1) A development agency is trying to create a fishing industry in a small coastal village. Estimates of the total number of tons of fish caught per yer with different numbers of boats have been prepared. The annual costs of each boat (including the annualized capital costs as well as the labor costs) come to $20,000.

Tons of fish caught

1 boat 5

2 boats 9

3 boats 12

4 boats 11

a) First, assume that the value of the fish caught is $10,000 per ton. Calculate the marginal benefits, the marginal costs, and the net benefits, and show how many boats should be provided to achieve the most efficient outcome.

b) Second, if the only choice were between 4 boats or none, what would the value per ton have to be to justify choosing 4 boats?

c) Third, assume that the value per ton is unknown. Perhaps it depends on which kinds of fish are caught. Calculate how high the value would have to be in order to justify each added level of investment.

d) Suppose that there are 20 villages which could use this money for a fishing industry and that the same figures shown above apply to all of them. If the development agency has a fixed budget of $800,000 to spend on this type of project, how should it spend the money? Why?

2) As a result of tensions in the Middle East, oil prices shoot up again, raising the price of gasoline from $1.00 per gallon to $2.00. As a result, gas consumption dropped from 5 billion gallons to 4 billion. If the society relied on imported oil for all of its energy needs, what would the societal cost of these changes be? Display graphically as well.

3) A local government is faced with a choice for the development of a site that it owns. Project A is a commercial development that will have immediate costs of $100M and is expected to bring in rents and increased property taxes equal to $5M per year, starting at the end of the year and lasting for the expected 30 year life of the project.

Project B involves clearing the land at an immediate cost of $10M and making it available for housing. Because of possible problems of contamination on the site, the sale of the land for housing would not occur until the end of 4 years. At that time, the expected sales price would be $20M.

If the real discount rate is 4% and the other figures are all expressed in real terms, which project has a greater present value for the city?

4) An economic cost is a benefit lost. True or false? Why?

Answers to In-Class Portion of Mid-term

1) a) Net benefits are maximized at 3 boats.

b) If the choice is between 0 and 4 boats, you would have to value a ton of fish at $7273 or more to justify 4 boats. Four boats cost $80,000 and catch 11 tons of fish. So the average cost per ton is TC/TE or $80,000/11. You have to value the fish at more than the average cost if there are to be any net benefits from 4 boats. [Note that we use the average cost because the alternative is doing nothing (i.e., in this case the average cost is also the marginal cost of going from 0 to 4 boats.)]

c) If the value is unknown, you have to look at the MC/ME at each level to see how much the extra tons are costing you. That is the amount that you have to value each ton in order to justify each extra level of spending.: $4000 for 1 boat, $5000 for a second boat, $6667 for a third boat.

d) With a fixed budget of $800k, you want to spend it in the way that gives you the greatest total effect. Since the same costs and effects apply in each village, you maximize the effect by spending $40k for 2 boats in each village. You get 180 tons of fish, more than any other allocation will bring.

2) Higher oil prices drive the price of gasoline from $1 per gallon to $2, reducing the quantity consumed from 5B gallons to 4B. The effect, assuming a flat supply curve, is a loss in consumer surplus equal to ($1 x 4B) plus ($1 x 1B x 1/2), a total of $4.5B. Since these resources are largely owned by other nations, the full $4B payment is a cost to American society, along with the deadweight loss of $500M. To the extent that American-owned oil companies get higher profits (producer surplus), the societal loss would be less.

3) Project A has costs now of $100M. So the present value of costs is $100M. It has benefits of $5M per year for 30 years. This is like an annuity of a certain amount received every year. Table 13.3 reports that a dollar received every year for 30 years at 4% has a present value of $17.30. Multiplying by 5 million gives a present value of $86.5 M. So Project A has a net loss of $13.5M.

The PV of $5M a year for 30 years is not equal to $150M received in 30 years. That has a PV of .308 x $150M or just over $46M. Think about it. If you get $5M the first year, you have 29 years to get interest on it; for $5M in the second year, you have 28 years of interest and so on. So after 30 years you will have your $150M plus all of the interest you would have earned on it.

Project B costs $10M now and returns $20M in 4 years. A dollar in 4 years at 4% has a PV of 0.855. So this sum has a PV of $17.1M and the net benefits are $7.1M. So choose B.

