Solution to HW1

Solution to HW1 - 0.575*C0. This implies C0 = 0.7246....

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Ec411 Money and Banking Fall 2011 Solution to HW1 Question 1 a) b) I would label the first security a bond and the second a stock (loosely). F=$500 is the face value of the bond and x is the profit before debt payments per bond issued. c) Expected payoff for the first security = 0.5*$500 + 0.5*$500 =$500 Expected payoff for the second security = 0.5*$6500+0.5*$100 = $3300 Min(x,500) x 500 Max(x-500,0) x 500
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Question 2 a) b) The constraints are C0=Y0=1 and C1=Y1=0.1. The total utility is ln(1) + 0.5*ln(0.1)=- -1.51. c) The budget constraint is C1= Y0(1+r) +Y1-C0(1+r). This is a negatively-sloped line with slope equal to –(1+r). It should look something like: C1 C0 (1.5,3.28) (2,1.84) (2.5,1.182) (4.0,0.46)
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d) If r=0.15 then the budget constraint is C1= 1*(1+0.15) +0.1-C0(1+0.15) or C1 = 1.25- 1.15*C0. We know that at the optimum Marginal Utility (C1)/Marginal Utility(C0) =1/(1+r). Then, 1/C0 = (1.15)*0.5*(1/C1) or C1 = 0.575*C0 or 1.25-1.15*C0 =
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Unformatted text preview: 0.575*C0. This implies C0 = 0.7246. Hence, the agent saves 0.2754 and lends in the financial market which affords her consumption tomorrow equal to 1.25-1.15*0.7246=0.41671. The total utility with a financial market is ln(0.7246)+0.5*ln(0.41671) = -0.7598, way higher than without a financial market. Graphically, C1 C0 Budget Line e) If interest rates drop to 0.1, the budget line is now C1 = 1*(1.10) +0.1-C0*1.1, so it sort of rotates, but more towards the C1 axis. Equating the ratio of marginal utilities to the slope of the budget line, we get that C0 = 0.727 and C1 = 0.4003. So our consumer saves a bit less with the lower interest rates, increasing her consumption today and decreasing it tomorrow. The following graph supposedly illustrates the two cases, but my powerpoint drawing abilities are not good enough to make it very clear. C1 C0 (1,0.1) (0.7246,0.4167) U FM =-0.7598 U NFM =-1.51 C1 C0 (0.7246,0.4167) (0.727,0.4003)...
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This note was uploaded on 11/20/2011 for the course ECON 420 taught by Professor Silous during the Spring '11 term at Emory.

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Solution to HW1 - 0.575*C0. This implies C0 = 0.7246....

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