Lesson 4 Dagwood Homer Problem Worksheet Suppose we have Dagwood who has a current income of 150K and expected future income of 40K He has 50K in current wealth i e a 50K 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 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 05 answer the following questions Step 1 Calculating the Saver s Optimal Consumption Bundles See Lecture 8 The Dagwood Example The Numbers Lecture 9 The Dagwood Example The Graph A 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 Be sure to label the no lending no borrowing point NL NB B Now Dagwood can t help himself and opens up that envelope and ouch he says his a or current wealth has lost eighty percent 80 of its value and thus falls from 50K to 10K 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 C 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 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 B D 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 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 c f 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 a real interest rate of 0 05 Please answer the following questions Step 2 Calculating the Borrower s Optimal Consumption Bundles See Lecture 10 The Homer Example Modeling Non smoothing Preferences Lecture 11 The Homer Example The Numbers Lecture 12 The Homer Example The Graphs A 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 Be sure to label the no lending no borrowing point NL NB Now Homer of course is not affected by the crashing market since he has no envelope to open B 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 y f 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 Is Homer worse off or better off Explain hint what has happened to his budget constraint aka opportunity set C 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 05 negative 5 05 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 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 here Be sure to define what the income and substitution effects are and how they play a role in Homer 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 In this question we are 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 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 Step 3 Deriving the Savings Function See Lecture 13 Homer and Dagwood The Savings Graph A Using the results from 1B and 1C where a 10K 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 Be sure put all the relevant shift variables in brackets next to the Sd 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 B Using the results from 2B and 2C where yf 200K derive the desired savings function for Homer labeling the point from 2B 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 Be sure put all the relevant shift variables in brackets next to the …