# Chapter 11: Extending the Sticky-Price Model: IS- LM, International Side, and AS-AD

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1 Chapter 11 1 Final Chapter 11: Extending the Sticky-Price Model: IS- LM, International Side, and AS-AD J. Bradford DeLong Questions What is money-market equilibrium? What is the LM Curve? What determines the equilibrium level of real GDP when the central bank's policy is to keep the money stock constant? What is the IS-LM framework? What is an IS shock? What is an LM shock? What is the relationship between shifts in the equilibrium on the IS-LM diagram and changes in the real exchange rate?

2 Chapter 11 2 Final What is the relationship between shifts in the equilibrium on the IS-LM diagram and changes in the balance of trade? What is the aggregate supply curve? What is the aggregate demand curve? The IS curve as presented in Chapter 10 is enough to enable us to think about business cycles, as long as the central bank uses open market operations to set the real interest rate. But not all central banks peg interest rates today. Not all central banks that peg interest rates today pegged them in the past. So the analysis of Chapter 10 is not complete, because it lacks a theory of what determines the real interest rate in those cases in which it is not the interest rate but the money stock that is fixed. Moreover, even when central banks do peg interest rates, they usually peg not real but nominal interest rates. To think through the relationship between nominal and real interest rates, we need to understand the determinants of inflation. Thus this chapter, Chapter 11, is needed to build more analytical tools to extend the sticky-price model. In this chapter, we first derive an LM curve to serve as a sibling to the IS curve. The LM curve tells us how interest rates are determined when the stock of liquid money is fixed. The LM curve joins the IS curve in the IS-LM framework and diagram, which provides our analysis of the determinants of real GDP and the interest rate when the money stock is fixed.

3 Chapter 11 3 Final Second, we examine in more detail the international side. We examine the effects of changes in the economy s equilibrium on international economic variables, and the effects of changes abroad on the domestic economy s equilibrium. Third, we begin the process of understanding what determines the price level and the inflation rate in the sticky-price macroeconomic model. We summarize all the previous parts of Section IV in an aggregate demand or AD relationship that tells how aggregate demand is associated with the price level and the inflation rate. We also present a model of aggregate supply, AS, to understand the relationship between real GDP and the price level. Putting these two together generates the AS-AD framework, which allows us to analyze not just the level of real GDP but also how changes in real GDP affect the price level The Money Stock and the Money Market: The LM Curve Money Market Equilibrium Recall from Chapter 8 three facts about business and household demand for money, where demand for money is economist-speak for the quantity of readily-spendable liquid assets held in one s portfolio: Money demand is proportional to total nominal income P x Y.

4 Chapter 11 4 Final Money demand has a time trend, the result of slow changes in banking-sector structure and technology. Money demand is inversely related to the nominal interest rate. Money demand is inversely related to the nominal interest rate because the nominal interest rate is the opportunity cost of holding money. Money balances earn effectively zero real interest, and over time they lose their power to purchase real, useful goods and services at the rate of inflation π. If money balances were sold and the proceeds put into some other investment, they would earn the prevailing market real interest rate r. Thus the opportunity cost of holding wealth in the form of money is the nominal interest rate i = r + π e : the sum of the real interest rate r and the expected inflation rate π e. To keep our model simple, we ignore the time trend in velocity and write the demand for money as the function: M d P = Y V 0 + V i (r + π e ) Because the left hand side is the nominal money stock divided by the price level, this equation represents real money demand a demand for an amount of liquid power to purchase goods and services, rather than a demand for a stack of dollar bills. This equation shows that money demand is proportional to real GDP Y: the higher is real GDP, the more real money balances people wish to hold. The plus sign in front of the V i parameter means that velocity is an increasing function of the nominal interest rate, and thus money demand is a decreasing function of the nominal interest rate. The higher is the nominal interest rate, the higher is the opportunity cost of holding money, and the lower is the real quantity of money demanded, as Figure 11.1 shows.

5 Chapter 11 5 Final Figure 11.1: Money Demand and Money Supply Nominal Interest Rate =r+π Equilibrium Nominal Interest Rate Money Demand: (V - V (r+π)) 0 i Y Money Supply =M s Real Quantity of Money Legend: When the stock of liquid monetary assets is fixed, the equilibrium shortterm nominal interest rate is that at which households' and businesses' demand for liquid money is equal to the (fixed) money stock. In a sticky-price model, the price level P is predetermined and thus fixed. It cannot move instantly (as it could and did in the flexible-price model of Chapter 8) to make the money supply M s equal to money demand M d. Since the price level cannot move instantly to keep the money market in equilibrium, the nominal interest rate must adjust instead. So

