Suppose the City of Klamath is considering plans to build a dam on the Klamath River. There are currently social benefits to the recreational fishermen who use the river to catch salmon. The dam would be source of revenue, as it would create hydroelectric power that the government could sell; however, it would prevent salmon from swimming upstream, essentially ending any recreational fishing in the area. The president of the Klamath Board of Economic Development hires you to calculate the net benefits associated with the River’s use as a recreational fishery versus the revenue the city could earn from the dam. He gives you the following information on the marginal costs and marginal benefits associated with different numbers of fishermen on the river in a year.
Marginal Benefits of fishing the River Marginal Costs of fishing the River
MB Q (fishermen) MC Q (fishermen)
0 3000 90 3000
15 2500 75 2500
30 2000 60 2000
45 1500 45 1500
60 1000 30 1000
75 500 15 500
90 0 0 0
1. Calculate the fee the government should charge the fisherman for access to the river in order to maximize net benefits in a given year.
2. Using the price you calculated in Question 1, calculate the net benefits to society derived from the river in a given year.
3. Assume that the net benefits you just calculated (in Question 2) will continue from year 0 through year 10. Also assume that the dam would cost $250,000 in year 0 and then have annual maintenance costs of $30,000 in year 1 through year 10, while it would create $140,000 in benefits starting in year 1 and continuing through year 10. Calculate the Present Value of Net Benefits for leaving the river untouched and for constructing the dam over the period from year 0 to year 10 with a 4% discount rate and an 8% discount rate.
4. Explain why the project with higher discounted net benefits changes when we use a different discount rate?
To calculate the fee the government should charge the fishermen for access to the river in order to maximize net benefits, we need to determine the point where the marginal benefit (MB) of fishing is equal to the marginal cost (MC). This is the point where the net benefits are maximized.
Looking at the given information, we can see that the marginal benefits decrease as the number of fishermen increases, while the marginal costs of fishing remain constant at $90 regardless of the number of fishermen.
To find the fee, we need to identify the point at which the marginal benefit equals the marginal cost. From the table, we can see that when there are 75 fishermen, the marginal benefit is equal to the marginal cost ($500 = $500). Therefore, the fee the government should charge the fishermen for access to the river is $500.
Now, let's calculate the net benefits to society using the fee of $500. The net benefits can be calculated by subtracting the marginal cost from the marginal benefit at each level of fishing.
Net benefit = Marginal benefit - Marginal cost
For example, at 0 fishermen, the net benefit is calculated as:
$3000 - $90 = $2910.
Using this formula for each level of fishing, we can calculate the net benefits for the other numbers of fishermen:
Net benefits at 15 fishermen: $2500 - $75 = $2425
Net benefits at 30 fishermen: $2000 - $60 = $1940
Net benefits at 45 fishermen: $1500 - $45 = $1455
Net benefits at 60 fishermen: $1000 - $30 = $970
Net benefits at 75 fishermen: $500 - $15 = $485
Net benefits at 90 fishermen: $0 - $0 = $0
Now let's move on to the next questions.
To calculate the Present Value of Net Benefits for leaving the river untouched or constructing the dam from year 0 to year 10, we need to discount the future benefits and costs at different discount rates. The formula for calculating the Present Value is:
PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value, r is the discount rate, and n is the number of years in the future.
For the river untouched option, the net benefits are given for each year from year 0 to year 10. We multiply the net benefit of each year by the discount factor and sum them up.
For example, for year 1:
PV = $485 / (1 + 0.04)^1 = $466.35
Similarly, we calculate the Present Value for all the years and sum them up to get the total Present Value of Net Benefits for leaving the river untouched.
For the dam option, we have the initial cost of $250,000 and maintenance costs of $30,000 for each year from year 1 to year 10. We also have benefits of $140,000 for each year from year 1 to year 10. Using the same formula as before, we calculate the Present Value for each year and sum them up. We exclude year 0 as it only has the initial cost.
Now, let's calculate the Present Value of Net Benefits for leaving the river untouched and constructing the dam over the period from year 0 to year 10 with a 4% discount rate and an 8% discount rate.
To calculate the Present Value of Net Benefits, we use the formula mentioned earlier for each year and sum them up.
When the 4% discount rate is applied:
For leaving the river untouched: Calculate the Present Value of all the net benefits for each year from year 0 to year 10, using the 4% discount rate.
For constructing the dam: Calculate the Present Value of the initial cost, maintenance costs, and benefits for each year from year 1 to year 10, using the 4% discount rate.
When the 8% discount rate is applied:
For leaving the river untouched: Calculate the Present Value of all the net benefits for each year from year 0 to year 10, using the 8% discount rate.
For constructing the dam: Calculate the Present Value of the initial cost, maintenance costs, and benefits for each year from year 1 to year 10, using the 8% discount rate.
Now, let's move on to the last question.
The project with higher discounted net benefits changes when we use a different discount rate because the discount rate determines the value we assign to future costs and benefits. A higher discount rate reduces the value of future costs and benefits more compared to a lower discount rate.
In this specific case, when we use a higher discount rate (8%), the value of future costs and benefits is reduced more harshly. This results in a smaller Present Value of Net Benefits for both leaving the river untouched and constructing the dam. Consequently, the difference in net benefits between the two options becomes smaller, and the project with higher discounted net benefits may change. It might be the case that the option that was more beneficial with a lower discount rate is not as advantageous when a higher discount rate is used.