Question

Question 6 10 pts Suppose that there are 15 units of a resource left and two periods remaining in history during which to use these units. Let the marginal net benefit from consuming the resource be given by 30-Q where Q is the amount of the resource consumed. If the discount rate is 50%, the marginal user cost is given by O 10+2Q/3 O 2Q/3 O 10Q/3 O 15+Q

Answer 1

Q 6. Benefit/Cost analysis weighs the benefits to the costs of a resource. Since benefits and costs may occur at different time periods, we convert future values to a present value for a common comparison. To compute the present value of a future benefit or cost, the future value is divided by (1+r)t, where r is the interest rate expressed as a decimal and t is the number of years until the benefit or cost is incurred.

When a resource produces streams of benefits and costs over time, it is dynamic, rather than static. In a dynamic setting, the economically efficient allocation maximizes the present value of net benefits. At this allocation, PV (marginal net benefits) are equal across time periods. If this was not true, it will not be possible to increase the present value of net benefits by reallocating consumption across time periods. Dynamic efficiency is illustrated for the two period case.
In this two period example, demand and PV are the same for both periods.

Suppose that there are 15 units of a resource left and two periods remaining in history during which to use these units. Let the marginal net benefit from consuming the resource be given by 30-Q where Q is the amount of the resource consumed. If the discount rate is 50%, the marginal user cost is given is

Demand: Marginal benefit (Total Benefit – (Price x Quantity)) = ?

Supply: Marginal Cost = ((Price x Quantity) – Total Cost)) = ?

Stock of resource = 15 units

Discount rate: r = 0.50

MNB1 = MB1 - MC1 = 30-Q

In a dynamic setting, the economically efficient allocation maximizes the present value of net benefits. At this allocation, PV (marginal net benefits) are equal across time periods. Optimal allocation is found by setting MNB0 = PVMNB1 and the resource amount constraint q 1 = 15 - q0. Substituting the resource constraint into the equilibrium conditions one obtains.

(1)The total marginal cost of the two resources have to be equal at the time of transition, otherwise net benefits could be increased by switching over to lower-cost resource. In period before transition, the first resource is cheaper. After transition it is exhausted.
(2)The components of the TMC that is growing (the marginal user cost) represents a smaller portion of the TMC of the second resource than of the first resource. in both cases the marginal user cost is increasing at rate r, and the marginal cost of
extraction is constant.

PV = (MNB) ₁ = ((MNB) ₂

PV = (MB - MC) ₁ = (MB - MC) ₂

30-Q = (MB = Total Benefit – (Price x Quantity) - MC = (Price x Quantity) – Total Cost)

30-Q = (D = 2 = 8 - 0.4) x 2 = 15/0.50

= 10+2Q/3