6 Chapter 11 6 Final given the nominal money supply, the price level, and the level of real GDP, the economy s money market can be in equilibrium only if the nominal interest rate is: i = (r +π e ) = ( Y P) M s V 0 V i The nominal interest rate i=r+π e must be the level at which the money supply and money demand curves in Figure 11.1 cross. This must hold whether the money supply is automatically determined by the monetary system, or is explicitly controlled by the central bank. Suppose money supply is less than money demand, so that households and businesses want to hold more liquid money balances than exist. Businesses and households go to their banks and try to borrow to boost their cash holdings. Banks respond by raising the interest rates they charge for loans. As the nominal interest rate rises, the quantity of money demanded by households and businesses falls because the opportunity cost of holding money has risen. When the nominal interest rate has risen far enough that the quantity of money demanded is equal to the money supply, and households and businesses are no longer trying to increase their liquid money balances, then there is no more upward pressure on the nominal interest rate. On the other hand, suppose that money supply is greater than money demand, so that businesses and households are holding more liquid money balances than they want. They take these liquid money balances and deposit them at the bank. With more cash in their vaults as reserves, banks seek to make more loans, and in order to induce people to borrow they cut interest rates. As the nominal interest rate falls, the quantity of money

7 Chapter 11 7 Final demanded rises because the opportunity cost of holding money has fallen. When the nominal interest rate has fallen enough so that the quantity of money demanded is equal to the money supply, there is no more downward pressure on the nominal interest rate The LM Curve If the money stock is constant, then the fact that demand for money depends on real GDP Y means that the equilibrium nominal interest rate varies whenever real GDP Y varies. At each possible level of total income Y, there is a different curve showing money demand as a function of the nominal interest rate, as Figure 11.2 shows. With a fixed money supply, each of these money demand curves produces a different equilibrium nominal interest rate. If real GDP Y rises and the money supply M s does not, the nominal interest rate must rise too if the money market is to remain in equilibrium. With higher incomes, households and businesses want to hold more money. But if the money supply does not increase, then in aggregate their money holdings cannot grow. Something must curb their demand for liquid cash holdings and so keep money demand equal to money supply, and that something is a higher nominal interest rate, a higher opportunity cost of holding money.

8 Chapter 11 8 Final Figure 11.2: Money Demand Varies as Total Income Y Varies Nominal Interest Rate =r+π Interest rate for high level of Y Interest rate for moderate level of Y Money Demand for a high level of Y Interest rate for low level of Y Money Demand for a moderate level of Y Money Demand for a low level of Y Money Supply =M s Real Quantity of Money Legend: The higher the level of total income, the higher is the quantity of money demanded for any given interest rate, and (for a fixed money stock) the higher will be the equilibrium interest rate. If we draw another diagram with the nominal interest rate i=r+π on the vertical axis and the level of total income Y on the horizontal axis. For each possible value of Y on the x- axis, plot the point whose y-axis value is the equilibrium nominal interest rate, as in Figure The result is the LM curve the economy s current level of the real money stock M s /P. The LM curve slopes upward: at a higher level of real GDP Y, the equilibrium nominal interest rate is higher.

9 Chapter 11 9 Final Figure 11.3: From Money Demand to the LM Curve Nominal Interest Rate =r+π Money Supply and Money Demand Nominal Interest Rate =r+π LM Curve Interest rate for high level of Y Interest rate for moderate level of Y Interest rate for low level of Y Money Supply =M s Real Quantity of Money Total Income Y Low Level of Y Moderate Level of Y High Level of Y Legend: The LM Curve on the right tells us what the nominal interest rate will be for each value of national income Y. The equation for the LM curve is simply the money demand function rewritten with the real GDP by itself on the left-hand side: ( ) M P Y = V 0 + V i (r + π e ) This equation tells us that monetary policy changes that increase the nominal money supply shift the LM curve to the right: the same equilibrium nominal interest rate i corresponds to a higher level of real GDP Y. Monetary policy changes that decrease the nominal money supply shift the LM curve in and to the left. Similarly, a decline in the price level boosts the real money supply (M/P) and shifts the LM curve out to the right. A

10 Chapter Final rise in the price level decreases the real money supply (M/P) and shifts the LM curve in to the left. The IS-LM Framework As long as we know the expected inflation rate, the fact that the nominal interest rate is equal to the real interest rate plus the expected inflation rate means that we can plot the IS and LM curves on the same set of axes, as in Figure This is called the IS-LM diagram. The equilibrium level of real GDP and of the interest rate is at the point where the IS curve and the LM curve cross. At that level of real GDP and total income Y and the real interest rate r, the economy is in equilibrium in both the goods market and the money market. Aggregate demand is equal to total production, so inventories are stable (that's what the IS curve indicates); and money demand is equal to money supply (that's what the LM curve indicates). Box 11.1 shows how to calculate the economy s equilibrium position for some specific parameter values of the sticky-price model.

