You should be prepared to present or help work out the answers to these questions. Please bring a calculator with you to class.
A) Present Value
The social discount rate is the rate of exchange society uses for comparing the values of goods and services received in two different periods. It is the return on a riskless investment.
1) If the discount rate is 10%,
| a) what will be the value next year of $200 invested this year? | |
| b) what will be the value two years from now of $200 invested this year? | |
| c) what will be the value now of $200 received next year? | |
2) If the social discount rate is 5%, would society rather have goods valued at $100 now or $110 two years from now?
B) Marginal User Cost -- without discounting
Consumption of a scarce depletable good (e.g., a good in fixed supply) imposes costs (in terms of foregone consumption) above production or extraction costs.
In the stylized example in the reading, the world possesses 20 units of a resource that can be extracted at constant marginal cost $2.00 in period 1 or 2. Marginal social willingness to pay in each period is P = 8 - 0.4q.
1) Confirm that static efficiency applied in either period (ignoring the other) dictates q = 15.
2) But, if society consumes 15 units in period 1,
| a) compare the social value (marginal willingness to pay) of the last unit consumed in period 2 with that in period 1. | |
| b) compute the marginal user costs (the difference between marginal willingness to pay and marginal extraction cost) of these last units consumed. | |
| c) Compute the net social benefits of this allocation of resources between the two period, i.e., the area between the demand and marginal extraction cost curves. | |
3) Marginal net benefit (MNB) equals the difference between willingness to pay and marginal extraction costs. Superimpose period 2 MNB on the graph of period 1 MNB using distance from the right vertical axis as a measure of period 2 quantity demanded. (The graph will differ slightly from Figure 5.2 because there is no discounting.)
| a) Graphically determine the efficient allocation of the good between the two periods and the marginal user cost in each period. | |
| b) Confirm the graphical result by equating MNB in the two periods, i.e., set MNB1 = 8 - 0.4q1 - 2 to MNB2 = 8 - 0.4(20-q1) - 2 and solving for first period quantity and MNB. | |
| c) Compute the net social benefits of this allocation of resources between the two period, i.e., the area between the demand and marginal extraction cost curves and compare it with that computed in (2c) above. | |
4) The MNB you found for each period in (3) is the dynamically efficient marginal user cost in that adding it to marginal extraction costs maximizes the net social benefits of consumption in the two periods. How might this user cost be imposed in practice?
C) Dynamic Efficiency – with discounting.
Use the same facts as in (B), but now assume a 10% discount rate for period 2 consumption. The present value of the marginal net benefit of period 2 consumption is (8 - .4q - 2)/(1 + .1).
1) Compute the vertical and horizontal intercepts for this new MNB curve and superimpose it on a new version of the graph.
2) Compare the dynamically efficient allocation of the good between periods and marginal user cost for this case with the case with no discounting.
3) Show graphically that any other allocation would reduce the net social benefit from consumption.
4) What happens to the dynamically efficient inter-period allocation of goods and marginal user cost as the discount rate rises?
5) Suppose the marginal extraction cost rose to $4.00 in each period. Find the dynamically efficient allocation and marginal user cost.
6) Return to the conditions of (C1). What happens to the dynamically efficient inter-period allocation of goods and marginal user cost as the marginal extraction cost in period 2 falls? (Drawing the graph again may help.)
1) Explain Rawls’ "veil of ignorance" as a principle of justice.
2) What, in its most basic form, is the sustainability criterion?
3) Show that the allocation you derived in (B) is sustainable.
4) Figure 5.3 provides the allocation and prices (in current dollars) of the allocation you found graphically in (C2). Show that his allocation is not sustainable.
5) Explain how society could make this dynamically efficient allocation sustainable.
6) Explain the alternative versions of the sustainability criterion that have been proposed to address the problem of substituting physical for natural capital.
7) To which version would you subscribe if you rejected anthropocentric value systems.
8) Tietenberg believes that the frequency of inefficient allocations encountered in practice creates a special opportunity for moving to sustainable allocations. Explain.