Problem
Happy Days are here again. In this problem we re-visit Dagwood and Homer but this time, Dagwood cannot wait to open up that envelope and Homer, meanwhile, wishes he had one to open.....we are in the midst of a giant stock market rally!!!!
Let's begin with Dagwood's numbers. Dagwood's current income is $130K and expected income next period is $60K. Dagwood has current wealth equal to $30K before he opens up the envelope. Note that Dagwood, just like in the practice problem, prefers to perfectly smooth consumption across the two periods. Dagwood faces a real interest rate of 0.02 (2%) since Ben and the Fed have been pretty easy with the money supply fighting the recession.
1. Calculate Dagwood's optimal consumption bundle showing all work. Then draw a completely labeled graph depicting this initial optimal consumption bundle as point C*A.
2. The envelope comes in the mail and Dagwood is psyched, he is tired of his wealth disappearing. He opens up the envelope and finds that his wealth had risen by 50% to $45K (from $30K) and instead of yelling ouch like before, he yells yee-haw! Recalculate Dagwood's optimal consumption point and label on your graph as point C*B.
Now Bernanke, finally having something to smile about, decides to get interest rates back up to 'normal' levels, as he is very concerned about inflation. As such, Ben and the Fed get the real rate up to 0.06 (6%).
3. Re-calculate Dagwood's optimal consumption bundle given the change in the real rate of interest and label this third optimal point as C*C .
4. Is Dagwood better or worse off due to the increase 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. 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.
Let's move onto Homer. Homer's current income is $100K and expected income is $120K. He has no current or expected wealth and is definitely not into smoothing consumption. Homer prefers to consume twice as much this period relative to next period. He faces the same initial real rate that Dagwood faces.
5. Calculate Homer's optimal consumption point showing all work. Then draw a completely labeled graph depicting this initial optimal consumption bundle as point C*A.
Now the envelopes come in the mail and Homer gets nothing. He is jealous of his neighbors but he gets over it quickly, after all, he is Homer!
Now Bernanke, finally having something to smile about, decides to get interest rates back up to 'normal' levels, as he is very concerned about inflation. As such, Ben and the Fed get the real rate up to 0.06 (6%).
6. Re-calculate Homer's optimal consumption bundle given the change in the real rate of interest and add as point C*B. on your existing diagram.
7. Is Homer better or worse off due to the increase in the real rate of interest? Explain being sure to discuss exactly how the substitution and income effects play a role here. That is, how do they play a role in Homer's decision to alter his previously optimal bundle? Be sure to 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?).