econ 4 hw - Name Date last 4 PSU ID Economics 304WD...

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Name __________ __________ ___________ Date_________ last 4 PSU ID _______ Economics 304WD -- Homework - Lesson 4 – Consumption & Saving -- 110 points This HW assignment is very relevant to the Great Recession experienced in the US from December 2007 - June 2009. In particular, we experience a significant and negative wealth shock and map out how this effects the consumption decisions of households. We let the Fed 'come to the rescue' and lower real rates of interest to extremely low (and negative) levels, much like they did during the Great Recession! It is here that we can really see how and why consumers react differently to a change in real interest rates based on whether they are a saver or a borrower. The intuition is hopefully clear: the saver, Dagwood in what follows, is worse off due to the fall in real rates and Homer, our borrower, is better off due to the lower real rates. This homework also addresses the net (aggregate) effect on consumption in an economy that consists of both savers and borrowers (like economies do), and also considers the outcome if the borrowers become credit constrained, like many are given that so many mortgages are under water, much in line from the excerpt below ( Read the entire article ). We conclude by considering the idea that the Fed may be making matters worse with their zero interest rate policy. Edward Harrison at Credit Writedowns describes the Fed's zero interest rate policy as " toxic ," noting that it is a transfer from savers and fixed-income investors to borrowers. On net, this is stimulative if the spending propensities of the latter exceeds that of the former, but the willingness of the borrowers to spend is constrained by weak household balance sheets. The Fed is thus pushing on a string, and possibly even making matters worse by reducing the income flow to households. 1
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1. (30 points total – 5 points each part) Suppose we have Dagwood, who has a current income of $200K and expected future in- come of $100K. He has $100K in current wealth but this is before he opens that #[email protected]% envelope. He has zero expected future wealth. Dagwood’s behavior is consistent with the life-cycle theory of consumption. For one, he perfectly smooths consumption and two, since he is in his peak earning years; he is sav- ing now so that he can maintain his current level of consumption in the future. Given that Dagwood faces a real interest rate of 0.05, answer the following questions. a. Calculate Dagwood’s optimal consumption bundle showing all work. Note, for all C* calculations, round down to one decimal point. c* = c f * = 3
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b. Draw a completely labeled graph (the two-period consumption model) depicting this initial optimal consumption bundle and label it as point C* A . Be sure to label the no lending / no borrowing point = NL/NB. c. Now Dagwood can’t help himself and opens up that envelope and “ouch” he says, his current wealth has lost eighty percent (80%) of its value and thus falls from $100K to $20K. Recalculate Dagwood’s ‘new’ optimal consumption point and label on your graph as point C* B .
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