You are given the following information for the commodity market, in which taxes, planned investment, government spending on goods and services, and net exports are autonomous, but consumption and planned investment change as the interest rate changes:
Ca = 2,180 - 20rc = 0.6 Ip = 2,400 - 60r
G = 2,000 NX = -300 T = 1,800
The money market is described in problem 1.
(a) Compute the values of the marginal propensity to save, s, and the multiplier, k.
(b) Derive the equation for the autonomous planned spending Ap.
(c) Derive the equation for the IS curve, Y = kAp, and graph the IS curve when the interest rate equals 4.7, 5.0, 5.3, 5.6, and 5.9.
(d) Using your answers to part c of problem 1 and part c of this problem, explain at what interest rate and at which level of real income the commodity and money markets are both in equilibrium.
(e) In the first half of 2003, the Fed changed monetary policy because unemployment was too high and it feared any additional decline in the rate of inflation would result in deflation. Suppose that natural real GDP equals $12,060 and the equilibrium in part c is similar to economic conditions in the first half of 2003. Using your answers to parts d or e of problem 1 and part c of this problem, explain how the Fed should change the real money supply in order to move real income to natural real GDP in an effort to reduce unemployment and avoid a further reduction in the inflation rate.