3) In this question, were 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. Well 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 $100,000 today, but will earn no income during retirement. Instead of consuming today, the consumer can save at interest rate i. Recall that $X saved today will pay X(1+i) dollars during retirement (simplifying a bit on compounding). This question is very similar to the labor supply example in lecture.

a) If you only consume today, your consumption will be $100,000. 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?

b) Why can we interpret the interest rate as the price of current consumption? Think about the slope of the BC and tradeoffs...

c) 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 _____ after an increase in i because... This makes me consume... Assume that both C and R are normal goods.

d) 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.