In this question, we\'re going to demonstrate that under the right conditions, a

Question

In this question, we're going to demonstrate that under the right conditions, an increase in the interest rate can actually reduce the amount that a consumer wants to save. We'll phrase the problem in terms of consumers choosing between consumption today (C) on the x-axis, and consumption during retirement (R) on the y-axis - both axes measure consumption in dollars. The consumer has income $Y today, but will cam no income during retirement. Instead of consuming today, the consumer can save. Every $1 saved today will pay (1+i) dollars during retirement. This question is very similar to the labor supply example in lecture. If you only consume today, your consumption will be $Y. If you saved all your income today, what level of consumption could you have during retirement? Use this information to draw a budget constraint. What is the slope of this line - what tradeoff can you get for giving up $1 of current consumption? Explain why an increase in the interest rate is described as a decrease in the price of future consumption ? Think about the slope of the BC and tradeoffs... Draw a new budget line that reflects an increase in the interest rate (i.e. i rises). Make a table that shows the income and substitution effects of the interest rate increase, and briefly discuss the intuition/economics of why these effects change current and future consumption. For instance, the income effect starts with "I feel wealthier after an increase in i because... This makes me consume..." Assume that both C and R are normal goods. Based on your table, discuss what would have to be true about the income and substitution effects for this increase in the interest rate to reduce savings (i.e. increase current consumption)? Give some marginal utility based intuition for what circumstances might generate such income and substitution effects.

Explanation / Answer

The interest rate is the percent charged, or paid, for the use of money. It is charged when the money is being borrowed, and paid when it is being loaned. The interest rate that the lender charges is a percent of the total amount loaned. Similarly, the interest rate that an institution, such as a bank, pays to hold your money is a percent of the total amount deposited. Anyone can lend money and charge interest, or hold deposits and pay interest. However, it's usually the function of banks to to make loans or hold deposits. How do banks get the money to make loans? Banks use the deposits made by people who keep their savings or checking accounts with them. Banks convince people to make deposits by paying interest rates. Banks are paying depositors for the right of using their money. Banks then use that money to make loans. Banks charge borrowers a little higher interest rate than they pay depositors for that same money so they can profit for providing these services. Banks want to charge as much interest as possible on loans, and pay as little as possible on deposits, so they can be more profitable. At the same time, banks are competing with each other for those same deposits and loans. This competition keeps interest rates in a similar range. For more, see How Interest Rates Are Determined. How Do Interest Rates Work? Interest rates are charged not only for loans, but also for mortgages, credit cards and unpaid bills. The interest rate is applied to the total unpaid portion of your loan or bill. It's important to know what your interest rate is, and how much it adds to your outstanding debt. If your interest rate adds more to your debt than the amount your are paying, your debt could actually increase even though you are making payments. Although interest rates are very competitive, they aren't the same. A bank will charge higher interest rates if it thinks there's a lower chance the debt will get repaid. Some types of loans, like credit cards, are always assigned higher interest rates because they are more expensive to manage. Banks also charge higher rates to people they consider riskier. That's why it's important to know what your credit score is, and how to improve it. The higher your score, the lower the interest rate you will have to pay.

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