Assume the city of Tucson, Arizona, has an average annual streamflow of 75,000 acre-feet of surface water, plus a total non-renewable stock of 30 million acre-feet of groundwater.  The city is experience rapid growth and worsening water shortages.  The economist Vernon Smith has suggested that the city should allocate water deeds to the 80,000 acre-feet of annual surface water, and separate deeds to the 20,000,000 acre-feet of groundwater in the aquifer underlying the city, to each of the 400,000 households and firms located in the Tucson water district. The average household would own a share of the replenishable surface flow averaging 0.20 acre-feet per year (but less in drought years), plus 50 acre-feet of non-replenishable groundwater.  Households would pay the utility for the pumping and delivery of their water.

Both types of water deed would be freely divisible and marketable, probably through a water bank administered by Tucson's water utility.  New households moving into the area would have to buy water deeds from existing households through the water bank.  In theory at least, water consumption in Tucson would then have an explicit opportunity cost, and water would eventually be bid away from low-valued uses toward high-valued uses.  Your assignment is to explain how this market for water rights would work.

1. Calculate how many cubic feet are in an acre-foot (one acre flooded one foot deep).
2. Suppose households currently consume an average of 0.50 acre-feet annually.  Under the water banking system, any consumption above the 0.20 acre-feet surface allocation would be deducted from their groundwater allocation.  Explain how rational households would use their groundwater allocations (assume the demand choke price for water is finite). 
   
3. How would the market price for 0.001 acre-feet of groundwater (used once) compare with the market price for 0.001 acre-feet of annual surface water (available every year)?
4. Groundwater delivery (pumping) costs increase exponentially as groundwater levels fall. Users who use their groundwater allocations early increase future pumping costs for users who conserve more and use their groundwater allocations more slowly. Over time, this externality reduces the market value of groundwater deeds, and may actually discourage conservation. Should this externality be corrected? If so, what policy would you recommend to correct it?
5. Since the volume of annual surface flow is uncertain, the city would really be allocating percent shares of the total annual steramflow among users.  Suppose climate change increases annual variability of streamflow, although the mean annual streamflow remains the same.  How would this increased uncertainty affect rational water use under this plan?
   
6. Here's a no-brainer: suppose the city announced that it would implement such a plan two years from now, deeding shares to residents based on their water consumption levels this year and next year. What do you think would happen?