f07_ass2 - GS/ECON 5300 F2007 Assignment 2 due Wed November...

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GS/ECON 5300 F2007 Assignment 2 due : Wed. November 14 before class do all 5 questions : all count equally 1. Find all the Pareto optimal allocations in the following 2–person, 2–good economy, in which good X is a pure private good and good Z is a pure public good. The production possibility frontier for the economy has the equation 2 X + Z = 270 where X and Z are the aggregate quantities produced of the pure private good and of the pure public good, respectively. There are 2 people : person 1’s preferences can be represented by the utility function U 1 ( x 1 , z 1 ) = 2 ln x 1 + ln z 1 and person 2’s by the utility function U 2 ( x 2 , z 2 ) = ln x 2 + 2 ln z 2 where x h and z h are person h ’s consumption of the pure private good and pure public good respectively. 2. Suppose that there are only two people in a country. Person 1’s preferences can be repre- sented by the utility function U 1 ( x 1 , z 1 ) = x 1 + Az 1 - 1 2 α ( z 1 ) 2 and person 2’s by the utility function U 2 ( x 2 , z 2 ) = x 2 + Az 2 - 1 2 β ( z 2 ) 2 where x h and z h
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