This HW assignment is very relevant to the Great Recession experienced in the US

Question

This HW assignment is very relevant to the Great Recession experienced in the US from December 1997 - June 1999. 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 (Click Here for 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. (30 points total). Suppose we have Dagwood, who has a current income of $350K and expected future income of $100K. He has $ 80K in current wealth (i.e., ‘a’ = $80K), but this is before he opens that #$@% envelope. He has $20K expected future wealth (i.e., af = $20K).

Dagwood’s behavior is consistent with the life-cycle theory of consumption. For one, he perfectly smoothes consumption and two, since he is in his peak earning years, he is saving now so that he can maintain his current level of consumption in the future. Given that Dagwood faces a real interest rate of 0. 04, answer the following questions.

a) (5 points) Calculate Dagwood’s optimal consumption bundle showing all work. Then draw a completely labeled graph (the two period consumption model) depicting this initial optimal consumption bundle as point C*A (please use the space below). Note, for all C* calculations, round down to one decimal point.

(10 points for a completely labeled graph – be sure to label the no lending / no borrowing point = NL/NB and the slope of each budget constraint)

b) (5 points) Now Dagwood can’t help himself and opens up that envelope and “hallp" he says, his “a” or current wealth has lost seventy five percent (75%) of its value and thus falls from $80K to $20K. Recalculate Dagwood’s ‘new’ optimal consumption point and label on your graph as point C*B. Is Dagwood worse off or better off? Explain (hint, what has happened to his budget constraint (aka opportunity set)).

THE FED TO THE RESCUE!

c) (5 points) In steps Ben Bernanke (he was chair of the Fed when the Great Recession hit the US economy in 2008) and with the agreement of the FOMC (Federal Open Market Committee), the Fed conducts massive amounts of open market purchases and get the real rate of interest all the way down to - .04 (negative 4% = -.04). Recalculate the optimal bundle for Dagwood and add this point to your graph and label as point C*C. (Note, point C*C incorporates the shock to wealth in part b))

d) (5 points) Is Dagwood better or worse off due to the fall in the real rate of interest? Explain being sure to discuss exactly how the substitution and income effects play a role here. Be sure to define what the income and substitution effects are and how they play a role in Dagwood’s decision to alter his previously optimal bundle (we are comparing part b) to part c)). Also, comment on whether these income and substitution effects work in the same or opposite direction (i.e., is it a tug of war or do they work in the same direction?) in this particular case.

Explanation / Answer

a) Present income + future income /2 = consumption

(350 + 100 +100) /2 = $275K = C*A

b) (350 + 100+20+20)/2 = $245K = C*B

He is definitely worse off with this reduced consumption. His budget constraint line will pivot inside.

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