Suppose we have Stash who likes to perfectly smooth his consumption: C1 = C2= C*

Question

Suppose we have Stash who likes to perfectly smooth his consumption: C1 = C2= C*. His current income is $100K ($100K means $100,000), his expected future income is $50K, and his current wealth is $20K. (Future wealth is zero.) The interest real rate is - 5%.

1. Increase in the Real Interest Rate: Now suppose the unemployment rate has declined to 4.5% and the latest release of the PCE price index shows inflation has suddenly spiked up to 4%. In response, Jerome Powell manages to get the real interest rate up to 5%. With expected future income at $100K, recalculate Stash’s new optimal bundle, CC*, and the new level of current saving, S. Show all work.

2. What is the total effect of the increase in the real rate on Stash’s current and future consumption from CB* to CC*? (Calculate C1 and C2 in going from CB* to     CC*? “” means change.)   Show all work.

3. Did the increase in the real interest rate make Stash better off or worse off? That is, does the new optimal bundle increase or decrease current and future consumption, C1 and C2? Explain by using the substitution effect and the income effect:

Provide the reasoning behind the substitution effect in Stash’s case (i.e.,     “the substitution effect causes current consumption to go _________ (up/down) because … and future consumption to go ______________________      (up/down) because… Then, do the same thing for the income effect.    If these effects are in opposite directions, which dominates (according to Graph A) in Stash’s case?  

Explanation / Answer

The law of diminishing marginal utility is a law of economics stating that as a person increases consumption of a product while keeping consumption of other products constant, there is a decline in the marginal utility that person derives from consuming each additional unit of that product.

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