Groundwater needs to be allocated between two periods, knowing that it will be totally used up in period two.

The marginal benefit from consuming water is

            MB = 200 – 2Q

and is the same for both periods.

The marginal extraction cost (MEC) = 20 and is the same in both periods.

The total available water supply is 140 units, and the discount rate is 20%.

a. What is the equation for net marginal benefits (NMB) is year 1?

b. If, in year one, NMB = 0, how much water would be purchased? if the quantity = 0, how much is the NMB? if all 140 units of water are purchased, how much is NMB?

c. Graph this two-period extraction problem, remembering to “discount” the equation for NMB in year 2. Label your graph completely.

d. What is the optimal allocation of water between the two years? Show all of your work and label these amounts on your graph.

e. If the discount rate rises, what do you think will happen to your answers in part (d)? (you do not need to use actual numbers, but talk about what happens when discount rates rise)