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Consider the inter-temporal model of consumption studied in class, with two possible periods. Assume that initially that an individual is a saver. If the interest rate rises, which statement is false?Group of answer choicesThe individual will never become a borrower.The individual will necessarily increase their savings.The individual must remain a saverThe individual could increase or decrease their savings, but she must remain a saver.

Question

Consider the inter-temporal model of consumption studied in class, with two possible periods. Assume that initially that an individual is a saver. If the interest rate rises, which statement is false?Group of answer choicesThe individual will never become a borrower.The individual will necessarily increase their savings.The individual must remain a saverThe individual could increase or decrease their savings, but she must remain a saver.

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Solution

The false statement is: The individual will necessarily increase their savings.

Here's why:

  1. In the inter-temporal model of consumption, individuals make decisions about how much to consume and save in the present and future, considering factors like income, interest rates, and their preferences for current versus future consumption.

  2. If an individual is initially a saver and the interest rate rises, it becomes more attractive to save because the return on savings is higher. However, it does not necessarily mean that the individual will increase their savings.

  3. The individual's response to the interest rate increase will depend on their preferences and the substitution and income effects. The substitution effect encourages more saving because it makes future consumption cheaper relative to current consumption. But the income effect could lead to less saving because the individual can now reach their saving goal with less current saving due to the higher return.

  4. Therefore, it's possible that the individual could save more, save less, or keep their saving the same after the interest rate increase. They could even switch from being a saver to a borrower if the income effect is strong enough. So, the statement "The individual will necessarily increase their savings" is false.

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