ECON 704 Midterm: Prelim2016B_704_Cole
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For the (cid:133)rst t =2 periods (yes t is even) a household(cid:146)s current productivity level (cid:18)t and its labor e ort lt are private informa- tion, and only it(cid:146)s output yt is public information. During the remaining t =2 periods, the household(cid:146)s output level yt and productivity (cid:18)t is publicly observable. An allocation includes mappings (consumption) ct((cid:18)t ) and (output) yt((cid:18)t ); which map to r+ and are measurable w. r. t. (cid:18)t (and hence cannot depend upon the future). The output requirement implies the household(cid:146)s labor e ort is yt((cid:18)t )=(cid:18)t: all households have the same preferences and their payo , given this notation, is. E( txt=0 (cid:12) t(cid:2)u(ct((cid:18)t )) (cid:0) v(yt((cid:18)t )=(cid:18)t((cid:18)t ))(cid:3)) This is a small open economy which can borrow and lend at gross interest rate r: so the economy faces the budget constraint. Give some intuition for your answer: sketch how you would prove your claim(s) in part e.
