Answers to Textbook Questions and Problems CHAPTER 12 Aggregate Demand II: Applying the IS–LM Model Questions for Review 1. The aggregate demand curve represents the negative relationship between the price level and the level of national income. In Chapter 10, we looked at a simplified theory of aggregate demand based on the quantity theory. In this chapter, we explore how the IS–LM model provides a more complete theory of aggregate demand. We can see why the aggregate demand curve slopes downward by considering what happens in the IS–LM model when the price level changes. As Figure 12-1(A) illustrates, for a given money supply, an increase in the price level from P1 to P2 shifts the LM curve upward because real balances decline; this reduces income from Y1 to Y2. The aggregate demand curve in Figure 121(B) summarizes this relationship between the price level and income that results from the IS–LM model. 2. The tax multiplier in the Keynesian-cross model tells us that, for any given interest rate, the tax increase causes income to fall by ΔT [ – MPC/(1 – MPC)]. This IS curve shifts to the left by this amount, as in Figure 12-2. The equilibrium of the economy moves from point A to point B. The tax increase reduces the interest rate from r1 to r2 and reduces national income from Y1 to Y2. Consumption falls because disposable income falls; investment rises because the interest rate falls. Note that the decrease in income in the IS–LM model is smaller than in the Keynesian cross, because the IS–LM model takes into account the fact that investment rises when the interest rate falls. 3. Given a fixed price level, a decrease in the nominal money supply decreases real money balances. The theory of liquidity preference shows that, for any given level of income, a decrease in real money balances leads to a higher interest rate. Thus, the LM curve shifts upward, as in Figure 12-3. The equilibrium moves from point A to point B. The decrease in the money supply reduces income and raises the interest rate. Consumption falls because disposable income falls, whereas investment falls because the interest rate rises. 4. Falling prices can either increase or decrease equilibrium income. There are two ways in which falling prices can increase income. First, an increase in real money balances shifts the LM curve downward, thereby increasing income. Second, the IS curve shifts to the right because of the Pigou effect: real money balances are part of household wealth, so an increase in real money balances makes consumers feel wealthier and buy more. This shifts the IS curve to the right, also increasing income. There are two ways in which falling prices can reduce income. The first is the debt-deflation theory. An unexpected decrease in the price level redistributes wealth from debtors to creditors. If debtors have a higher propensity to consume than creditors, then this redistribution causes debtors to decrease their spending by more than creditors increase theirs. As a result, aggregate consumption falls, shifting the IS curve to the left and reducing income. The second way in which falling prices can reduce income is through the effects of expected deflation. Recall that the real interest rate r equals the nominal interest rate i minus the expected inflation rate πe: r = i – πe. If everyone expects the price level to fall in the future (i.e., πe is negative), then for any given nominal interest rate, the real interest rate is higher. A higher real interest rate depresses investment and shifts the IS curve to the left, reducing income. Problems and Applications 1. a. If the central bank increases the money supply, then the LM curve shifts downward, as shown in Figure 12-4. Income increases and the interest rate falls. The increase in disposable income causes consumption to rise; the fall in the interest rate causes investment to rise as well. b. If government purchases increase, then the government-purchases multiplier tells us that the IS curve shifts to the right by an amount equal to [1/(1 – MPC)]ΔG. This is shown in Figure 12-5. Income and the interest rate both increase. The increase in disposable income causes consumption to rise, while the increase in the interest rate causes investment to fall. c. If the government increases taxes, then the tax multiplier tells us that the IS curve shifts to the left by an amount equal to [–MPC/(1 – MPC)]ΔT. This is shown in Figure 12-6. Income and the interest rate both fall. Disposable income falls because income is lower and taxes are higher; this causes consumption to fall. The fall in the interest rate causes investment to rise. d. We can figure out how much the IS curve shifts in response to an equal increase in government purchases and taxes by adding together the two multiplier effects that we used in parts (b) and (c): ΔY = {[(1/(1 – MPC)]ΔG} – {[MPC/(1 – MPC)]ΔT} Because government purchases and taxes increase by the same amount, we know that ΔG = ΔT. Therefore, we can rewrite the above equation as: ΔY = [(1/(1 – MPC)) – (MPC/(1 – MPC))]ΔG ΔY = ΔG. This expression tells us how output changes, holding the interest rate constant. It says that an equal increase in government purchases and taxes shifts the IS curve to the right by the amount that G increases. This shift is shown in Figure 12-7. Output increases, but by less than the amount that G and T increase; this means that disposable income Y – T falls. As a result, consumption also falls. The interest