11 Chapter Final Figure 11.4: The IS-LM Diagram Real Interest Rate r LM Curve Equilibrium Interest Rate IS Curve Real GDP Y Equilibrium Real GDP Legend: What is the economy's equilibrium? The economy's equilibrium is that point at which the IS and LM Curves cross. Along the IS Curve, total production is equal to aggregate demand. Along the LM Curve, the quantity of money demanded by households and businesses is equal to the money stock. Where the curves cross both the goods market and the money market are in balance. Box Example: IS-LM Equilibrium

12 Chapter Final Suppose the economy's marginal propensity to expend [MPE] is 0.5, that the initial level of baseline autonomous spending A 0 is \$5000 billion, and that a one percentage point increase in the real interest rate will reduce the sum of investment and net exports by \$100 billion. Suppose further that the inflation rate π is constant at 3% per year, and that the initial LM curve is: Y = \$ \$ (r + π) Then the economy's initial IS curve will then be: A Y = 0 1 MPE I + X ε r ε r 1 MPE r = \$ \$10000 r = \$10000 \$20000 r The initial equilibrium of the economy is at the one point which is on both the IS and the LM curves. Where is that point? Find it by substituting the LM-curve expression for Y into the IS curve: Y = \$10000 \$20000 r = \$ \$ (r + 3) \$6000 = (\$ \$100000) r r =.05 = 5% r equals 5% per year. And if r equals 5% per year, then equilibrium real GDP Y equals \$9000 billion.

13 Chapter Final Figure 11.5: IS-LM Equilibrium Example Real Interest Rate r LM Curve: Y=\$1000+\$1000 x (r+π) [inflation rate π=3%] Equilibrium Interest Rate: 5% IS Curve: Y=\$10000-\$200 x r Real GDP Y Equilibrium Real GDP: \$9000 IS Shocks Any change in economic policy or the economic environment that increases autonomous spending, such as an increase in government purchases, shifts the IS curve to the right. If the money stock is constant, it moves the economy up and to the right along the LM curve on the IS-LM diagram, as Figure 11.6 shows. The new equilibrium will have both a higher level of real interest rates and a higher equilibrium level of real GDP.

14 Chapter Final Figure 11.6: Effect of a Positive IS Shock Real Interest Rate r An increase in autonomous spending (like an increase in government purchases) shifts the IS curve to the right... LM Curve...It raises the equilibrium interest rate... Old IS Curve Real GDP Y...And it raises the equilibrium level of real GDP. Legend: An expansionary shift in the IS curve raises both real GDP Y and the real interest rate r. Exactly how the total effect of an expansionary shift in the IS curve is divided between increased interest rates and increased real GDP depends on the slope of the LM curve. Box 11.2 provides an example of how to calculate exactly what the effects are. If the LM curve is nearly horizontal (or if the central bank is targeting the money stock--in which case there is no LM curve as such) there will be little or no increase in interest rates. The increase in equilibrium real GDP will be the same magnitude as the outward shift in the

15 Chapter Final IS curve. If the LM curve is very steeply sloped, then there will be a big effect on interest rates and little effect on real GDP. The LM curve will be steeply sloped if demand for money is extremely interest inelastic, and it takes a large change in interest rates to cause a small change in households' and businesses' desired holdings of money. Box Example: An IS Shock Suppose that, as in Box 11.1, the economy's IS curve is: A Y = 0 1 MPE I + X ε r ε r 1 MPE r = \$ \$10000 r = \$10000 \$20000 r And its LM curve is: Y = \$ \$ (r + π) with inflation rate π is constant at 3% per year. Thus the initial equilibrium is as in Box 11.1, with real GDP Y at \$9000 billion and the real interest rate r at 5%. Now suppose that there is a positive real shock to the economy: there is no immediate increase in potential GDP, yet new technological breakthroughs lead businesses to become more optimistic and generate an increase in baseline investment I 0 (and thus in baseline autonomous spending A 0 ) of \$150 billion. What happens to the economy's equilibrium level of output and interest rates? The new IS curve is:

16 Chapter Final Y = A + I MPE I + X ε r ε r \$ \$150 r = \$10000 r = \$10300 \$20000 r 1 MPE Thus the IS curve shifts out and to the right by \$300 billion--the magnitude of the shift in baseline autonomous spending times the multiplier. The LM curve remains unchanged at: Y = \$ \$ (r + π) So, with inflation constant at 3% per year, the new equilibrium can be found by setting the values of Y produced by the IS and LM curve to be equal to each other: Y = \$10300 \$20000 r = \$ \$ (r + 3) \$6300 = (\$ \$100000) r r = 5.25% With the real interest rate r equal to 5.25% per year, annual equilibrium real GDP Y equals \$9250 billion. A \$300 billion outward shift in the IS curve has led to an 0.25% increase in the real interest rate and a \$250 billion increase in real GDP. The higher interest rate has "crowded out" one-sixth of the shift in autonomous spending.

17 Chapter Final Figure 11.7: Calculating the Effect of an IS Shift Real Interest Rate r A \$150 billion increase in baseline investment generates, with an MPS of 0.5, a \$300 billion outward shift in the IS curve... LM Curve: Y=\$1000+\$1000 x (r+π) [inflation rate π=3%]...which raises the equilibrium real interest rate by 0.25%... Old IS Curve: Y=\$10000-\$200 x r...and raises equilibrium real GDP by \$250. Real GDP Y LM Shocks An increase in the money stock will shift the LM curve to the right. The larger money supply means that any given level of real GDP will be associated with a lower equilibrium nominal interest rate. Such an outward LM shift will shift the equilibrium position of the economy down and to the right along the IS curve, as Figure 11.8 shows. The new equilibrium position will have a higher level of equilibrium real GDP and a lower interest rate. Box 11.3 provides an illustrative example of such an expansionary LM shift. Conversely, a decrease in the money supply or any other contractionary LM shock that shifts the LM curve in and to the left will shift the economy up and to the left along the IS curve, resulting in higher equilibrium interest rates and a lower equilibrium value of real GDP.

