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* =

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* =

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* =

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.