Smith receives $100 of income this period and $100 next period. At an interest rate of 10

Question:

Smith receives $100 of income this period and $100 next period. At an interest rate of 10 percent, he consumes all his current income in each period. He has a diminishing marginal rate of time preference between consumption next period and consumption this period. True or false: If the interest rate rises to 20 percent, Smith will save some of his income this period. Explain.