18 Chapter Final Note the difference between how the money market works in this sticky-price model and in the flexible-price model presented in Section III. In the flexible-price model, the real interest rate balanced the supply and demand for loanable funds flowing through the financial markets. Changes in the money stock had no effect on either the real or the nominal interest rate, the sum of the real interest rate and the expected inflation rate. Instead, the price level adjusted upward or downward to keep the quantity of money demanded equal to the money supply. Here in the sticky-price model the price level is... sticky. It cannot adjust instantly upward or downward. So an imbalance in money demand and money supply does not cause an immediate change in the price level. Instead, it causes an immediate change in the nominal interest rate.

19 Chapter Final Figure 11.8: The Effect of an Expansionary LM Shock Real Interest Rate r An increase in the money stock shifts the LM curve to the right......it lowers the equilibrium interest rate... LM Curve Old IS Curve Real GDP Y...And it raises the equilibrium level of real GDP. Legend: An expansionary shift in the LM curve raises real GDP Y and lowers the equilibrium interest rate r. Box Example: Calculating the Effect of an LM Shock Suppose that, as in Boxes 11.1 and 11.2, the economy's marginal propensity to expend [MPE] is 0.5, the initial level of baseline autonomous spending A 0 is \$5000 billion, and a 1 percentage point increase in the real interest rate reduces the sum of investment and net exports by \$100 billion. Then the economy's initial

20 Chapter Final IS curve is the same: A Y = 0 1 MPS I + X ε r ε r 1 MPS r = \$ \$ r = \$10000 \$20000 r Suppose further that the economy's initial LM curve is represented by the equation: Y = \$ \$ (r + π) and that the inflation rate π is constant at 3% per year. Thus the initial equilibrium of the economy is with real GDP Y at \$9000 billion and the real interest rate r at 5%. Now suppose the central bank conducts an expansionary open market operation. It buys bonds for cash and increases the supply of money in the economy, shifting the LM curve to: Y = \$ \$ (r + π) So, with inflation constant at 3% per year, the new equilibrium can be found by setting the values of Y produced by the IS and LM curve to be equal to each other: Y = \$10000 \$20000 r = \$ \$ (r + 3) \$4800 = (\$ \$100000) r r =.04 = 4% With the real interest rate r equal to 4% per year, annual equilibrium real GDP Y equals \$9200 billion--a \$200 billion increase in annual equilibrium real GDP.

21 Chapter Final Figure 11.9: Expansionary Shift in the LM Curve: Real Interest Rate r Old LM Curve: Y=\$1000+\$1000 x (r+π) [inflation rate π=3%]...which lowers the equilibrium real interest rate by 1%... Expansionary open market operations shift the LM curve out by \$1200 IS Curve: Y=\$10000-\$200 x r Real GDP Y...and raises equilibrium real GDP by \$200. Interest Rate Targets The intersection of the IS and LM curves determines short-run equilibrium values of real GDP when the money stock is fixed. It provides a flexible and useful framework for analyzing the expenditure-driven determination of output, money market equilibrium, and interest rates. Even the case in which the central bank is targeting the interest rate can be viewed in the IS-LM framework. An interest rate target can be seen as simply a flat, horizontal LM curve at the target level of the interest rate.

22 Chapter Final Figure 11.10: IS-LM Framework with an Interest Rate Target Real Interest Rate r Central bank targeting the interest rate = horizontal LM curve IS curve Real GDP Y Legend: When the central bank targets and fixes the interest rate, we can think of the LM curve as being a horizontal line. Classifying Economic Disturbances The IS-LM framework allows economists to classify shifts in the economic environment and changes in economic policy into four basic categories. A surprisingly large number of economic disturbances affect aggregate demand and can be fitted into the IS-LM framework. Changes that Affect the LM Curve

23 Chapter Final First, any change in the nominal money stock, in the price level, or in the trend velocity of money will shift the LM curve's location. Second, any change in the interest sensitivity of money demand--in how easy households and businesses find it to economize on their holdings of real money balances--will change the slope of the LM curve. Moreover, the fact that the IS-LM diagram is drawn with the real interest rate--the long-term, risky, real interest rate--on the vertical axis has important consequences. The LM curve is a relationship between the short-run nominal interest rate and the level of real GDP at a given, fixed level of the real money supply: ( ) M P Y = V 0 + V i (i) As long as the spread between the short-term, safe, nominal interest rate i in the LM equation and the long-term, risky, real interest rate r in the IS equation is constant, there are no complications in drawing the LM curve onto the same diagram as the IS curve. But what if the expected rate of inflation π e, the risk premium, or the term premium between short and long-term interest rates changes? Then the position of the LM curve on the IS-LM diagram shifts either upward (if expected inflation falls, or if the risk premium rises, or if the term premium rises) or downward (if expected inflation rises, or if the risk premium falls, or if the term premium falls). Figure illustrates what happens to the position of the LM curve if the expected inflation rate rises. Thus changes in financial market expectations of future Federal Reserve policy, future inflation rates, or simply changes in the risk tolerance of bond traders shifts the LM curve. Not only disturbances in the money market, but broader shifts in the financial markets that alter the relationship between the nominal interest rates on short-term safe

