3. Yield Curve and Expectations Theory Suppose that: 1) The interest on a one-year bond today is 3%; 2) The interest on a one-year bond starting one year from now is expected to be 4% per year; 3) The interest on a one-year bond starting two years from now is expected to be 5% per year; 4) The risk premium on a two-year bond is 0.5%; and 5) The risk premium on a three-year bond is 1.0%. The expectations theory on yield curve states that returns on a long-term bond are assumed to equal the geometric mean of the expected returns on a series of short-term bonds. That is 1+im:=[(1+i.)(1+4x)(1+-2) --- (1+i: n-1)] Where is the actual interest rates of long-term bonds with maturity of m at time t. And e are the expected short-term interest rates (with one-period maturity) at time t+s. Additionally, appropriate risk premium should be added on top of it in market equilibrium. Use that information to answer the following questions. a) According to the expectations theory, what is the interest rate today on a two-year bond? Show your work b) According to the expectations theory, what is the interest rate today on a three-year bond? Show your work c) Plot the yield curve. d) Consider the Keynesian sticky-price model in which the central bank directly sets the money supply. Suppose the central bank conducts a monetary expansion by permanently increasing the growth rate of money supply. What effect do you expect on the yield curve in this model? (Hint: Sticky-price model assumes that the price level is rigid.)