accrue at the end of each of

 

the 30 years, calculate the net benefits of leasing the land.

 

(b) Some analysts in the agency argue that the annual real benefits are likely to grow at a rate of

 

2 percent per year due to increasing population and county income. Recalculate the net benefits

 

assuming that they are correct. K4020 Problem Set 2 Page 2 of 3 7. Imagine that the current owner of the land in the previous exercise was willing to sell the land for $2.2

 

million. Assuming this amount equaled the social opportunity cost of the land, calculate the net benefits

 

if the county were to purchase the land as a permanent wildlife refuge. In making these calculations,

 

first assume a zero annual growth rate in the $102,000 of annual real benefits; then assume that these

 

benefits grow at a rate of 2 percent per year. K4020 Problem Set 2 Page 3 of 3

 







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