In this particular case, the income and substitution effects work in the opposite direction.
When it comes to substitution effect on this particular case, current consumption becomes less expensive relative to future consumption when real interest rates fall. Thus, he substitutes away from future consumption toward current consumption. When it comes to income effect on this particular case, he feels poorer thus, cuts back on current and future consumption. Also, he will increase current saving.
This is because lower real interest rates reduce real income such as interest income.
Also, the future value of current resources falls as real interest falls.
2. (NEW GRADER) (30 points total) 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 (cf). Homer’s current income equals $100K and his future expected income = $100K. 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.
a) (5 points) Solve for Homer’s optimal consumption basket today (C*) and his optimal consumption basket next period (Cf*). Please provide a completely labeled graph depicting