Questions: Consider a nonrenewable resource that can be consumed either today (period 1) or tomorrow (period 2) and has a finite supply of 10 units. Assume the inverse demand for the resource in both periods is: P1=100-5Q1 P2=100-5Q2 Assume the marginal cost of extracting the resource is constant at 20 and the social discount rate is 10 percent (r= .10). What is the efficiency condition? Select all that apply. a. MSR1 = MSR2/(1+r) b. MNB1 = MNB2/(1+r) c. NB1 = NB2 d. MNB1 = MNB2

Consider a nonrenewable resource that can be consumed either today (period 1) or tomorrow (period 2) and has a finite supply of 10 units. Assume the inverse demand for the resource in both periods is:
P1=100-5Q1
P2=100-5Q2

Assume the marginal cost of extracting the resource is constant at 20 and the social discount rate is 10 percent (r= .10).
What is the efficiency condition? Select all that apply.
a. MSR1 = MSR2/(1+r)
b. MNB1 = MNB2/(1+r)
c. NB1 = NB2
d. MNB1 = MNB2

Transcript text: Consider a nonrenewable resource that can be consumed either today (period 1) or tomorrow (period 2) and has a finite supply of 10 units. Assume the inverse demand for the resource in both periods is: \[ \begin{array}{l} P \_1=100-5 Q_{-} 1 \\ P_{-} 2=100-5 Q_{-} 2 \end{array} \] Assume the marginal cost of extracting the resource is constant at $\$ 20$ and the social discount rate is 10 percent $(r=$ $.10)$. What is the efficiency condition? Select all that apply. a. MSR_1 = MSR_2/(1+r) b. MNB_1 = MNB_2/(1+r) c. NB_1 = NB_2 d. MNB_1 = MNB_2

Solution

To determine the efficiency condition for the consumption of a nonrenewable resource over two periods, we need to consider the marginal net benefits (MNB) in each period and how they relate to the social discount rate.

The marginal net benefit (MNB) is the difference between the price (P) and the marginal cost (MC) of extracting the resource. Given the inverse demand functions and the constant marginal cost, the MNB for each period can be expressed as:

MNB_1 = P_1 - MC = (100 - 5Q_1) - 20
MNB_2 = P_2 - MC = (100 - 5Q_2) - 20

The efficiency condition for allocating a nonrenewable resource over time is that the present value of the marginal net benefits should be equal across periods. This is because the resource should be allocated in such a way that the discounted marginal net benefits are equalized, reflecting the opportunity cost of consuming the resource today versus tomorrow.

Given the social discount rate $ r = 0.10 $, the efficiency condition is:

\[ MNB_1 = \frac{MNB_2}{1 + r} \]

This condition ensures that the allocation of the resource maximizes the present value of net benefits over the two periods.

Now, let's evaluate the options:

a. MSR_1 = MSR_2/(1+r)

This option refers to marginal social rates, which are not directly relevant to the problem of allocating a nonrenewable resource over time based on marginal net benefits. Therefore, this is not the correct efficiency condition.

b. MNB_1 = MNB_2/(1+r)

This is the correct efficiency condition, as it states that the marginal net benefit in period 1 should equal the discounted marginal net benefit in period 2.

c. NB_1 = NB_2

This option suggests that the net benefits (total, not marginal) should be equal across periods, which is not the correct efficiency condition for resource allocation over time.

d. MNB_1 = MNB_2

This option suggests that the marginal net benefits should be equal without considering the discount rate, which is incorrect for intertemporal allocation.

In summary, the correct efficiency condition is:

The answer is b: MNB_1 = MNB_2/(1+r)

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