Fossil aquifer use

Consider allocating 100 units of aquifer water between two periods. To make things a bit different, let the two periods be generations. You are given the following facts:

1. The MB of a unit of water in each period is $500.
   
2. Marginal costs in each period are given by: MCi=4Qi, where MCi and Qi are the marginal cost and quantity in period i.
   
3. Used water is gone and does not return to the aquifer.
   
4. The interest rate is 100% (one hundred percent).
   

The interest rate is large because the two generations are many years apart.

1. Find the efficient allocation of water. Show your work. If the government wanted to allocate the water by selling it, how much should it charge?
   
2. Suppose someone else proposed splitting the water evenly. Use an appropriate diagram to show what problem this would cause and explain it in words. Calculate the size of the problem.