24 Chapter Final bonds and the real interest rate paid by corporations undertaking long-term risky investments will affect the IS-LM equilibrium. Figure 11.11: A Rise in Expected Inflation Moves the LM Curve Downward Real Interest Rate r...which lowers the equilibrium real interest rate... A rise in expected inflation means that the same nominal interest rate is now associated with a lower real interest rate. So a fall in expected inflation generates a downward shift in the LM curve... LM Curve IS Curve Real GDP Y complications:...and raises the equilibrium level of real GDP. Legend: The fact that the interest rate relevant to the IS curve is a real and the interest rate relevant to the LM curve is a nominal rate is a source of a change in expected inflation lowers the real interest rate that corresponds to any given nominal interest rate, and so shifts the LM curve down on the IS-LM diagram.

25 Chapter Final Changes that Affect the IS Curve However, shifts in the IS curve are probably more frequent than shifts in the LM curve, for more types of shifts in the economic environment and economic policy affect planned expenditure than affect the supply and demand for money. Any change in the effect of a shift in interest rates on investment spending will change the slope of the IS curve. So will any change in either the sensitivity of exports to the exchange rate, or any change in the sensitivity of the level of the exchange rate to the level of domestic interest rates. Furthermore, anything that affects the marginal propensity to spend--the MPE will change the slope of the IS curve and the position of the IS curve as well. Any shift in the marginal propensity to consume C y will change the MPE. Thus if households decide that income changes are more likely to be permanent (raising the marginal propensity to consume) or more likely to be transitory (lowering the marginal propensity to consume), they will raise or lower the MPE. Changes in tax rates have a direct effect on the MPE. So do changes in the propensity to import. Thus, for example, the imposition or removal of a tariff on imports to discourage them will affect the position and the slope of the IS curve. Last but not least, changes in the economic environment and in economic policy taht shift the level of autonomous spending shift the IS curve. Anything that affects the baseline level of consumption C 0 affects autonomous spending--whether it is a change in demography that changes desired savings behavior, a change in optimism about future levels of income, or any other cause of a shift in consumer behavior. Anything that affects the baseline level of investment I 0 affects autonomous spending--whether it is a wave of innovation that increases expected future profits and desired investment, a wave of irrational overoptimism or overpessimism, a change in tax policy that affects not the

26 Chapter Final level of revenue collected but the incentives to invest, or any other cause. Changes in government purchases affect autonomous spending. In sum, almost anything can affect the equilibrium level of aggregate demand on the IS- LM diagram. Pretty much everything does affect it at one time or another. One of the principal merits of the IS-LM is its use in sorting and classifying the determinants of equilibrium output and interest rates The Exchange Rate and the Trade Balance The IS-LM Framework and the International Sector The IS-LM Framework and the Exchange Rate In our sticky-price model, the real exchange rate ε is equal to speculators' opinion of its baseline fundamental value,ε 0, minus a parameter ε r times the difference between the real domestic interest rate (r) and the foreign interest rate abroad (r f ): ε = ε 0 ε r ( r r f ) Thus the effects of changes in domestic conditions on the value of the real exchange rate are easy to predict. As long as the domestic real interest rate does not change, domestic conditions will have no impact on the exchange rate. If the exchange rate shifts, it will do so for other, external reasons.

27 Chapter Final Figure 11.12: IS-LM and the Exchange Rate Real Interest Rate r An outward, expansionary shift in the LM curve Real Interest Rate r...which lowers the equilibrium real interest rate... LM Curve IS Curve...and raises the equilibrium level of real GDP... Real GDP Y Exports...will raise the real exchange rate... Real Exchange Rate ε...and boost exports. Real Exchange Rate ε Legend: Rightward shifts in the IS and inward shifts in the LM curve will lower the exchange rate, the value of foreign currency, and reduce net exports. Changes in the IS and LM curves that do change the domestic real interest rate will change the real exchange rate, however, by an amount equal to the parameter ε r times the shift in the domestic interest rate. A rightward expansionary shift in the IS curve and a leftward contractionary shift in the LM curve both lower the value of the exchange rate. A leftward contractionary shift in the IS curve and a rightward expansionary shift in the LM curve will both raise the value of the exchange rate, as Figure shows.

