economics questions to be modified

CH14, Problem 1 – You are given the following two IS curves that show how real GDP (Yt) in the current time period t depends on the current interest rate and interest rates in previous periods, where rt is the interest rate in time period t. Furthermore each time period corresponds to a quarter or three months.

1. Yt= 8800-25Rt-25Rt-t - 25Rt-2 - 25Rt-3 - 20Rt-4 - 20Rt-5 - 20Rt-6 - 15Rt-7 - 15Rt-8 - 10Rt-9 2. Yt= 8400 - 5Rt - 5Rt-1 - 5Rt-2 - 5Rt-3 - 5Rt-4 - 10Rt-5 - 15Rt-6 - 15Rt-7 - 15Rt-8 - 20Rt-9

(a) Verify that initially real GDP equals 8,000 for both IS curves.

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) Suppose that the Fed lowers the interest rate to 3% and keeps it there for the next 10 quarters. Calculate real GDP for the next 10 quarters for each IS curve.

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) For each IS curve, what is the total increase in real GDP?

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

100 billion.

(d) For each IS curve, how many quarters does it take for the incease in real GDP to equal one-half of the total increase?

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 twentyone

months, for real GDP to increase by 50 billion or one-half of the total increase in real GDP.

(e) Using Figure 14-2 above, explain which one of the IS curves resembles the economy’s response to a change in the interest rate prior to 1991 and which one resembles its response since 1991. Explain how your answer is related to the interest-rate parameters in each IS equation.

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) Given your answers to parts b-d, explain how the changes in the monetary policy effectiveness lag and the interest-rate multiplier affects how much and how long monetary policymakers must change interest rates in response to any given demand shock.

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.

CH17, Problem 2 – Suppose that the equation for the aggregate demand is Y = $9,000 + Ms / P, where Ms is the nominal money supply and P is the price level. Initially the nominal money supply equals $3,000. In addition, suppose that the expectations of firms and workers are rational in the sense when people make the best forecasts they can with the available data.

(a) Calculate points on the aggregate demand curve when the price level equals 0.8, 1/0, 1.2, 1.25, and 1.5, given the initial value of the nominal money supply.

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) Suppose that natural real GDP equals $12,000 and that the short-run supply curve is given in the table below, where the price surprise equals P – Pe and Pe is the expected price level: Price surprise -0.2 0.0 0.2 0.25 0.5

Real GDP 11,900 12,000 12,100 12,125 12,250

Given that the expected price level is initially 1.0, explain why the economy is in long-run equilibrium when the price level equals 1.0 and real GDP equals $12,000.

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) Suppose that the real exchange rate declines as it did in 2006-2007 and as a result, aggregate demand increases. Also assume that the decline in the real exchange rate will persist over time. As a result of this decline, the new equation for the aggregate demand is Y = $9,600 + Ms / P. Given no change in the nominal money supply, calculate the points on the new aggregate demand curve when the price level equals 0.8, 1.0, 1.2, 1.25, and 1.5, given the initial value of the nominal money supply. Using the table given in part b, explain what the new equilibrium price level and level of real GDP are in the short run, given the price surprise induced by the decline in the real exchange rate?

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) Monetary policymakers respond to the decline in the real exchange rate in one of three ways: (i) they do nothing and leave the nominal money supply as is; (ii) they change the money supply so as to return the price level to its level as given in part b; or (iii) they change the money supply so as to maintain the price level as determined by your answer to part c. For each of these cases, assume that this is how monetary policymakers have behaved in the past and this is how firms and workers expect them to behave in response to the decline in the real exchange rate. Calculate what the long-run equilibrium price level is and what the expected price level is under each response by monetary policymakers. Calculate by how much monetary policymakers must change the nominal money supply for the expectations of firms and workers to be realized.

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, Ms, must be such that

12,000 = 9,600 + Ms/1.0 or Ms = 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, Ms, must be such that 12,000 = 9,600 +

Ms/1.2 or Ms/1.2 = 12,000 − 9,600 = 2,400. Therefore, Ms = 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.

CH17, Problem 3 – Suppose that instead of persisting as is assumed in problem 2, the decline in the real exchange rate is only temporary in that the real exchange rate is only temporary in that after the initial change in the price level that you found in part c of problem 2, aggregate demand returns to its original level.

(a) Given that monetary policymakers, firms, and workers all recognize that the decline in the real exchange rate is only temporary and given the three policy responses described in part d of problem 2, again calculate what the long-run equilibrium price level is and what the expected price level is under response by monetary policymakers. Again calculate by how much monetary policymakers must change the nominal money supply for the expectations of firms and workers to be realized.

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 Ms′so that 12,000 = 9,000 + Ms′/1.2 or Ms′/1.2 =12,000 − 9,000 or Ms′ =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) Compare your answers to part d of problem 2 with those of part a of this problem and explain why they are different.

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) Explain what data or other factors that monetary policymakers, firms, workers might analyze in attempting to determine if the decline in the real exchange rate is temporary or will persist. Finally, suppose that monetary policymakers are better able than firms and workers to determine if a change in the real exchange rate is temporary or will persist and that firms and workers know this. Given your answer to part d of problem 2 and part a of this problem, explain how once monetary policymakers have determined whether the change in the real exchange rate is only temporary or will persist, they could signal their findings to firms and workers.

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 policy-

makers 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.