Assignment 2Natural Resources

1. Consider two consecutive years, labelled 0 and 1. You are currently at the start of year 0. The following information is available. There is a single fixed stock of a non-renewable resource; the magnitude of this stock at the start of year 0 is 224 (million tonnes). The inverse resource demand functions for this resource in each of the years are:P0=a-bq0andP1=a-bq1,in which a = 107 and b = 1. The constant marginal cost of resource extraction is 5. The social welfare function is discounted utilitarian in form, with a social utility discount rate of 0.1.

(a)Given that the objective is to maximize social welfare over periods 0 and 1, calculate the amounts of resource that should be extracted in each period, subject to the restriction that at least 104 units of the resource should be left (unextracted) for the future at the end of period 1.

(b)What is the resource price in each period?

2.Consider a three-period model of nonrenewable resource extraction. Lay out the maximization problem in a way analogous to the two-period model, and determine the explicit expression for user cost.

3.Derive the condition for the optimal rotation when a forest also provides species habitat services.

4.What types of benefits and costs are involved when forests that were previously open to commercial forestry are now placed in preservation status?

5.What would the biological growth curve look like if a critical stock size exists below which growth rates become negative and the stock evolves to zero?

6.What would be the efficiency implications of granting a fishery to one individual as a sole owner?

7.Why is there a difference between the maximum sustained yield and the economically efficient sustained yield?