28 Chapter Final The effects of a change in domestic conditions on the real exchange rate are straightforward. The change in the exchange rate is proportional to the change in the real interest rate: ε = ε r r What determines the size of the proportionality factor ε r, and thus the interest sensitivity of the exchange rate? It is a function of foreign exchange speculators' willingness to bear risk and their assessment of how long differentials between domestic and foreign interest rates will persist. If speculators think differences in interest rates will last for a long time, the interest sensitivity of the exchange rate will be high. If speculators fear bearing risk, the interest sensitivity will be small. The IS-LM Framework and the Balance of Trade The effects in the IS-LM framework of changes in domestic conditions on the balance of trade are a little more complicated. Changes in r affect the exchange rate, which affects gross exports. Changes in total income Y affect imports. Figure sketches out the chief causal links.

29 Chapter Final Figure 11.13: Effect of Change in Domestic Conditions on the Exchange Rate and the Balance of Trade Change in Domestic Conditions Change in Exchange Rate Change in Equilibrium Values of Y, r Change in Gross Exports Change in Imports Change in Net Exports The effect on net exports is the difference between the effect of a change in the interest rate on gross exports (remember: the higher the domestic interest rate, the lower the value

30 Chapter Final of the exchange rate and the lower the value of gross exports) and the effect of a change in real GDP on imports: NX= GX IM = ( ε r r) ( IM y Y) As the economy moves up or to the right (or both) on the IS-LM diagram, net exports fall. Box 11.4 provides an illustrative example of how to calculate the effect of a shock to the economy on the overall balance of trade. Box Example: An LM Shock and the Balance of Trade Suppose that the economy's marginal propensity to spend [MPS] is 0.5, that the marginal propensity to import IM y is.15, that the initial level of baseline autonomous spending A 0 is \$5000 billion, and that a 1 percentage point increase in the real interest rate reduces investment spending by \$80 billion, and reduces the value of the exchange rate by 10 percent. Suppose further that each one percent increase in the exchange rate increases net exports by \$2 billion. Then the economy's initial IS curve is: A Y = 0 1 MPE I + X ε r ε r 1 MPE r = \$ \$ \$ r = \$10000 \$20000 r If the economy's initial LM curve is: Y = \$ \$ (r + π) and if the inflation rate π is constant at 3% per year, then the initial equilibrium of the economy is with equilibrium annual real GDP is \$9000 billion and the real interest rate is 5%.

31 Chapter Final Now suppose the central bank conducts expansionary open market operations to shift the LM curve out to: Y = \$ \$ (r + π) The new equilibrium can be found by setting the values of Y produced by the IS and LM curve to be equal to each other: r = 4% Y = \$9200 The IS-LM diagram equilibrium has shifted, with a \$200 billion increase in annual equilibrium real GDP, and a 1 percentage point decline in the real interest rate. Figure 11.14: Effects of Expansionary Monetary Policy Real Interest Rate r Old LM Curve: Y=\$1000+\$1000 x (r+π) [inflation rate π=3%]...which lowers the equilibrium real interest rate by 1%... Expansionary open market operations shift the LM curve out by \$1200 IS Curve: Y=\$10000-\$200 x r Real GDP Y...and raises equilibrium real GDP by \$200.

32 Chapter Final The decrease in the real interest rate increases the real exchange rate by: ε r r = 10 (.01) = 0.10 and the rise in the real exchange rate increases gross exports by: X ε ε = \$ = +\$20 The \$200 billion increase in real national income increases imports by: IM y Y = 0.15 \$200 = \$30 Thus the LM shock changes annual net exports by the difference between the two: NX= GX IM = \$20 \$30 = \$10 It shrinks net exports by \$10 billion a year. International Shocks and the Domestic Economy Three different types of international shocks will affect the IS-LM equilibrium. The first is a shift in foreign demand for domestic exports--the result, usually, of changes in foreign real GDP. The second is a shift in the foreign real interest rate, and the third is a change in foreign exchange speculators' view about the fundamental value of the exchange rate. An increase in foreign demand for home-country exports will affect the domestic economy in the same way as any other expansionary IS shock. The increase in export demand is an increase in baseline autonomous spending A 0. It shifts the IS curve rightward by an amount A 0 /(1-MPS). This rightward IS shift raises the equilibrium level of real GDP and, to the extent that the LM curve is upward sloping, raises the real interest

33 Chapter Final rate. The increase in the real interest rate would make exports more expensive to foreigners, and put some countervailing downward pressure on exports. The increase in the equilibrium level of real GDP would raise demand for imports. Figure shows the major links in the causal chain. Figure 11.15: Effect of an Increase in Foreign Demand for Exports Real Interest Rate r An expansion of foreign demand for exports shifts the IS curve outward......it raises the equilibrium real interest rate to the extent that the LM curve slopes upward... LM Curve Higher real interest rates reduce the exchange rate Old IS Curve Real GDP Y and put some downward countervailing pressure on exports...and it raises equilibrium real GDP which raises imports If the Federal Reserve is targeting the real interest rate, then the change in real GDP Y generated by a rise Y f in foreign total income is straightforward to calculate. The effect on real GDP Y is simply the rise in foreign incomes times their propensity to spend on our exports times the multiplier:

