Suppose that the equation for autonomous planned spending, Ap, is Ap = 6,200 – 200r and the value of the multiplier, k, is 2.5.
(a) Derive the equation for the IS curve, Y = kAp. Graph the IS curve for interest rates between 0 and 8, with intervals of one-half of a percentage point.
(b) Suppose the equation for the LM curve is Y = 13,500 + 100r. Use this equation to explain the level of income at which there is a zero lower bound on the federal funds rate, the interest rate that the Fed controls.
(c) Graph the LM curve for interest rates between 0 and 8, with intervals of one-half of a percentage point.
(d) Suppose that the term premium is 1.0 percentage point and the risk premium is 2.0 percentage points. With Figure 5-11 as a guide, use the LM curve with the zero lower bound and the term premium and risk premium to graph the LM curve for the government bond rate and the LM curve for the private bond rate at interest rates between 0 and 8, with intervals of one-half of a percentage point.
(e) Use the graphs of the IS curve and the three LM curves to explain what the equilibrium interest rates for the federal funds rate, the government bond rate, and the private bond rate are and what the equilibrium level of income is.