Question

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

M B = 159 − 2.1 Q a n d M C = 36 + 0.9 Q

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

What is the Optimal barrels of oil that should be extracted in the current period (suppose we don’t need to be concerned with any future periods)

2) Now, 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?

3) Again, assume that society needs to allocate the reserve across the current and future period (2 periods, 5 years each), but now the discount rate is 6.5%

4) What is the socially efficient quantity for period 1?

5) What is the socially efficient quantity for period 2?

6) Suppose new oil reserve is discovered, now the total oil reserve is 100 tons. What will be the new socially efficient quantity for period 1?

7) Continue assuming total reserve is 100 tons. Based on your answer from last question, what is the total user cost incurred from period 1?

(Hint: did period 1's decision affect period 2?)

Answer 1

1) we will produce upto the level at which-

MB=MC

So, 159-2.1Q= 36+0.9Q

123= 3Q,. Q= 41.

It is the optimal quantity that needs to be produced.