34 Chapter Final Y = X f Y f 1 MPE which can also be written, if we replace the MPE by the parameters that determine it: X Y = f Y f 1 C y (1 t) + IM y The change in net exports is the difference between the change in gross exports produced by the expansion in foreign demand, and the change in imports produced by the rise in domestic national income: NX= GX IM This difference can be written as a function of domestic and foreign national income: NX= X f Y f IM y Y And we already calculated the change in domestic national income, so we can substitute it in to obtain: NX= X f Y f IM y X f Y f 1 MPE IM NX= ( X f Y f ) 1 y 1 MPE As long as the multiplier times the propensity to import is less than one, an increase in foreign incomes will raise net exports. The second type of international shock, an increase in the foreign interest rate r f, also has an immediate impact on the domestic economy but through different channel channels. An increase in the foreign interest rate raises the value of the exchange rate, and so boosts exports. The increase in exports shifts the IS curve to the right, leading to a higher level

35 Chapter Final of equilibrium real GDP and--to the extent that the LM curve is upward-sloping--to higher real interest rates. The consequences of such a shift are similar to those of an increase in foreign incomes save for the direction in which the exchange rate moves. The third type of international shock is a sudden change in speculators' expectations ε 0 of the long-run fundamental exchange rate. Consider an upward shock to ε 0. It would have effects identical to an increase in interest rates overseas: the exchange rate would rise, the IS curve would shift outward, equilibrium real GDP would increase, and--to the extent that the LM curve is upward sloping--the domestic real interest rate would increase as well. Box 11.5 works through an example of such a shock to exchange market speculators expectations. Box Example: A Shock to International Investors' Expectations Suppose that the economy's LM curve is represented by the equation: Y = \$ \$ (r + π) and that the inflation rate π is constant at 3% per year. Suppose further that the economy's marginal propensity to spend [MPS] is 0.5, that the marginal propensity to import IM y is.15, that the initial level of baseline autonomous spending A 0 is \$5000 billion, that a 1 percentage point increase in the real interest rate reduces investment spending by \$40 billion and reduces the value of the exchange rate by 10 percent, and that each one percent increase in the exchange rate increases net exports by \$6 billion. Then the economy's initial IS curve is:

36 Chapter Final A Y = 0 1 MPE I + X ε r ε r 1 MPE r = \$ \$ \$ r = \$10000 \$20000 r The initial equilibrium has annual real GDP at \$9000 billion and a real interest rate of 5%. Consider a sudden upward shock of ten percent, as foreign exchange speculators' lose confidence in the value of the domestic currency, to their opinions ε 0 of the long-run fundamental value of the real exchange rate. Such a shock shifts the IS curve to the right, raising the level of real GDP on the IS curve for a given, fixed level of the real interest rate by an amount: X ε ε 0 1 MPE The shifted IS curve is then: Y = A + A MPE I + X ε r ε r 1 MPE r = A + X ε 0 ε 0 1 MPE Y = \$ \$ \$ I r + X ε ε r 1 MPE r r = \$10120 \$20000 r The new equilibrium can be found by setting the values of Y produced by the IS and LM curve to be equal to each other: \$ \$1000 (r + π) = Y = \$10120 \$200 r \$6120 = \$1200 r r = 5.1% Y = \$9100

37 Chapter Final Equilibrium annual real GDP increases by \$100 billion as the raised exchange rate boosts exports, and the domestic real interest rate rises by 0.1%. The increase in the domestic real interest rate means that the final change in the real exchange rate: ε = ε 0 ε r r ε = = +9 is less than the 10 percent magnitude of the initial shock: higher domestic real interest rates have offset some of the effect of the change in foreign exchange speculators' opinions. The increase in the domestic real interest rate also means that some domestic investment has been "crowded out" by the interest rate effects of the export boom: I = I r r = \$ = \$4 The total effect on gross exports from the net change in the exchange rate is: GX = X ε ε = \$6 9 = +\$54 Since the total change in imports is: IM = IM y Y = 0.15 \$100 = \$15 The total change in net exports from the shift in expectations is +\$39 billion.

38 Chapter Final 11.3 Aggregate Demand The Price Level and Aggregate Demand What happens to the level of real GDP as the price level rises? If the nominal money supply is fixed, then an increase in the price level reduces real money balances and shifts the LM curve back and to the left. The equilibrium real interest rate rises, and the equilibrium level of real GDP falls, as Figure shows. Figure 11.16: A Rise in the Price Level Shifts the LM Curve Left (If the Nominal Money Supply Is Fixed) Interest Rate As the price level rises......the LM curve shifts leftward... IS Curve...and real GDP falls. Real GDP

39 Chapter Final Legend: For a fixed level of the nominal money stock, an increase in the price level is a contractionary shift in the economy. The higher the price level, the lower the real money stock. The lower the real money stock, the further to the left is the LM curve. The further to the left is the LM curve, the lower is real GDP. Suppose we draw another diagram, this time with the price level on the vertical axis and the level of real GDP on the horizontal axis. We use this new diagram to plot what the equilibrium level of real GDP is for each possible value of the price level. For each value of the price level, we calculate what the LM curve is and use the IS-LM diagram to calculate the equilibrium level of real GDP. As Figure 11.7 shows, we find if the nominal money supply is fixed a downward-sloping relationship between the price level and real GDP. With the nominal money stock held fixed, a rise in the price level increases the real money stock, and shifts the LM curve to the left because the position of the LM curve depends on the value of the real money stock. A leftward shift in the LM curve reduces the equilibrium level of real GDP and increases the interest rate. The lower the price level, the higher are real money balances, the lower is the interest rate, the higher is aggregate demand, and the higher is the equilibrium level of real GDP. Economists call this curve according to which a lower price level means higher aggregate demand the aggregate demand curve.

