260AHomeworkProblems - 11/16/2011 260AHomeworkProblems...

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11/16/2011 260AHomeworkProblems 12:53 PM 1 Econ 260A Homework problems 1. Consider an economy populated by a representative consumer with utility function m R F U 2 1 2 1 , where F , R and m are consumption of food, recreation and a numeraire. F and R use water as the only input and are produced according to the production functions F W F and R W R , and the endowments of water and numeraire are 1 R F W W and respectively. a. Find the competitive equilibrium and consumer utility in a situation where there are markets for m and W F but not for W R and use F has the right to use the entire stock. That is, our representative consumer can use as much of the water as she wishes for F , up to the entire endowment. b. Find the representative consumer’s utility with complete markets. 2. A representative consumer’s utility function is b a w m bw aw U 2 for 2 and m b a U 4 2 otherwise, where w and m are consumption of groundwater and a numeraire. The consumer is endowed with units of numeraire. Extracting groundwater uses numeraire according to the cost function cDw C , where D is the depth of the aquifer. Extraction changes the depth according to R w D . The variables w , m , D are all functions of time; parameters a , b , c , R , , and r (the interest rate) are all positive. a. Find the steady state value of D that would result from maximizing the present value of utility. b. Find the steady state value of D that would result from independent extraction, where the representative consumer takes D as given, independent of her own actions. How would steady state utility be affected by a technological advance that cuts c in half? c. Imagine that a management agency attempts to implement the solution in part a. by creating ‘rights’ to water in the aquifer. Each user would receive a ‘water account’ with a pro rata share of water then in storage; a pro rata share of recharge would be credited (added) to each account and the user’s withdrawal would be deducted. Will this policy achieve the efficient outcome? 3.
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This note was uploaded on 12/26/2011 for the course ECON 260A taught by Professor Deacon during the Fall '10 term at UCSB.

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260AHomeworkProblems - 11/16/2011 260AHomeworkProblems...

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