Question

Environmental Economics Question:

Assume that there is a limited supply of coal. This coal will be
extracted over **two days**. The marginal benefit of
extracting coal in period t is as follows: **MBt =
10-Qt**

The marginal cost of extracting coal = 0. The **discount rate
is 25%**. The total quantity of coal is as follows:
**Q1+Q2= 10**

**Solve for the optimal quantity of coal to extract on
each day. And solve for the price of coal****each day.**

Thanks!

Answer #1

So, here the marginal benefit for each period is given by, “MB=10-q” and the “MC” is “0” for each period. So, the “PVNB” for period1 is given by.

=> PVNB1 = MB1-MC1 = 10-q1 and the same for period2 is given by.

=> PVNB2 = (MB2-MC2)/1.25 = (10-q2)/1.25. So, at the equilibrium “PVNB1” must be equal to “PVNB2”.

=> 10-q1 = (10-q2)/1.25, => 1.25*(10-q1) = 10-q2 = 10 -(10-q1) = 10 - 10 + q1 = q1.

=> 1.25*(10-q1) = q1, => 1.25*10 – 1.25q1 = q1, => 2.25*q1 = 12.5, => q1 = 12.5/2.25 = 5.56.

=> q1 = 5.56, => q2 = 10-q1 = 4.44, => q2 = 4.4, the quantity extraction in each periods are given by, “q1=5.56” and “q2=4.44”. Now, the corresponding prices in each period are given by.

=> P1=10-q1=4.4 and P2=10-q2 = 5.56.

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