rate rises, causing investment to fall. 2. a. The invention of the new high-speed chip increases investment demand, meaning that at every interest rate, firms want to invest more. The increase in the demand for investment goods shifts the IS curve out and to the right, raising income and employment. Figure 12-8 shows the effect graphically. The increase in income from the higher investment demand also raises interest rates. This happens because the higher income raises demand for money; since the supply of money does not change, the interest rate must rise in order to restore equilibrium in the money market. The rise in interest rates partially offsets the increase in investment demand, so that output does not rise by the full amount of the rightward shift in the IS curve. Overall, income, interest rates, consumption, and investment all rise. If the Federal Reserve wants to keep output constant, then it must decrease the money supply and increase interest rates further in order to offset the effect of the increase in investment demand. When the Fed decreases the money supply, the LM curve will shift up and to the left. Output will remain at the same level and the interest rate will be higher. There will be no change in consumption and no change in investment. The interest rate will increase by enough to completely offset the initial increase in investment demand. b. The increased demand for cash shifts the LM curve up. This happens because at any given level of income and money supply, the interest rate necessary to equilibrate the money market is higher. Figure 12-9 shows the effect of this LM shift graphically. The upward shift in the LM curve lowers income and raises the interest rate. Consumption falls because income falls, and investment falls because the interest rate rises due to the increase in money demand. If the Federal Reserve wants to keep output constant, then it must increase the money supply in order to lower the interest rate and bring output back to its original level. The LM curve will shift down and to the right and return to its old position. In this case, nothing will change. c. At any given level of income, consumers now wish to save more and consume less. Because of this downward shift in the consumption function, the IS curve shifts inward. Figure 12-10 shows the effect of this IS shift graphically. Income, interest rates, and consumption all fall, while investment rises. Income falls because at every level of the interest rate, planned expenditure falls. The interest rate falls because the fall in income reduces demand for money; since the supply of money is unchanged, the interest rate must fall to restore money-market equilibrium. Consumption falls both because of the shift in the consumption function and because income falls. Investment rises because of the lower interest rates and partially offsets the effect on output of the fall in consumption. If the Federal Reserve wants to keep output constant, then it must increase the money supply in order to reduce the interest rate and increase output back to its original level. The increase in the money supply will shift the LM curve down and to the right. Output will remain at its original level, consumption will be lower, investment will be higher, and interest rates will be lower. d. An increase in expected inflation will reduce people’s demand for money. This fall in the demand for money will shift the LM curve down and to the right, as illustrated in Figure 12-11. The interest rate will have to fall to maintain equilibrium in the money market, and this fall in the interest rate will increase investment spending. Equilibrium output will rise, and so will consumption. If the Federal Reserve wants to keep output constant, then it must decrease the money supply. The LM curve will shift back to its old position and nothing will change. 3. a. The IS curve is given by Y = C(Y – T) + I(r) + G. We can plug in the consumption and investment functions and values for G and T as given in the question and then rearrange to solve for the IS curve for this economy: Y = 300 + 0.60(Y – 500) + 700 – 80r + 500 Y – 0.60Y = 1,200 – 80r (1 – 0.60)Y = 1,200 – 80r Y = (1/0.40) (1,200 – 80r) Y = 3,000 – 200r. This IS equation is graphed in Figure 12-12 for r ranging from 0 to 8. Figure 12-12 b. The LM curve is determined by equating the demand for and supply of real money balances. The supply of real balances is 3,000/3 = 1,000. Setting this equal to money demand, we find: 1,000 = Y – 200r. Y = 1,000 + 200r. This LM curve is graphed in Figure 12-12 for r ranging from 0 to 8. c. If we take the price level as given, then the IS and the LM equations give us two equations in two unknowns, Y and r. We found the following equations in parts (a) and (b): IS: Y = 3,000 – 200r. LM: Y = 1,000 + 200r. Equating these, we can solve for r: 3,000 – 200r = 1,000 + 200r 2,000 = 400r r = 5. Now that we know r, we can solve for Y by substituting it into either the IS or the LM equation. We find Y = 2,000. Therefore, the equilibrium interest rate is 5 percent and the equilibrium level of output is 2,000, as depicted in Figure 12-12. d. If government purchases increase from 500 to 700, then the IS equation becomes: Y = 300 + 0.60(Y – 500) + 700 – 80r + 700. Simplifying, we find: Y = 3,500 – 200r. This IS curve is graphed as IS2 in Figure 12-13. We see that the IS curve shifts to the right by 500. Figure 12-13 By equating the new IS curve with the