Problem Set # 9 Solutions


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1 Poblem Set # 9 Solutions Chapte 12 #2 a. The invention of the new highspeed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease in the demand fo investment goods shifts the cuve out, aising income and employment. 2 B 1 A The incease in income fom the highe investment demand also aises inteest ates. This happens because the highe income aises demand fo money; since the supply of money does not change, the inteest ate must ise in ode to estoe equilibium in the money maket. The ise in inteest ates patially offsets the incease in investment demand, so that output does not ise by the full amount of the ightwad shift in the cuve. Oveall, income, inteest ates, consumption, and investment all ise. b. The inceased demand fo cash shifts the cuve up. This happens because at any given level of income and money supply, the inteest ate necessay to equilibate the money maket is highe A 1 B 2 1
2 The upwad shift in the cuve lowes income and aises the inteest ate. Consumption falls because income falls, and investment falls because the inteest ate ises. c. At any given level of income, consumes now wish to save moe and consume less. Because of this downwad shift in the consumption function, the cuve shifts inwad. 1 A 2 B Income, inteest ates, and consumption all fall, whil einvestment ises. Income falls because at evey level of the inteest ate, planned expenditue falls. The inteest ate falls, because the fall in income educes demand fo money; since the supply of money is unchanged, the inteest ate must fall to estoe moneymaket equilibium. Consumption falls both because of the shift in the consumption function and because income falls. Investment ises because of the lowe inteest ates and patially offsets the effect of the fall in consumption. d. Expected inflation ises, so if the nominal inteest ate emains the same, the eal inteest ate has fallen. (Odinaily we think of both inflation and expected inflation (and indeed often pices) as fixed in the shot un.) If the cental bank maintains the same nominal inteest ate, the eal inteest ate fall shows up as the cuve shifts down and to the ight (it dops by the incement to expected inflation); this povides the equivalent of a monetay stimulus, aising output though the usual channels until inflation ises as the shot un ends and we ente the long un.
3 Chapte 12 #5 a. False; the elationship between inteest ates and investment is though the cuve. b. The cuve epesents the elationship between the inteest ate and the level of income that aises fom equilibium in the maket fo goods and sevices. That is, it descibes the combinations of income and the inteest ate that satisfy the equation = C( T) + I()+G. If investment does not depend on the inteest ate, then nothing in the equation depends on the inteest ate; income must adjust to ensue that the quantity of goods poduced,, equals the quantity of goods demanded, C + I + G. Thus, the cuve is vetical at this level, as shown in the Figue. Monetay policy has no effect on output, because the cuve detemines. Monetay policy can affect only the inteest ate. In contast, fiscal policy is effective: output inceases by the full amount that the cuve shifts. c. False: money demand affects, not the cuve. d. The cuve epesents the combinations of income and the inteest ate at which the money maket is in equilibium. If money demand does not depend on the inteest ate, then we can wite the equation as M/P = L(). Fo any given level of eal balances M/P, thee is only one level of income at which the money maket is in equilibium. Thus, the cuve is vetical, as shown in the Figue. Fiscal policy now has no effect on output; it can affect only the inteest ate. Monetay policy is effective: a shift in the cuve inceases output by the full amount of the shift. e. If money demand does not depend on income, then we can wite the equation as M/P = L(). Fo any given level of eal balances M/P, thee is only one level of the inteest ate at which the money maket is in equilibium. Hence, the cuve is hoizontal, as shown in Figue Fiscal policy is vey effective: output inceases by the full amount that the cuve shifts. Monetay policy is also effective: an incease in the money supply causes the inteest ate to fall, so the cuve shifts down, as shown in Figue
4 f. The cuve gives the combinations of income and the inteest ate at which the supply and demand fo eal balances ae equal, so that the money maket is in equilibium. The geneal fom of the equation is M/P = L(, ). Suppose income inceases by $1. How much must the inteest ate change to keep the money maket in equilibium? The incease in inceases money demand. If money demand is extemely sensitive to the inteest ate, then it takes a vey small incease in the inteest ate to educe money demand and estoe equilibium in the money maket. Hence, the cuve is (nealy) hoizontal, as shown in Figue An example may make this cleae. Conside a linea vesion of the equation: M/P = e f. Note that as f gets lage, money demand becomes inceasingly sensitive to the inteest ate. Reaanging this equation to solve fo, we find = (e/f) (1/f)(M/P). We want to focus on how changes in each of the vaiables ae elated to changes in the othe vaiables. Hence, it is convenient to wite this equation in tems of changes: = (e/f) (1/f) (M/P). The slope of the equation tells us how much changes when changes, holding M fixed. If (M/P) = 0, then the slope is / = (e/f). As f gets vey lage, this slope gets close and close to zeo. If money demand is vey sensitive to the inteest ate, then fiscal policy is vey effective: with a hoizontal cuve, output inceases by the full amount that the cuve shifts. Monetay policy is now completely ineffective: an incease in the money supply does not shift the cuve at all. We see this in ou example by consideing what happens if M inceases. Fo any given (so that we set = 0), / (M/P) = ( 1/f); this tells us how much the cuve shifts down. As f gets lage, this shift gets smalle and appoaches zeo. (This is in contast to the hoizontal cuve in pat (c), which does shift down.)
5 Chapte 12 #6 To aise investment while keeping output constant, the govenment should adopt a loose monetay policy and a tight fiscal policy, as shown in Figue In the new equilibium at point B, the inteest ate is lowe, so that investment is highe. The tight fiscal policy educing govenment puchases, fo example offsets the effect of this incease in investment on output. The policy mix in the ealy 1980s did exactly the opposite. Fiscal policy was expansionay, while monetay policy was contactionay. Such a policy mix shifts the cuve to the ight and the cuve to the left, as in Figue The eal inteest ate ises and investment falls. Chapte 12 #8 The figue to the left shows what the  model looks like fo the case in which the Fed holds the money supply constant. The figue to the ight shows what the model looks like if the Fed adjusts the money supply to hold the inteest ate constant; this policy makes the effective cuve hoizontal. Holding the Money Supply Constant Holding the Inteest Rate Constant a. If all shocks to the economy aise fom the exogenous changes in the demand fo goods and sevices, this means that all shocks ae to the cuve. Suppose a shock causes the cuve to shift fom 1 to 2. The figues below show what effect this has on output unde the two policies. It is clea that output fluctuates less if the Fed follows a policy of keeping the money
6 supply constant. Thus, if all shocks ae to the cuve, then the Fed should follow a policy of keeping the money supply constant. Holding the Money Supply Constant Holding the Inteest Rate Constant b. If all shocks in the economy aise fom exogenous changes in the demand fo money, this means that all shocks ae to the cuve. If the Fed follows a policy of adjusting the money supply to keep the inteest ate constant, then the cuve does not shift in esponse to these shocks the Fed immediately adjusts the money supply to keep the money maket in equilibium. It is clea that output fluctuates less if the Fed holds the inteest ate constant and offsets shocks to money demand by changing the money supply, then all vaiability in output is eliminated. Thus, if all shocks ae to the cuve, then the Fed should adjust the money supply to hold the inteest ate constant, theeby stabilizing output. Holding the Money Supply Constant Holding the Inteest Rate Constant
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