ECON 304 Questions(3 Questions)

ECON 304 Questions

Economics 304

Homework #3 – Dagwood and Homer and the Savings Function

Due Wednesday, 9/23 at the beginning of class – you must hand in homework in the section you are registered in – no late papers accepted!

Instructions: Please show all work or points will be taken off. Good luck!

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.

2. (30 points total) Dagwood’s neighbor, Homer Simpson, does not abide by the life cycle theory of consumption. Homer has a “let’s live life like it’s our last day” mentality and thus, he prefers to consume more today, relative to the future. In particular, Homer prefers to consume exactly twice as much today (c), relative to consumption next period (cf). Homer’s current income equals $150K and his future expected income = $150K. He has no wealth (neither current nor expected) since he lives like today is his last! Homer faces an initial real interest rate of 0.04, just like our friend Dagwood. Please answer the following questions.

a) (5 points) Solve for Homer’s optimal consumption basket today (C*) and his optimal consumption basket next period (Cf*). Please provide a completely labeled graph depicting these results and label this point as C*A.

(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)

Now Homer, of course, is not affected by the crashing market since he has no envelope to open!

b) (5 points) Homer goes to work and the rumor being spread around the work place is that future demand is increasing as Homer works in the ‘green energy’ field and business (grants, etc) has never been better. As a result, Homer revises his estimate of future income (yf) up to $250K (his current income is not effected). Recalculate the optimal bundle for Homer and add this point to your graph and label as point C*B. Is Homer 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 and the Fed and they conduct massive amounts of open market purchases and get the real rate of interest all the way down to – .04 (negative 4%). Recalculate the optimal bundle for Homer and add this point to your graph and label as point C*C. (Note, point C*C incorporates the shock to Homer’s future income in part b)).

d) (5 points) Is Homer 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 in Homer’s consumption decisions. 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.

3. a) (30 points total) (5 points) What is the net effect of this expansionary monetary policy (i.e., negative real rates of interest) on consumption, all else constant (this is after the shock to Dagwood’s wealth (a) and Homer’s expected income (ye))? To answer this question, assume we have an equal amount of “Dagwoods” and “Homers” so we can simply add the change in Dagwood’s consumption to the change in Homer’s consumption. Please give the actual change in aggregate consumption, given this expansionary policy.

b) (5 points) Now consider the case where Homer is credit constrained and thus, cannot qualify for cheap loans since his balance sheet is a wreck. As such, the real rate of interest that Homer faces is 08% (r = 0.08), and not the ultra low negative real rate = -.04 that Dagwood (who has a solid balance sheet) faces. Please re-answer part a) above, assuming that Homer faces a real rate of 0.08 and Dagwood faces a real rate of (-.04). Use the actual numbers, that is, add the change in Dagwood’s consumption (you already did this in 3a)) to the change in Homer’s consumption, given that he faces a real rate of 0.08, all else constant. Are your results consistent with this pic (click Here)? Why or why not?

c) (5 points) Are your results in b) consistent with this passage, why or why not?

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.

write your answer to part c) here.

We are now going to derive and draw (depict) two desired savings functions for Homer and Dagwood respectively. Note importantly that savings in the present context is defined simply as y-c, that is, current income minus current consumption (these are both “flow” variables). Note also that savings can be positive or negative, it depends on whether you are a saver or borrower. In this assignment, Homer is the borrower so his savings is negative where Dagwood is the saver, and thus, his savings are positive. To derive a savings function we let real interest rates vary and map out the corresponding change in desired savings, all else constant.

c) Using the results from 1 b) and 1 c), where a = $20K, derive the desired savings function (for Dagwood) labeling the point from 1b) as point A and the results from 1c) as point B. Connect the points and we have the savings function for Dagwood. Make sure you put in parentheses next to the savings function what we are holding constant and show your work.

(5 points for a completely labeled graph – be sure put all the relevant shift variables in brackets next to the Sd as we did in class)

We now move on to the results for Homer. We are going to do the exact same exercise that we did for Dagwood. Note that since Homer is a borrower, his savings is negative and thus, all points in the diagram will be left of the origin.

d) Using only the results from 2b) and 2c), where yf = $250K, derive the desired savings function (for Homer) labeling the point from 2 b) as point A and the point from 2c) as point B. Connect the points and we have the savings function for Homer. Make sure you put in parentheses next to the savings function what we are holding constant.

5 points for a completely labeled graph – be sure put all the relevant shift variables in brackets next to the Sd as we did in class and please show your work.

e) (5 points) . Suppose you were Ben Bernanke’s cousin and was head of the central bank in an economy filled with Dagwoods (savers). Suppose also that your economy was in a recession and you wanted to stimulate consumption today in pursuit of your dual mandate (try to get the economy to grow at potential, achieve NAIRU). Suppose the current real rate of interest is zero. Would you raise or lower real interest rates to stimulate consumption? Explain in detail using the substitution and income effects.