Refer to Thinking and Problem Solving question 1. In that question, we assumed that the consumer earned $50 in period 1 and $150 in period 2, and that saving and borrowing were both interest-free. Let’s see if we can’t add even more real-life detail to this problem.
a. Draw a new budget constraint for the consumer if the period 1 income remains at $50, but the period 2 income falls to $100. Use the ideas of the income and substitution effects to describe how this change would affect the optimal choice of the consumer.
b. Now let’s add another wrinkle: an interest rate. We’ll use the same endowment point from Thinking and Problem Solving question 1. Construct a budget constraint for a consumer that can earn 20% interest by saving money in period 1 for use in period 2 but also has to pay 20% interest to borrow money from period 2 for use in period 1. (These interest rates are high so that the impact is obvious on your graph; the results will still hold—although less dramatically—with lower interest rates.) What is the substitution effect of the addition of the interest rate? The income effect is more complicated, because it depends on the consumer’s preferences, which could be revealed by the pre-interest-rate behavior.
c. In December 2010, the average interest rate on money market and savings accounts was 0.7%, but the average rate on a variable rate credit card was 14.4%. Obviously the previous assumption that the interest rate is the same for borrowers and savers is not very realistic. Again, using more dramatic interest rates, can you construct a budget constraint for a consumer with the same initial endowment as previously that faces a 1% interest rate for saving and a 50% interest rate for borrowing? What do you notice about this budget constraint?