Suppose that the equation for an economy’s IS curve is Y = 13,500 - 300r. Large fluctuations in stock prices cause people to move funds in and out of assets included in M2, resulting in an unstable demand for money. Due to that unstable money demand, the demand for money fluctuates between (M/P)d = 0.25Y - 50r and (M/P)d = 0.2Y - 40r The real money supply, Ms/P, equals $2,500.
(a) Given that the demand for money is (M/P)d = 0.25Y - 50r verify that the equation for the LM curve is Y = 10,000 + 200r by showing that the demand for money equals $2,400 at the following combinations of income and the interest rate: ($10,000, 0); ($10,400, 2); ($11,400, 7); ($12,000, 10). Graph these points, labeling the LM curve as LMA.
(b) Given that the demand for money is (M/P)d = 0.2Y - 40r, verify that the equation for the LM curve is Y = 12,500 + 200r by showing that the demand for money equals $2,400 at the following combinations of income and the interest rate: ($12,500, 0); ($12,900, 2); ($13,900, 9); ($14,500, 10). Graph these points, labeling the LM curve as LMB.
(c) Graph the IS curve at interest rates equal to 0, 2, 7, and 10. Use your graphs of the IS and LM curves to find the equilibrium level of income and the equilibrium interest rate when the demand for money equals 0.25Y - 50r and when the demand for money equals 0.2Y - 40r.
(d) Suppose that natural real GDP equals $12,000. Use your answers to part c to explain what problem the economy faces when the demand for money equals 0.25Y – 50r and the problem the economy faces when the demand for money equals 0.2Y – 40r.
(e) Suppose that monetary policymakers want to target the interest rate in order to keep real GDP equal to natural real GDP. Given that natural real GDP is $12,000, what is the interest rate that monetary policymakers must target? In order to reach this target, what must monetary policymakers set the real money supply equal to when the demand for money is (M/P)d = 0.25Y - 50r and when it is (M/P)d = 0.2Y - 40r?