Consider the allocation of a depletable resource over two periods. There are Qba
ID: 1168715 • Letter: C
Question
Consider the allocation of a depletable resource over two periods. There are Qbar=4 units of the stock available. The total benefits derived from using the resource are defined as TBt= 20qt- (1/2qt^2) and the total cost of extracting the resource is defined as TCt=5qt
What are the values of q0 and q1 that maximize the net benefits of using the resource if the discount rate is 10%? What if the discount rate is 5%?
Now suppose there are Qbar = 30 units of the stock available. How do the answers to part (a) change? What is your intuition?
What is the shadow price in period zero?
Explanation / Answer
Solution :
Total benefits = 20Qt - ( 1/2 Qt2 )
Total costs = 5 Qt
Marginal Benefit = 20 - 1/2 X 2 Qt
Marginal cost = 5
Net benefit is maximized when the marginal benefit is equal to the marginal cost
20 - 1/2 X 2 Qt = 5
20 -5 = Qt
Qt = 15 units
The value of Q0 and Q1 that maximize the net benefits of using the resource is 15 units .
If Qbar = 30 units of the stock available then more units of stock is available .