A consumer is making saving plans for this year and next. She knows her real income after taxes will be $50,000 in both years. Any part of her income saved this year will earn a real interest rate of 10% between this year and next year. Currently, the consumer has no wealth (no money in the bank or other financial assets, and no debts). There is no uncertainty about the future.
Based on Abel, Bernanke and Croushore, 10th edition, Chapter 4, Numerical Problems No. 1.
A consumer is making saving plans for this year and next. She knows her real income after
taxes will be $50,000 in both years. Any part of her income saved this year will earn a real
interest rate of 10% between this year and next year. Currently, the consumer has no wealth
(no money in the bank or other financial assets, and no debts). There is no uncertainty about
the future.
a) Formally derive the consumer’s intertemporal budget constraint.
b) Using the given numerical values rewrite and graph the budget line.
c) Find the consumer’s PVLR.
The consumer wants to save an amount this year that will allow her to (1) make college tuition
payments next year equal to $16,800 in real terms; (2) enjoy exactly the same amount of
consumption this year and next year, not counting tuition payments as part of next year’s
consumption; and (3) have neither assets nor debts at the end of next year.
d) In the context of the model, describe the household optimization problem. Explain the
trade-offs the consumer faces.
e) Determine numerically based on the instructions above: How much should the consumer
save this year? How much should she consume?
f) Now, assume that her current income rises from $50,000 to $54,200 while the other
variables are held at their original values. How are the amounts that the consumer should
save and consume affected?
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