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 =
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.
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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