LM curve derived in part (b), we can solve for the new equilibrium interest rate: 3,500 – 200r = 1,000 + 200r 2,500 = 400r 6.25= r. We can now substitute r into either the IS or the LM equation to find the new level of output. We find: Y = 2,250. Therefore, the increase in government purchases causes the equilibrium interest rate to rise from 5 percent to 6.25 percent, while output increases from 2,000 to 2,250. This is depicted in Figure 1213. e. If the money supply increases from 3,000 to 4,500, then the LM equation becomes: (4,500/3) = Y – 200r, or Y = 1,500 + 200r. This LM curve is graphed as LM2 in Figure 12-14. We see that the LM curve shifts to the right by 500 because of the increase in real money balances. Figure 12-14 To determine the new equilibrium interest rate and level of output, equate the IS curve from part (a) with the new LM curve derived above: 3,000 – 200r = 1,500 + 200r 1,500 = 400r 3.75 = r. Substituting this into either the IS or the LM equation, we find Y = 2,250. Therefore, the increase in the money supply causes the interest rate to fall from 5 percent to 3.75 percent, while output increases from 2,000 to 2,250. This is depicted in Figure 12–14. f. If the price level rises from 3 to 5, then real money balances fall from 1,000 to 3,000/5 = 600. The LM equation becomes: Y = 600 + 200r. As shown in Figure 12-15, the LM curve shifts to the left by 400 because the increase in the price level reduces real money balances. Figure 12-15 To determine the new equilibrium interest rate, equate the IS curve from part (a) with the new LM curve from above: 3,000 – 200r = 600 + 200r 2,400 = 400r 6 = r. Substituting this interest rate into either the IS or the LM equation, we find Y = 1,800. Therefore, the new equilibrium interest rate is 6, and the new equilibrium level of output is 1,800, as depicted in Figure 12-15. g. The aggregate demand curve is a relationship between the price level and the level of income. To derive the aggregate demand curve, we want to solve the IS and the LM equations for Y as a function of P. That is, we want to substitute out for the interest rate. We can do this by solving the IS and the LM equations for the interest rate: IS: Y = 3,000 – 200r 200r = 3,000 – Y. LM: (M/P) = Y – 200r 200r = Y – (M/P). Combining these two equations, we find: 3,000 – Y = Y – (M/P) 2Y = 3,000 + M/P Y = 1,500 + M/2P. Since the nominal money supply M equals 3,000, this becomes: Y = 1,500 + 1,500/P. This aggregate demand equation is graphed in Figure 12-16. Figure 12-16 How does the increase in fiscal policy of part (d) affect the aggregate demand curve? We can see this by deriving the aggregate demand curve using the IS equation from part (d) and the LM curve from part (b): IS: Y = 3,500 – 200r 200r = 3,500 – Y. LM: (3,000/P) = Y – 200r 200r = Y – (3,000/P). Combining and solving for Y: 3,500 – Y = Y – (3,000/P), or: Y = 1,750 + 1,500/P. By comparing this new aggregate demand equation to the one previously derived, we can see that the increase in government purchases by 200 shifts the aggregate demand curve to the right by 250. How does the increase in the money supply of part (e) affect the aggregate demand curve? Because the AD curve is Y = 1,500 + M/2P, the increase in the money supply from 3,000 to 4,500 causes it to become Y = 1,500 + 2,250/P. By comparing this new aggregate demand curve to the one originally derived, we see that the increase in the money supply shifts the aggregate demand curve to the right. 4. a. The IS curve is given by: Y = C(Y – T) + I(r) + G. We can plug in the consumption and investment functions and values for G and T as given in the question and then rearrange to solve for the IS curve for this economy: Y = 500 + 0.75(Y – 1,000) + 1,000 – 50r + 1,000 Y – 0.75Y = 1,750 – 50r (1 – 0.75)Y = 1,750 – 50r Y = (1/0.25) (1,750 – 50r) Y = 7,000 – 200r. The LM curve is determined by equating the demand for and supply of real money balances. The supply of real balances is 6,000/2 = 3,000. Setting this equal to money demand, we find: 3,000 = Y – 200r. Y = 3,000 + 200r. Equating the IS and LM equations, we can solve for r: 7,000 – 200r = 3,000 + 200r 4,000 = 400r r = 10. Now that we know r, we can solve for Y by substituting it into either the IS or the LM equation. We find: Y = 5,000. Therefore, the equilibrium interest rate is 10 percent and the equilibrium level of output is 5,000. This is labeled as point a in Figure 12-17 in part e below. b. If taxes fall by 20% then taxes are now equal to 800 and we can recalculate the IS curve equation: Y = 500 + 0.75(Y – 800) + 1,000 – 50r + 1,000 Y – 0.75Y = 1,900 – 50r (1 – 0.75)Y = 1,900 – 50r Y = (1/0.25) (1,900 – 50r) Y = 7,600 – 200r. Equating the new IS and old LM equations, we can solve for r: 7,600 – 200r = 3,000 + 200r 4,600 = 400r r = 11.5. Now that we know r, we can solve for Y by substituting it into either the IS or the LM equation. We find: Y = 5,300. Therefore, the equilibrium interest rate is 11.5 percent and the equilibrium level of output is 5,300. The decrease in taxes will shift the IS curve to the right. The new equilibrium point is labeled as point b in Figure 12-17 in part e below. The tax multiplier measures the change in equilibrium output divided by the change in taxes, or 300/-200 = -1.5. c. To find the value of the money supply that will keep the interest rate at the original level of 10 percent after the tax cut, rewrite the LM curve equation so that it is a function of M: M/2 = Y – 200r Y = M/2 + 200r. Now we can equate this new equation for the LM curve with the new IS curve, plug in the value of 10 for the interest rate r and solve for the money supply M: 7,600 – 200r = M/2 + 200r 7,600 – 200(10) = M/2 + 200(10) M = 7,200. If the money supply has a value of 7,200 then the level of output is 5,600. The increase in the money supply will shift the LM curve to the right. This new equilibrium point is illustrated as point c in Figure 12-17 in part e below. The tax multiplier measures the change in equilibrium output divided by the change in taxes, or 600/-200 = -3. d. To find the value of the money supply that will keep output at the original level of 5,000 after the tax cut, rewrite the LM curve equation so that it is a function of M, and solve for r: M/2 = Y – 200r 200r = Y – M/2 r = Y/200 – M/400. Rewrite the IS curve equation so that r is defined as a function of Y: Y = 7,600 – 200r 200r = 7,600 – Y r = 7,600/200 – Y/200. Now we can equate these new equations for the IS and LM curves, plug in the value of 5,000 for the level of output Y and solve for the money supply M: 7,600/200 – Y/200 = Y/200 – M/400 7,600 – Y = Y – M/2 M = 4,800. \ If the money supply has a value of 4,800 then the level of the interest rate is 13. The decrease in the money supply will shift the LM curve to the left. This new equilibrium point is illustrated as point d in Figure 12-17 in part e below. The tax multiplier measures the change in equilibrium output divided by the change in taxes, or 0/-200 = 0. Note that this problem could have been solved in a different way. From the IS curve equation, if you know Y is equal to 5,000 then you can solve for the interest rate r. You can then plug these values for output and the interest rate into the LM curve equation and solve for the money supply M. e. The four equilibrium points are illustrated in Figure 12-17. Figure 12-17 5. a. This statement is false. Investment is part of planned expenditure, so changes in investment have an impact of the IS curve and not the LM curve. b. This statement is true. The IS curve represents the relationship between the interest rate and the level of income that arises from equilibrium in the market for goods and services. That is, it describes the combinations of income and the interest rate that satisfy the equation Y = C(Y – T) + I(r) + G. If investment does not depend on the interest rate, then nothing in the IS equation depends on the interest rate; income must adjust to ensure that the quantity of goods produced, Y, equals the quantity of goods demanded, C + I + G. Thus, the IS curve is vertical at this level, as shown in Figure 12-18. Monetary policy has no effect on output, because the IS curve determines Y. Monetary policy can affect only the interest rate. In contrast, fiscal policy is effective: output increases by the full amount that the IS curve shifts. c. This statement is false. Money demand helps determine equilibrium in the money market, and this will have an impact on the LM curve and not the IS curve. d. This statement is true. The LM curve represents the combinations of income and the interest rate at which the money market is in equilibrium. If money demand does not depend on the interest rate, then we can write the LM equation as: M/P = L(Y). For any given level of real balances M/P, there is only one level of income at which the money market is in equilibrium. Thus, the LM curve is vertical, as shown in Figure 12-19. Fiscal policy now has no effect on output; it can affect only the interest rate. Monetary policy is effective: a shift in the LM curve increases output by the full amount of the shift. e. This sentence is true. If money demand does not depend on income, then we can write the LM equation as M/P = L(r). For any given level of real balances M/P, there is only one level of the interest rate at which the money market is in equilibrium. Hence, the LM curve is horizontal, as shown in Figure 12-20. Fiscal policy is very effective: output increases by the full amount that the IS curve shifts. Monetary policy is also effective: an increase in the money supply causes the interest rate to fall, so the LM curve shifts down, as shown in Figure 12-20. f. This statement is true. The LM curve gives the combinations of income and the interest rate at which the supply and demand for real balances are equal, so that the money market is in equilibrium. The general form of the LM equation is: M/P = L(r, Y). Suppose income Y increases by $1. How much must the interest rate change to keep the money market in equilibrium? The increase in Y increases money demand. If money demand is extremely sensitive to the interest rate, then it takes a very small increase in the interest rate to reduce money demand and restore equilibrium in the money market. Hence, the LM curve is (nearly) horizontal, as shown in Figure 12-21. An example may make this clearer. Consider a linear version of the LM equation: M/P = eY – fr. Note that as f gets larger, money demand becomes increasingly sensitive to the interest rate. Rearranging this equation to solve for r, we find r = (e/f)Y – (1/f)(M/P). We want to focus on how changes in each of the variables are related to changes in the other variables. Hence, it is convenient to write this equation in terms of changes: Δr = (e/f)ΔY – (1/f)Δ(M/P). The slope of the LM equation tells us how much r changes when Y changes, holding M fixed. If Δ(M/P) = 0, then the slope is