4) Yes, an economic cost is a benefit lost. The concept of opportunity costs states that the OC is the value of the resource in its best alternative use, i.e., the use it is not in because it is being used in this project. What is being foregone by one project is the benefits that you would have gotten from the next best alternative use of those resources.

Other questions

2) As an energy efficiency measure, a tax credit is proposed for purchases of solar water heaters for the home. The market price of the heaters is $1600. The proposal is to give a 50% tax credit when they are purchased. In other words, the credit reduces the after-tax cost to consumers in half, to $800. Before the credit, the estimate is that 200,000 solar water heaters will be purchased. With the credit, the estimate is for 250,000 sales.

From a societal perspective, what does the value of the energy savings have to be to make this policy worthwhile?

Regardless of whether the program is worthwhile from a social perspective, what insights can you suggest about the cost-effectiveness of this tax credit proposal as a method for encouraging energy efficiency?

3) Buy or Lease?

Your agency can buy new trucks at a cost of $30,000 each or it can lease them for $7000 a year (paid at the end of each year) for 5 years. The trucks have a useful life of 5 years. What should you do if the discount rate you face is 5%? If it is 10%? Suppose that the trucks have a salvage value of $2000 when their useful life is through. Show the impact of that change.

2. The cost of this policy to society is the cost of the 50,000 extra solar water heaters that will be produced and purchased. If they cost $1600 each, then the cost is $80M. The reduction in energy use must be valued at at least this amount in order for the policy to be socially beneficial. Of course, the argument for a tax credit makes sense only if there is some reason why the price of energy is below its true, social cost. If the price does give a correct measure of the social cost, then a subsidy will lead to overconsumption of solar water heaters and a resulting loss for society. If you draw a diagram, which has the price at half the true social cost, you will see that consumers keep buying more even though the marginal benefits (as measured by the demand curve) are lower than the true costs. External costs could be the result of pollution or of foreign policy constraints imposed by dependence on foreign oil.

Even if you want to encourage use of solar energy, this tax credit may not be a good method. Basically, taxpayers are going to subsidize 250,000 purchases, to the tune of $800 each, in order to induce an extra 50,000 purchases (from 200,000 to 250,000). This is a total taxpayer cost of $200M, a cost of $4000 for each extra purchase. Note that since the units actually cost $1600, it would be much cheaper for taxpayers to buy the units and give them away. Of course, then the question would be who would get them? But the point is that there may be cheaper methods--installing them in public projects or issuing a regulation requiring them in certain new projects. The proposed tax credit provides a "windfall" to those who would have purchased the units even in the absence of the credit. That term is used, somewhat loosely, to refer to gains that are unmerited; in this case, because the gainers did not change their behavior in any way to merit it.

1) The gain (benefit) to society is the gain in consumer's surplus, the strip added to the area "below the demand curve and above the price/cost). It is a rectangle equal to 10 cents times 50 million =$5M; and the triangle equal to 10 cents times 10 million times 1/2=$500k. Or a total benefit of $5.5M.

2) The costs of the tax to society are only the triangle ("deadweight loss") equal to $0.50 times 50 million times 1/2 or $12.5M. In addition, smokers pay a tax equal to $0.50 times 450 million or $225M.

3) Bus company:

There are different ways to go about calculating the answer. One is to look at the total gains and losses to all groups. Bus consumers gain the consumer surplus strip created by the lower price. It is the rectangle: (120 million times 10 cents=12 million dollars) + the triangle: (15 million times 10 cents times 1/2=750,000 dollars). A total benefit of 12.75 million dollars

The bus company loses $7.5M of revenue. In addition it must expend $2.35M in real resources. The total cost to the bus company is $9.85M. The net gain, the social benefit, is $2.9M.

Note that much of the consumers' gain is a transfer from the taxpayers who subsidize the bus company. We could also use an approach that nets out the transfer payments. What is the cost of the bus expansion to society? It is the $2.35M to pay for the extra busses, drivers, etc.

What are the benefits to society? This is a little trickier, but if you think about it, we are asking "What is the benefit to society of providing the extra 15 million passenger kilometers?" The value of this extra service is the amount people are willing to pay for it--the amount under the demand curve from 120 million to 135 million. The total value of this extra service is (30 cents times 15 million=$4.5 plus the $750k in the triangle--a total of $5.25M. But since it costs $2.35 to provide this service, the net benefit is $2.9M. This is the same answer we got above when we included the transfer payment gains and losses.

4) Too complex and varied to provide "an answer."