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 2 1 30 points total 5 points each part Suppose we have Dagwood who has a current income of 200K and expected future income of 100K He has 100K in current wealth but this is before he opens that 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 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 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 cf 3 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 c cf 4 d Is Dagwood worse off or better off Explain hint what has happened to his budget constraint aka opportunity set e The Fed decides to conduct massive amounts of open market purchases and get the real rate of interest all the way down to 05 negative 5 05 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 c c cf 5 f 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 c to part e 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 5 points each part 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 relative to consumption next period Homer s current income equals 150K and his future expected income 150K He has no wealth neither current nor expected Homer faces a real interest rate of 0 05 Please answer the following questions 6 a Calculate Homer s optimal consumption bundle showing all work c cf 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 7 Now Homer of course is not affected by the crashing market since he has no envelope to open c 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 As a result Homer revises his estimate of future income up to 200K 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 c cf d Is Homer worse off or better off Explain e The Fed decides to conduct massive amounts of open market purchases and get the real rate of interest all the way down to 5 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 c 8 c cf f 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 3 30 points total 5 points each part a What is the net effect of this expansionary monetary policy i e negative real rates of interest on consumption all else constant 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 consumption given this expansionary policy 9 Change in Dagwood s consumption Change in Homer s consumption Net change in consumption b 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 10 r 0 10 and not the ultra low negative real rate 05 that Dagwood who has a solid balance sheet …