Δr/ΔY = (e/f). As f gets very large, this slope gets closer and closer to zero. If money demand is very sensitive to the interest rate, then fiscal policy is very effective: with a horizontal LM curve, output increases by the full amount that the IS curve shifts. Monetary policy is now completely ineffective: an increase in the money supply does not shift the LM curve at all. We see this in our example by considering what happens if M increases. For any given Y (so that we set ΔY = 0), Δr/Δ(M/P) = (–1/f); this tells us how much the LM curve shifts down. As f gets larger, this shift gets smaller and approaches zero. (This is in contrast to the horizontal LM curve in part (c), which does shift down.) 6. a. To raise investment while keeping output constant, the government should adopt a loose monetary policy and a tight fiscal policy, as shown in Figure 12-22. In the new equilibrium at point B, the interest rate is lower, so that investment is higher. The tight fiscal policy—reducing government purchases, for example—offsets the effect of this increase in investment on output. b. The policy mix in the early 1980s did exactly the opposite. Fiscal policy was expansionary, while monetary policy was contractionary. Such a policy mix shifts the IS curve to the right and the LM curve to the left, as in Figure 12-23. The real interest rate rises and investment falls. rises from Y to Y2. The increase in output occurs because the lower interest rate stimulates investment, which increases output. Since the level of output is now above its long-run level, prices begin to rise. A rising price level lowers real balances, which raises the interest rate. As indicated in Figure 12-24, the LM curve shifts back to the left. Prices continue to rise until the economy returns to its original position at point A. The interest rate returns to r1, and investment returns to its original level. Thus, in the long run, there is no impact on real variables from an increase in the money supply. (This is what we called monetary neutrality in Chapter 5.) b. An increase in government purchases shifts the IS curve to the right, and the economy moves from point A to point B, as shown in Figure 12-25. In the short run, output increases from Y to Y2, and the interest rate increases from r1 to r2. The increase in the interest rate reduces investment and “crowds out” part of the expansionary effect of the increase in government purchases. Initially, the LM curve is not affected because government spending does not enter the LM equation. After the increase, output is above its longrun equilibrium level, so prices begin to rise. The rise in prices reduces real balances, which shifts the LM curve to the left. The interest rate rises even more than in the short run. This process continues until the long-run level of output is again reached. At the new equilibrium, point C, interest rates have risen to r3, and the price level is permanently higher. Note that, like monetary policy, fiscal policy cannot change the long-run level of output. Unlike monetary policy, however, it can change the composition of output. For example, the level of investment at point C is lower than it is at point A. c. An increase in taxes reduces disposable income for consumers, shifting the IS curve to the left, as shown in Figure 12-26 In the short run, output and the interest rate decline to Y2 and r2 as the economy moves from point A to point B. Initially, the LM curve is not affected. In the longer run, prices begin to decline because output is below its long-run equilibrium level, and the LM curve then shifts to the right because of the increase in real money balances. Interest rates fall even further to r3 and, thus, further stimulate investment and increase income. In the long run, the economy moves to point C. Output returns to Y, the price level and the interest rate are lower, and the decrease in consumption has been offset by an equal increase in investment. 8. Figure 12-27(A) shows what the IS–LM model looks like for the case in which the Fed holds the money supply constant. Figure 12-27(B) shows what the model looks like if the Fed adjusts the money supply to hold the interest rate constant; this policy makes the effective LM curve horizontal. a. If all shocks to the economy arise from exogenous changes in the demand for goods and services, this means that all shocks are to the IS curve. Suppose a shock causes the IS curve to shift from IS1 to IS2. Figures 12-28(A) and (B) show what effect this has on output under the two policies. It is clear that output fluctuates less if the Fed follows a policy of keeping the money supply constant. Thus, if all shocks are to the IS curve, then the Fed should follow a policy of keeping the money supply constant. b. If all shocks in the economy arise from exogenous changes in the demand for money, this means that all shocks are to the LM curve. If the Fed follows a policy of adjusting the money supply to keep the interest rate constant, then the LM curve does not shift in response to these shocks—the Fed immediately adjusts the money supply to keep the money market in equilibrium. Figures 1229(A) and (B) show the effects of the two policies. It is clear that output fluctuates less if the Fed holds the interest rate constant, as in Figure 12-29(B). If the Fed holds the interest rate constant and offsets shocks to money demand by changing the money supply, then all variability in output is eliminated. Thus, if all shocks are to the LM curve, then the Fed should adjust the money supply to hold the interest rate constant, thereby stabilizing output. 