Question

Suppose the Marginal Benefit and Marginal Cost for crude oil at any given period is:   

MB=159−2.1QandMC=36+0.9Q

Where price is measured in dollars and quantity is measured in barrels. The total oil reserve is 50 tons.

assume that society needs to allocate the reserve across the current and future period(2 periods,5 years each)

suppose the discount rate is zero what is the socially efficient quantity for period 1?

Answer 1

We can see that marginal benefit is a downward sloping curve and MC is increasing. So, when MC=MB, that will be the optimal output. But here we have 2 periods but the discount rate is 0, so he values each period equally at present. From this, we can say consumption will be same across both periods and it should be 50/2 =25

For no-constrain, optimal quantity is -

159-2.1Q = 36+0.9Q

123 = 3Q

Q=41

Since 25<41, it is acceptable, thus the optimal quantity for the first period is 25.