26 Jul WHAT WOULD BE THE MARKET PRICE OF WATER IN THIS MARKET?
Question 3 There are two farmers whose farms are located along a canal that is fed water from a rive Show more Question 3 There are two farmers whose farms are located along a canal that is fed water from a river. Farmer Johns land is close to the mouth of the canal while Farmer Annes land is downstream from Farmer John. A fixed 100 acre-feet of water flow into the canal every day. Farmers John and Anne both produce tomatoes which they can sell on the market for $1 per unit. The production of both farmers depends on the amount of water they use (WA and WJ respectively both in units of acre-feet of water) and the amount of land they choose to farm (LA and LJ respectively in square meters of land and unconstrained). Their production depends on these two inputs in the following way Q = 120W -W^2 +WL Every additional square meter of land used is an increasing distance away from the farmers access point to the canal. Therefore there is an additional cost of transporting the water needed to farm each addition square meter of land (fixed regardless of the amount of water) of L. Finally there is a fixed cost of farming of 900. All put together this means that the profit for each farmer is = 120W -W^2 +WL-L-900 Initially there is no control on the water use in the canal (first come first served) no cost of removing water from the canal and trading is not allowed. (a) How much water and land would each farmer use how much output would they each produce and how much profit would they each make? (b) A Water Users Association is established for this canal that is tasked with maximizing the social net welfare of water used from the canal. If the Water Users Association is allowed to allocation water how much would they allocate to each farmer? How much land would each farmer use as a result and how much quantity would they each produce? (c) The Water Users Association is made up of the farmers who use water from the canal along with some additional members from the local government. Farmer John has a lot of influence. He makes the argument that the Water Users Association really shouldnt be dictating the amount of water each farmer should use and instead should set up a water market and allow trading of water between the farmers (assume zero transaction and transportation costs). They agree with him and set up such a market. What would be the market price of water in this market? (HINT: recall what you learned about the price of a permit in a cap and trade market and how it relates to the value of the constraint). Who would sell the water who would buy the water and how much would they trade between them? (d) Is the outcome in part (c) welfare maximizing (recall that welfare here is A +B)? Is the allocation of welfare in part (c) more or less equitable than in part (b)? Show less
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