The town of Dusty View, Saskatchewan has only two residents - Justin and Sarah - and has a water supply shortage in the summer. The municipal water utility charges a break even price of $100 per unit of water but the system capacity is limited to 500 units. Justin and Sarah's marginal utility functions for water in the summer are as follows:
MU(Justin) = 1600 - 4W
MU(Sarah) = 1200 - 4W
a) Determine the demand functions for Justin and Sarah and the total demand for water in Dusty View. Show that there will be a summer water shortage.
b) Suppose the town decides to increase the price of water until there is no excess demand. Calculate the new price and the gains from trade (individual consumer surpluses and town profit) resulting from this decision.
c) Now suppose the town decides against using price to ration water and instead allocates the water fairly between Sarah and Justin - 250 units each - and reverts to charging $100 per unit. Assume resale between Sarah and Justin is impossible. Calculate the gains from trade in this case. Why is it better/worse than the solution in b)?
d) Now suppose resale is possible under the 250 unit per person allocation plan. What will be the final result? How does it compare with the result in b)?