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Unformatted text preview: The difference is due to the fact that the above solution is an approximation to the actual change in r. 3. The Euler condition for this problem is u&(c 1 ) = 1/2[E[u&(c 2 )]], or since utility is quadratic and so marginal utility is linear: u&(c 1 ) = 1/2[u&(E[c 2 ])]. Thus, 24  2c 1 = [24  2E[c 2 ]] ] 24  2c 1 = 12  E[c 2 ] (1) r = 0 Y c 1 + c 2 = y 1 + y 2 Y c 1 + E[c 2 ] = y 1 + E[y 2 ] y 2 ~ U[3,9] Y E[y 2 ] = 6 Y c 1 + E[c 2 ] = 12 Y E[c 2 ] = 12  c 1 (2) Substituting (2) into (1) yields: 24  2c 1 = 12  (12  c 1 ) = c 1 Y c 1 = 8. 4. There are 3 strategies conditional on owning the plot of land: One can harvest every year, every two years or every three years. Let V i denote that value of harvesting after the ith year. Ophelia should be willing to buy the land for at most V = max{V 1 ,V 2, V 3 }. V 1 = 10/2 + V 1 /2 Y V 1 = 10 V 2 = 36/4 + V 2 /2 Y V 2 = 12 V 3 = 77/8 + V 3 /8 Y V 3 = 11 Hence V = 12....
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 Fall '07
 AKERLOF

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