9. a. The analysis of changes in government purchases is unaffected by making money demand dependent on disposable income instead of total expenditure. An increase in government purchases shifts the IS curve to the right, as in the standard case. The LM curve is unaffected by this increase. Thus, the analysis is the same as it was before; this is shown in Figure 12-30. b. A tax cut causes disposable income Y – T to increase at every level of income Y. This increases consumption for any given level of income as well, so the IS curve shifts to the right, as in the standard case. This is shown in Figure 12-31. If money demand depends on disposable income, however, then the tax cut increases money demand, so the LM curve shifts upward, as shown in the figure. Thus, the analysis of a change in taxes is altered drastically by making money demand dependent on disposable income. As shown in the figure, it is possible for a tax cut to be contractionary. 10. a. The goods market is in equilibrium when output is equal to planned expenditure, or Y = PE. Starting with this equilibrium condition, and making the substitutions from the information given in the problem, results in the following expression for equilibrium output Y: Y = C + I + G Y = C(Y – T) + I(r) + G Y = a + b(Y – T) + c – dr + G (1 – b)Y = a – bT + c – dr + G Y = a-bT+c-dr+G . 1-b b. The slope of the IS curve is measured as: Dr . DY From the equation in part (a), the slope of the IS curve can be found as follows: Dr 1 1 (1-b) = = = . Dy (DY /Dr) -(d /(1-b)) d Mathematically, as the parameter d becomes a larger number, the slope becomes a smaller number in absolute value terms and the IS curve becomes flatter. Intuitively, if the parameter d is a larger number, then investment is more responsive to changes in the interest rate. Any given decrease in the interest rate will cause a larger increase in investment and, via the multiplier effect, cause a larger increase in equilibrium output Y. This makes the IS curve flatter. c. A $100 increase in government spending will cause a larger horizontal shift in the IS curve than a $100 tax cut. From the equation for equilibrium output in part (a), note that the impact of the tax cut depends on the marginal propensity to consume, as given by the parameter b. If the MPC is 0.75, for example, then a $100tax cut will shift the IS curve by only $75. Intuitively, this makes sense because the entire $100 increase in government spending will be spent, whereas only a portion of the tax cut will be spent, and the rest will be saved depending on the size of the MPC. d. Money-market equilibrium occurs where the demand for real balances is equal to the supply of real balances. Using the given information about the demand for real balances, we can solve for the equilibrium interest rate: M = L(r,Y) = eY - fr P M fr = eY - P eY M r = - f fP e. The slope of the LM curve is measured as Dr . DY From the equation in part (d), the slope of the LM curve is e/f. As the parameter f becomes a larger number, the slope becomes smaller and the LM curve becomes flatter. Intuitively, as the parameter f becomes a larger number, money demand is more responsive to changes in the interest rate. This means that any increase in income that leads to an increase in money demand will require a relatively small increase in the interest rate to restore equilibrium in the money market. f. The size of the horizontal shift in the LM curve caused by a change in the money supply M can be measured by looking at where the LM curve crosses the horizontal axis. From the equation in part (d), set r equal to zero and solve for Y to find the horizontal intercept: the LM curve crosses the horizontal axis where Y = M/eP. Mathematically, a $100 change in the money supply has a smaller effect on the horizontal intercept the larger the value of the parameter e. When the parameter e is larger, money demand is more responsive to changes in income Y, and the LM curve is steeper. Intuitively, if income increases and the parameter e is relatively larger, then money demand increases by a larger amount. This then requires a larger increase in the interest rate to restore money-market equilibrium and the LM curve becomes relatively steeper. Overall, the increase in the money supply will lower the interest rate and increase investment spending and output. When output rises, so does money demand, and if the parameter e is relatively large, then the interest rate will need to rise by a larger amount to restore equilibrium in the money market. The overall effect on equilibrium output is relatively smaller, as given by the smaller horizontal shift in the LM curve. The parameter f has no effect on the size of the horizontal shift in the LM curve caused by a change in the money supply. The parameter f affects the vertical shift and the slope of the LM curve but not the horizontal shift. g. To derive the aggregate demand curve, substitute the result for part (d) into the result for part (a) and solve for Y: Y = a-bT +c+G - d eY - M 1-b 1-bŁ f fPł Y 1+ de = a-bT +c+G + dM Ł f (1-b)ł 1-b f (1-b)P Y = f (a-bT +c+G)+ dM f (1-b)+de غ f (1-b)+deøßP h. The aggregate demand curve has a negative slope, as can be seen from the equation in part (g) above. An increase in the price level P will decrease the value of the second term on