Final answer:
An increase in interest rates leads to both a substitution effect, favoring future consumption (increased savings), and an income effect, increasing both present and future consumption. Therefore, option b is correct as it suggests reduced savings both when young and when old, but personal time preference can influence actual savings behavior.
Step-by-step explanation:
The income impact of an increase in interest rates on savings behavior, assuming consumption is considered a normal good, is option b. This would reduce savings both when paying (young age) and when old. This is because the interest rate increase would lead to a substitution effect where future consumption is more attractive due to higher future returns on savings. However, it would simultaneously have an income effect, encouraging increased consumption in both the present and future, given the characterization of consumption as a normal good. Hence, individuals might choose to consume more now as well as more in the future, which could reduce savings at both young and old ages.
However, the actual behavior would depend on personal time preference. Adults, who often exhibit a better time preference, might still choose to save more for the future, foreseeing the benefits of compound interest. On the contrary, this might not be the same for children or those with a strong preference for immediate consumption. Additionally, higher interest rates generally reduce borrowing rates for investment by businesses and consumption by households, which might also lead to a reduction in immediate savings rates.