4. A risk-free one-year bond has a price equal to pt = 1 and a constant payoff equal to Rf 2 1. The risk-free interest rate is therefore R$ 1. a. Using the fundamental pricing equation, show algebraically that for a representative investor with power utility of consumption with risk aversion parameter y and an annual discount factor of 8, the risk-free interest rate must be equal to the expression below (1 point): 1 Rf 8 b. Interpreting the equation above, we can draw conclusions about how real interest rates behave as a function of three different inputs: investors' subjective discount factor 8, the rate of annual consumption growth C++1/ct, and investors' subjective aversion to risk y. Explain the real-world intuition as to why each result listed below should occur. (1 point each) i. When people are impatient, risk-free interest rates are high. ii. Risk-free interest rates are high when annual consumption growth is high. iii. Real interest rates are more sensitive to consumption growth when people are more risk averse. 4. A risk-free one-year bond has a price equal to pt = 1 and a constant payoff equal to Rf 2 1. The risk-free interest rate is therefore R$ 1. a. Using the fundamental pricing equation, show algebraically that for a representative investor with power utility of consumption with risk aversion parameter y and an annual discount factor of 8, the risk-free interest rate must be equal to the expression below (1 point): 1 Rf 8 b. Interpreting the equation above, we can draw conclusions about how real interest rates behave as a function of three different inputs: investors' subjective discount factor 8, the rate of annual consumption growth C++1/ct, and investors' subjective aversion to risk y. Explain the real-world intuition as to why each result listed below should occur. (1 point each) i. When people are impatient, risk-free interest rates are high. ii. Risk-free interest rates are high when annual consumption growth is high. iii. Real interest rates are more sensitive to consumption growth when people are more risk averse