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Unformatted text preview: Economics 202A Final Exam Answers Fall Semester 2007 1.(a) The Hamiltonian for this problem is H = u ( c ) + & ( y + ra & c ) : The &rstorder conditions are @H @c = u ( c ) & & = 0 ; _ & = & & @H @a = & ( & r ) : 0 = lim t !1 e & &t & ( t ) a ( t ) : (b) Since now u ( c ) = c & 1 = ; we can write the last equation as u 00 ( c )_ c = u ( c ) ( & r ) ; or as _ c c = & u ( c ) cu 00 ( c ) ( & r ) = ( r & ) : (c) We need to solve the equation a (0) = Z 1 h c (0)e ( r & & ) t & y i e & rt d t for the initial (optimal) consumption level, c (0) : The solution is c (0) = a (0) + ( y=r ) R 1 [e ( r & & ) t ] e & rt d t = a (0) + ( y=r ) R 1 e ( r & & ) t & rt d t = a (0) + ( y=r ) [ ( r & ) & r ] & 1 n e [ ( r & & ) & r ] t j 1 o = [ & ( & 1) r ] [ a (0) + ( y=r )] : The assumption that ( & 1) r & = ( r & ) & r < 0 ensures that above, lim t !1 e [ ( r & & ) & r ] t = 0. (d) Looking at the preceding consumption function, we see the three ways a rise in the interest rate r will aect saving: 1 1. The marginal propensity to consume out of total wealth is & & ( & & 1) r: When r rises, that coe&cient falls with an eect proportional to & . This is the substitution eect....
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This note was uploaded on 08/01/2008 for the course ECON 202A taught by Professor Akerlof during the Fall '07 term at University of California, Berkeley.
 Fall '07
 AKERLOF
 Economics

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