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mid_ans_F02 - p 1 = e 1 λθ − 1 ∆ m 1(d Thus the...

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Midterm Exam’s Answer Key University of California at Berkeley Econ 202A, Macro Theory Fall 2002 George Akerlof, Andrea De Michelis October 29, 2002 1. Shapiro-Stiglitz The investor solves: ( p H = 10 + 1 / 2 1 . 25 p L + 1 / 2 1 . 25 p H p L = 0 + 1 / 4 1 . 25 p H + 3 / 4 1 . 25 p L The solution is: p H = 25 . 0 , p L = 12 . 5 . Thus, a risk neutral investor is willing to pay no more than $25. Note: if one assumes that fundamental asset equation is of the form interest rate time asset value equals fl ow bene fi ts plus expected (not discounted) capital gains, then p H is $20. 2. Near-rationality (a) p 0 = arg max p p ( m 0 p p ) p 0 = p 0 = m 0 since in equilibrium p p . (b) p 1 = arg max p p ( m 1 p p 0 ) = arg max p p ( m 0 + ε p m 0 ) p 1 = m 0 (1 + . 5 ε ) Thus, by not reoptimizing the fi rm looses p 1 q 1 ( p 1 ) p 0 q 1 ( p 0 ) = . 25 ε 2 m 2 0 (c) Yes, it is near-rational because the loss is of an order of magnitude smaller than the shock. 3. Exchange Rates (a) Using the LM equation: p 0 = m 0 φ y + λ r . (b) Thus, p 1 = m 1 φ y + λ r = p 0 + m 1 . (c) Recall that in equilibrium: e t e = ( λθ ) 1 ( p t p ) . Thus, e 0 = e 1 ( λθ ) 1 ( p
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Unformatted text preview: p 1 ) = e 1 + ( λθ ) − 1 ∆ m 1 . (d) Thus, the exchange has to overshoot by: e − e 1 = ( λθ ) − 1 ∆ m 1 . 4. Consumption The Euler condition for the problem is: u ( c t ) = E t u ( c t +1 ) , or since utility is quadratic and so marginal utility is linear: u ( c t ) = u ( E t c t +1 ) . (a) Thus, 1 − ac 1 = 1 − bE 1 c 2 = 1 − dE 1 c 3 , or E 1 c 2 = a b c 1 and E 1 c 3 = a d c 1 . When she plans consumption in period 1, her expected income is 3 Y , she sets c 1 so that c 1 + a b c 1 + a d c 1 = 3 Y ⇒ c ∗ 1 = 3 bd bd + ab + ad Y . (b) When she plans consumption in period 2, her expected income is 3 Y + ε 1 − c 1 , she sets c 2 so that c 2 + b d c ∗ 1 = 3 Y + ε 1 − c ∗ 1 ⇒ c ∗ 2 = 3 ad bd + ab + ad Y + d d + b ε 1 . 1...
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