economics questions to be modified

Homework Week 6 Answers

The homework is worth 20 points, so each answer will have points distribution at the

instructor’s discretion.

Chapter 14 1. a. Given that the interest rate has been 4 percent for the last ten quarters, then for IS curve

I, real GDP equals 8,800 − 25(4) − 25(4) − 25(4) − 25(4) − 20(4) − 20(4) − 20(4) − 15(4) − 15(4) − 10(4) = 8,000. For IS curve II, real GDP equals 8,400 − 5(4) − 5(4) − 5(4) − 5(4) − 10(4) − 15(4) − 15(4) − 15(4) − 20(4) = 8,000.

b. For IS curve I, real GDP in the first quarter equals 8,800 − 25(3) − 25(4) − 25(4) − 25(4) − 20(4) − 20(4) − 20(4) − 15(4) − 15(4) − 10(4) = 8,025. Using the same IS curve, it is easy to show that for quarters two through ten, real GDP equals 8,050, 8,075, 8,100, 8,120, 8,140, 8,160, 8,175, 8,190, and 8,200, respectively. For IS curve II, real GDP in the first quarter equals 8,400 − 5(3) − 5(4) − 5(4) − 5(4) − 5(4) − 10(4) − 15(4) − 15(4) − 15(4) − 20(4) = 8,005. Using the same IS curve, it is easy to show that for quarters two through ten, real GDP equals 8,010, 8,015, 8,020, 8,025, 8,035, 8,050, 8,065, 8,080, and 8,100, respectively.

c. Real GDP increases by 200 billion for IS curve I. The increase in real GDP for IS curve II equals 100 billion.

d. For IS curve I, it takes four quarters, or twelve months, for real GDP to increase by 100 billion or one-half of the total increase in real GDP. For IS curve II, it takes seven quarters, or twenty-one months, for real GDP to increase by 50 billion or one-half of the total increase in real GDP.

e. IS curve I resembles the economy’s response prior to 1991. The increase in output in response to a decline in the interest rate is larger than for IS curve II and one-half of the total increase in output occurs much sooner with IS curve I as compared to IS curve II. IS curve II resembles the economy’s response to a change in the interest rate since 1991. The reasons why IS curve I resembles the economy’s response prior to 1991 is that its interest rate parameters for the first six quarters are larger than those of IS curve II, and it is only for that last quarter that IS curve I has a smaller interest rate parameter than that of IS curve II. These parameters reflect the fact that since 1991, the monetary policy effectiveness lag has been longer and the interest-rate multiplier has been smaller.

f. The answers to Parts b through d indicate that for IS curve II, real GDP rises less than it does for IS curve I during any of the first seven time periods, for any given increase in the interest rate. Therefore, the changes in the policy effectiveness lag and the interest- rate multipliers mean that monetary policymakers now have to change interest rates more in response to a given demand shock than they did previously.

Chapter 17

2. a. The equation for the aggregate demand curve is Y = 9,000 + 3,000/P, given that the nominal money supply is initially 3,000. If the price level equals 0.8, the point on the aggregate demand curve is Y = 9,000 + 3,000/0.8 = 9,000 + 3,750 = 12,750. The same calculation shows that the following points are on the aggregate demand curve: (12,000, 1.0), (11,500, 1.2), (11,400, 1.25), and (11,000, 1.5).

b. The long-run equilibrium values of real GDP and the price level are where aggregate demand and long-run aggregate supply are equal. Long-run equilibrium also requires the price level to equal the expected price level or equivalently that the price surprise is zero. Since the long-run aggregate supply curve is vertical at natural real GDP and since natural real GDP equals 12,000, the long-run equilibrium values of real GDP and the price level are also 12,000 and 1.0, given that the expected price level is initially 1.0.

c. The decrease in the real exchange results in an increase in aggregate demand so that the new equation for the aggregate demand curve is Y = 9,600 + 3,000/P, given the initial value of the nominal money supply. Therefore, if the price level equals 0.8, the point on the new aggregate demand curve is Y = 9,600 + 3,000/0.8 = 9,600 + 3,750 = 13,350. The same calculation shows that the following points are on the new aggregate demand curve: (12,600, 1.0), (12,100, 1.2), (12,000, 1.25), and (11,600, 1.5). The new level of aggregate demand and short-run aggregate supply are equal at real GDP equal to 12,100 and a price surprise equal to .2. Therefore, the new equilibrium price level equals 1.2 in the short run.