the right side, and therefore output Y will fall. i. An increase in the money supply, an increase in government spending, and a decrease in taxes all shift the aggregate demand curve to the right, as can be seen from the equation for the aggregate demand curve found in part (g). Looking at the first term on the right side, we see that an increase in G or a decrease in T will increase the value of this term and shift the aggregate demand curve to the right. Looking at the second term on the right side, an increase in the money supply for any given value of the price level will increase the value of output and therefore shift the aggregate demand curve to the right. If the parameter f has a value of zero, then the first term on the right side is zero and changes in government spending and taxes do not affect the aggregate demand curve. In this case, the LM curve is vertical and changes in fiscal policy that shift the IS curve have no effect on output. Monetary policy is still effective in this case, and an increase in the money supply will still shift the aggregate demand curve to the right. In this case, the aggregate demand curve is given by: M Y = . eP Context ▪ Chapter 10 introduced the model of aggregate demand and supply. ▪ Chapter 11 developed the IS-LM model, the basis of the aggregate demand curve. IN THIS CHAPTER, YOU WILL LEARN: ▪ how to use the IS-LM model to analyze the effects of shocks, fiscal policy, and monetary policy ▪ how to derive the aggregate demand curve from the IS-LM model ▪ several theories about what caused the Great Depression Equilibrium in the IS -LM model The IS curve represents equilibrium in the goods market. Y CY T Ir G= ( − )+ ( )+ The LM curve represents money market equilibrium. MP LrY= ( , ) The intersection determines Y1 the unique combination of Y and r that satisfies equilibrium in both markets. Policy analysis with the IS -LM model Y CY T Ir G= ( − )+ ( )+ r MP LrY= ( , ) We can use the IS-LM model to analyze the r1 effects of • fiscal policy: G and/or T • monetary policy: MY Y1 An increase in government purchases 1. IS curve shifts right r 1 by G 1−MPC causing output & income to rise. 2. This raises money demand, causing the interest rate to rise… 3. …which reduces investment, so the final increase in Y 1 is smaller than G 1−MPC A tax cut Consumers save r (1−MPC) of the tax cut, so the initial boost in spending is smaller for ΔT than for an equal ΔG… and the IS curve shifts by −MPC 1. T 1−MPC …so the effects on r and Y are smaller for ΔT than for an equal ΔG. Monetary policy: An increase in M 1. ΔM > 0 shifts the LM curve down (or to the right) 2. …causing the interest rate to fall 3. …which increases investment, causing output & income to rise. Interaction between monetary & fiscal policy ▪ Model: ▪ Monetary & fiscal policy variables (M, G, and T ) are exogenous. ▪ Real world: ▪ Monetary policymakers may adjust M in response to changes in fiscal policy, or vice versa. ▪ Such interactions may alter the impact of the original policy change. The Fed’s response to ΔG > 0 ▪ Suppose Congress increases G. ▪ Possible Fed responses: 1. hold M constant 2. hold r constant 3. hold Y constant ▪ In each case, the effects of the ΔG are different… Response 1: Hold M constant If Congress raises G, r the IS curve shifts right. If Fed holds M constant, then LM curve doesn’t r2 r1 shift. Results: = −Y Y Y2 1 Y1Y2 Y = −r r r2 1 Response 2: Hold r constant If Congress raises G, r the IS curve shifts right. To keep r constant, Fed increases M r2 r1 to shift LM curve right. Results: = −Y Y Y3 1 Y1Y2Y3 Y =r 0 Response 3: Hold Y constant If Congress raises G, r LM2 the IS curve shifts right. To keep Y constant, r3 Fed reduces M r2 r1 to shift LM curve left. Results: =Y 0 Y1Y2 Y = −r r r3 1 Shocks in the IS -LM model IS shocks: exogenous changes in the demand for goods & services. Examples: ▪ stock market boom or crash change in households’ wealth ΔC ▪ change in business or consumer confidence or expectations ΔI and/or ΔC Shocks in the IS -LM model LM shocks: exogenous changes in the demand for money. Examples: ▪ A wave of credit card fraud increases demand for money. ▪ More ATMs or the Internet reduce money demand. NOW YOU TRY Analyze shocks with the IS-LM model Use the IS-LM model to analyze the effects of 1. a housing market crash that reduces consumers’ wealth 2. consumers using cash in transactions more frequently in response to an increase in identity theft For each shock, a. use the IS-LM diagram to determine the effects on Y and r. b. figure out what happens to C, I, and the unemployment rate. ▪ During 2001: ▪ 2.1 million jobs lost, unemployment rose from 3.9% to 5.8%. ▪ GDP growth slowed to 0.8% (compared to 3.9% average annual growth during 1994–2000). Causes: 1) Stock market decline C Causes: 2) 9/11 ▪ increased uncertainty ▪ fall in consumer & business confidence ▪ result: lower spending, IS curve shifted left Causes: 3) Corporate accounting scandals ▪ Enron, WorldCom, etc. ▪ reduced stock prices, discouraged investment Fiscal policy response: shifted IS curve right ▪ tax cuts in 2001 and 2003 ▪ spending increases ▪ airline industry bailout ▪ NYC reconstruction ▪ Afghanistan war Monetary policy response: shifted LM curve right What is the Fed’s policy instrument? ▪ The news media commonly report the Fed’s policy changes as interest rate changes, as if the Fed has direct control over market interest rates. ▪ In fact, the Fed targets the federal funds rate—the interest rate banks charge one another on overnight loans. ▪ The Fed changes the money supply and shifts the LM curve to achieve its target. ▪ Other short-term rates typically move with the federal funds rate. What is the Fed’s policy instrument? Why does the Fed target interest rates instead of the money supply? 