Applied Economics 3611 - Assignment 3

Environmental and Natural Resource Economics

Questions set #3

Preparation for quiz #3

Problem 1: NPV

In a village along a river there is an old bridge that engineers have warned needs to be replaced. A new bridge will cost $1 million. If the bridge is built, this cost will be experienced in the following year, at t = 1. The discount rate is r = .05 and a planning horizon of 10 years has been adopted. It is known that the new bridge will create benefits (due to a decline in travel time) of $120,000 per year for each of the 10 years from t = 1 to t = 10.

  1. (15 points) Compute the present value (today, at t = 0) of the cost of the project to be built at t = 1.

  2. (15 points) Compute the present value (today, at t = 0) of the benefit over 10 years from t = 1 to t = 10. Should the plant be built?

  3. (15 points) Finally, let’s say the new bridge, being safer than the old one, will also save one life per decade. Suppose also that we can put a dollar value on how much we care about saving that life (call this the “value of a statistical life”). What should the value of the statistical life be in order to change the decision in part b.?

  4. (15 points) Now suppose a member of the city council argues successfully that the planning for this project should use a discount rate of r′ = .03 rather than the original value of r = .05. Discuss how this change will affect the decision. How would you advise the council, as a staff economist, to select the “best” discount rate for the project?

Problem 2: Fishery Sustainable Yield

A fishery is characterized by the following sustainable-yield function:

h(E) = E \left(1 - \frac{E}{250}\right).

Part (a) - Maximum Sustainable Yield (10 points)

Using the fact that the derivative of h is dh/dE = 1 - (E/125), find the effort level associated with the maximum sustainable yield. (Set the derivative of h equal to zero and solve for E.) What is harvest at E^{MSY}?

Part (b) - Net Benefits (15 points)

Suppose the price of fish is P = 75 and the cost of effort is a = 51. Write down the net-benefit (profit) function and find the value of E at which net benefits are maximized. Use the fact that the derivative of NB is dNB/dE = 24 - (3/5)E. (Set the derivative of NB equal to zero and solve for E.) Find the associated level of net benefits, or profit. (Plug your E^* into the NB function.)

Part (c) - (10 points)

Suppose the fishery is unregulated, open access. How much effort will commercial fishers exert? (Set the NB equal to zero and solve for E.) Do you think this level of harvest, repeated year after year, would cause problems for the future of the fishery?