Suppose we have Dagwood, who has a current income of $200K and expected future income of $60K. 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. 04, answer the following questions.
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. Note, for all C* calculations, round down to one decimal point.
b) Now Dagwood can't help himself and opens up that envelope and "ouch" he says, his "a" or current wealth has lost sixty percent (60%) of its value and thus falls from $50K 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?