1) They are easier to measure than the money supply. 2) The Fed might believe that LM shocks are more prevalent than IS shocks. If so, then targeting the interest rate stabilizes income better than targeting the money supply. (See problem 8 on p.364.) IS-LM and aggregate demand ▪ So far, we’ve been using the IS-LM model to analyze the short run, when the price level is assumed fixed. ▪ However, a change in P would shift LM and therefore affect Y. ▪ The aggregate demand curve (introduced in Chap. 10) captures this relationship between P and Y. Deriving the AD curve r LM(P ) Intuition for slope r2 LM(P1) of AD curve: r1 P (M/P ) LM shifts left Y r P P2 I P1 Y Monetary policy and the AD curve The Fed can increase aggregate demand: M LM shifts right r I Y at each value of P Fiscal policy and the AD curve Expansionary fiscal policy (G and/or T ) increases agg. demand: T C IS shifts right Y at each value of P IS-LM and AD-AS in the short run & long run Recall from Chapter 10: The force that moves the economy from the short run to the long run is the gradual adjustment of prices. In the short-run equilibrium, if then over time, the price level will Y Y rise Y Y fall Y Y= remain constant A negative IS shock 1 shifts IS and AD left, causing Y to fall. IS1 P In the new short-run equilibrium, Y Y IS1 Over time, P gradually falls, causing: • SRAS to move down • M/P to increase, which causes LM to move down Over time, P gradually falls, causing: • SRAS to move down • M/P to increase, which causes LM to move down IS1 This process continues IS1 until economy reaches a long-run equilibrium with Y Y= P THE SPENDING HYPOTHESIS: Shocks to the IS curve ▪ Asserts the Depression was largely due to an exogenous fall in the demand for goods & services—a leftward shift of the IS curve. ▪ Evidence: output and interest rates both fell, which is what a leftward IS shift would cause. THE SPENDING HYPOTHESIS: Reasons for the IS shift ▪Stock market crash reduced consumption ▪Oct 1929–Dec 1929: S&P 500 fell 17% ▪Oct 1929–Dec 1933: S&P 500 fell 71% ▪ Drop in investment ▪ Correction after overbuilding in the 1920s. ▪ Widespread bank failures made it harder to obtain financing for investment. ▪ Contractionary fiscal policy ▪ Politicians raised tax rates and cut spending to combat increasing deficits. THE MONEY HYPOTHESIS: A shock to the LM curve ▪ Asserts that the Depression was largely due to huge fall in the money supply. ▪ Evidence: M1 fell 25% during 1929–33. ▪ But, two problems with this hypothesis: ▪ P fell even more, so M/P actually rose slightly during 1929–31. ▪ nominal interest rates fell, which is the opposite of what a leftward LM shift would cause. ▪ Asserts that the severity of the Depression was due to a huge deflation: P fell 25% during 1929–33. ▪ This deflation was probably caused by the fall in M, so perhaps money played an important role after all. ▪ In what ways does a deflation affect the economy? ▪ The stabilizing effects of deflation: ▪P (M/P) LM shifts right Y ▪ Pigou effect: P (M/P ) consumers’ wealth C IS shifts right Y ▪ The destabilizing effects of expected deflation: E π r for each value of i I because I = I (r ) planned expenditure & agg. demand income & output ▪ The destabilizing effects of unexpected deflation: debt-deflation theory P (if unexpected) transfers purchasing power from borrowers to lenders borrowers spend less, lenders spend more if borrowers’ propensity to spend is larger than lenders’, then aggregate spending falls, the IS curve shifts left, and Y falls Why another Depression is unlikely ▪ Policymakers (or their advisers) now know much more about macroeconomics: ▪ The Fed knows better than to let M fall so much, especially during a contraction. ▪ Fiscal policymakers know better than to raise taxes or cut spending during a contraction. ▪ Federal deposit insurance makes widespread bank failures very unlikely. ▪ Automatic stabilizers make fiscal policy expansionary during an economic downturn. CASE STUDY The 2008–09 financial crisis & recession ▪ 2009: Real GDP fell, u-rate approached 10% ▪ Important factors in the crisis: ▪ early 2000s Federal Reserve interest rate policy ▪ subprime mortgage crisis ▪ bursting of house price bubble, rising foreclosure rates ▪ falling stock prices ▪ failing financial institutions ▪ declining consumer confidence, drop in spending on consumer durables and investment goods C H A P T E R S U M M A R Y 1. IS-LM model ▪a theory of aggregate demand ▪exogenous: M, G, T, P exogenous in short run, Y in long run ▪endogenous: r, Y endogenous in short run, P in long run ▪IS curve: goods market equilibrium ▪LM curve: money market equilibrium 55 C H A P T E R S U M M A R Y 2. AD curve ▪shows relation between P and the IS-LM model’s equilibrium Y. ▪negative slope because P (M/P) r I Y ▪ expansionary fiscal policy shifts IS curve right, raises income, and shifts AD curve right. ▪ expansionary monetary policy shifts LM curve right, raises income, and shifts AD curve right. ▪ IS or LM shocks shift the AD curve. 56 Solution Manual for Macroeconomics Gregory N. Mankiw 9781464182891, 9781319106058
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