Sally will earn $30,000 this year and $40,000 next year. The real interest rate is 20% between this year and next year; she can borrow or lend at this rate. She has no wealth at the start of this year and plans to finish next year having consumed everything she possibly can. She would like to consume the same amount this year as next year. The inflation rate is 0%.(a)How much should Sally save this year? How much will Sally consume in each of the two years?(c)How would your answers change if the real interest rate was 40%?
What will be an ideal response?
In general, S = Y(1) - C(1). So in year 2, she has consumption equal to
(1 + r)[Y(1) - C(1)] + Y(2) = C(2). Since C(1) = C(2), then (1 + r)[Y(1) - C(2)] + Y(2) = C(2).
This can be solved for C(2) to get C(2) = [(1 + r)Y(1) + Y(2)]/(2 + r).
| (a) | With r = 0.2, then C(2) = [(1.2 × $30,000) + $40,000]/2.2 = $34,545 = C(1). Then S = $30,000 - |
| (b) | With r = 0.4, then C(2) = [(1.4 × $30,000) + $40,000]/2.4 = $34,167 = C(1). Then S = $30,000 - |
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