d. If monetary policymakers respond to the decline in the real exchange rate by doing nothing and leaving the nominal money supply at its current level of 3,000, then the long-run equilibrium price level is 1.25, since that is where aggregate demand and the long-run aggregate supply are equal at the natural real GDP level of 12,000. If monetary policymakers change the money supply so as to return the price level to 1.0, which is what it was equal to in Part b, then the nominal money supply, M s, must be such that 12,000 = 9,600 + M s/1.0 or M s = 12,000 − 9,600 = 2,400. That is, monetary policymakers must reduce the nominal money supply to 2,400 for the price level and the expected price level to be equal at P = 1.0. If monetary policy changes the money supply so as to keep the price level equal to 1.2, which is what it was in Part c, then the nominal money supply, M s, must be such that 12,000 = 9,600 + M s/1.2 or M s/1.2 = 12,000 − 9,600 = 2,400. Therefore, M s = 1.2(2,400) = 2,880. That is, monetary policymakers must reduce the nominal money supply to 2,880 for the price level and the expected price level to be equal at P = 1.2.

3. a. If the decline in the real exchange rate is only temporary, so that the aggregate demand curve returns to its original level, then given no change in the nominal money supply, the economy is long-run equilibrium when the expected price level and the actual price level at 1.0. On the other hand, if monetary policymakers change the nominal money supply so as to maintain a price level equal to 1.2 when aggregate demand returns to its original level, then they must change the nominal money supply to M s′so that 12,000 = 9,000 + M s′/1.2 or M s′/1.2 = 12,000 − 9,000 or M s′ = 1.20(3,000) = 3,600. That is, monetary policymakers would have to increase the nominal money supply to 3,600 to keep the price level and expected price level equal to 1.2.

b. If monetary policymakers do nothing in the sense of not changing the nominal money supply, then expected and actual price level rise if the decline in the real exchange rate persists. The reason both price levels rise is that firms and workers know it takes a higher price level to offset the increase in aggregate demand caused by the decline in the real exchange rate, given that they expect monetary policymakers to take no steps to offset that increase in aggregate demand. On the other hand, if firms and workers know that the decline in the real exchange rate is only temporary, then they understand that the increase in aggregate demand is also only temporary. So if they expect that monetary policymakers are not going to take any steps to respond to the temporary changes in the

real exchange rate and aggregate demand, then they also know that the price level returns to 1.0, so that is the price level they expect. Note, however, that if the decline in the real exchange rate is expected to persist, so that the increase in aggregate demand is also expected to persist and firms and workers also expect monetary policymakers to take actions to reduce the price level to 1.0 in the face of that increase in aggregate demand, then monetary policymakers must reduce the nominal money supply enough to shift the aggregate demand curve back to its original level. Finally, if firms and workers expect that monetary policy makers will maintain the price level at 1.2, then when the decline in the real exchange rate is expected to persist, monetary policymakers must take action so as to reduce aggregate demand so that aggregate demand and long-run aggregate supply are equal to 12,000 at a price level of 1.2. That reduction in aggregate demand would require a decrease in the nominal money supply. On the other hand, if the decline in the real exchange is only temporary and so also is the increase in aggregate demand, then monetary policymakers would have to increase aggregate demand so as to keep aggregate demand and long-run aggregate supply equal to 12,000 at a price level of 1.2. That would require an increase in the nominal money supply.

c. Policymakers, workers, and firms would look to data from the foreign exchange markets and economic conditions in the rest of the world in an attempt to determine if there were changes in any of these areas that would cause the decline in the real exchange rate to either persist or only be temporary in nature. If monetary policymakers have always responded to changes in aggregate demand by not doing anything, then there is nothing that they can do to signal to workers and firms whether the change in the real exchange rate is going to persist or is only temporary. On the other hand, if monetary policymakers have responded to changes in aggregate demand so as to either maintain the price level at its pre- or post-surprise level, then what they do to the nominal money supply signals to firms and workers what they have discovered concerning the nature of change in the real exchange rate. For example, if workers and firms expect that monetary policymakers act so as to maintain the price level equal to 1.0, its pre-surprise level, then monetary policymakers can signal to workers and firms that the decline in the real exchange is only temporary by maintaining the nominal money supply at its pre-surprise level. On the other hand, if monetary policy makers discover that the decline in the real exchange rate is going to persist, then they can signal that to workers and firms by reducing the nominal money supply. Finally, you should be able to figure out how monetary policymakers can signal to firms and workers what they know about the change in the real exchange rate via a change in the nominal money supply if workers and firms expect monetary policymakers to maintain the price level at 1.2.