40 Chapter Final Figure 11.17: From the IS-LM Diagram to the Aggregate Demand Curve Interest Rate IS-LM Diagram As the price level rises......the LM curve shifts leftward... IS Curve Real GDP...and real GDP falls. Price Level Aggregate Demand As the price level rises... Aggregate Demand Curve Real GDP...real GDP falls.

41 Chapter Final Legend: For a fixed value of the nominal money stock, each possible value for the price level produces a different LM curve. Plot the equilibrium value of real GDP for that LM curve on the horizontal axis and the price level on the vertical axis. The result is the aggregate demand curve. In this aggregate demand curve we can see how, over time, adjustments in prices and wages might carry the economy from the sticky-price model equilibrium back to the flexible-price equilibrium in which real GDP is equal to potential output. If real GDP is less than potential output, prices might fall over time, and falling prices would carry the economy down and to the right along the aggregate demand curve, increasing real GDP. If real GDP is greater than potential output, prices might rise over time, and rising prices would carry the economy up and to the left along the aggregate demand curve, reducing real GDP. Monetary Policy and Aggregate Demand Modern central banks, however, do not fix the money stock and then sitting by passively watching the business cycle. So the derivation of the aggregate curve in the section above is a little distant from modern macroeconomies. Once we recognize that modern central banks play an active role in managing the macroeconomy, the analysis of aggregate demand is somewhat different. Modern central banks pay a lot of attention to the inflation

42 Chapter Final rate. When the inflation rate rises, the central bank tends to increase the real interest rate to try to reduce aggregate demand and cool off inflation. Stanford economist John Taylor, currently on leave at the Treasury Department as Undersecretary for International Affairs, has a simple model of how central banks act, called the Taylor rule. According to the Taylor rule, the central bank has a target value π for the inflation rate, and an estimate r* of what the normal real interest rate should be. If inflation is higher than its target value, the central bank raises the real interest rate above r*; Whenever inflation is lower than its target value, the central bank lowers the interest rate below r* according to a rule: r = r * +φ'' (π π') where the parameter φ determines how aggressively the central bank reacts to inflation. We take the Taylor rule, the model of how the central bank acts, and substitute its expression for the determinants of the real interest rate into the IS-curve equation: to obtain: Y = A 0 1 MPE I r + X ε ε r 1 MPE r A 0 ( ) Y = 1 MPE I + X ε r ε r 1 MPE r * φ" I + X ε r ε r 1 MPE (π π') This equation is too complex to work with, so once again it is useful to simplify. Define Y 0 to be the level of real GDP when the real interest rate is at its long-run normal value r*: Y 0 = A 0 1 MPE I r + X ε ε r 1 MPE r *

43 Chapter Final And define a new parameter φ, the Greek letter phi with one apostrophe attached to it, to be: φ'= φ" ( I + X ε r ε r) 1 MPE Then we can write our combination of the Taylor rule and the IS curve in the simple looking form: Y = Y 0 φ' (π π') which is called the monetary policy reaction function, and which is shown in Figure This monetary policy reaction function looks akin to the aggregate demand curve of the previous section. When prices increase in this case, when inflation is higher than the central bank wants it to be real GDP declines. There are, however, differences. The aggregate demand curve of the previous section was a relationship between the price level and real GDP. This monetary policy reaction function is a relationship between the inflation rate and real GDP. The aggregate demand curve assumed that the Federal Reserve sat like a potted plant while the business cycle proceeded. The monetary policy reaction function assumes that the Federal Reserve is engaged in the economy, trying to manage it to keep inflation close to the inflation target. Last, the monetary policy reaction function is a good model of how central banks actually behave.

44 Chapter Final Figure 11.18: The Monetary Policy Reaction Function Interest Rate IS Diagram As the price level rises......leads an inflationfighting central bank to raise interest rates... IS Curve Real GDP Inflation Rate Monetary Policy Reaction Function A higher inflation rate... Aggregate Demand Curve...real GDP falls. Real GDP

45 Chapter Final Legend: The actions of an inflation-fighting central bank lead to the same kind of downward-sloping relationship between prices and output as in the previous section. But in this case it is a higher inflation rate, not a higher price level, that associated with lower real GDP. Once again, however, this monetary policy reaction function offers a glimpse into how over time adjustments in prices and wages might carry the economy from the sticky-price equilibrium in which there is unemployment and a gap between GDP and potential output back to the flexible-price equilibrium in which real GDP is equal to potential output. If real GDP is less than potential output, inflation might fall over time, and the central bank reducing interest rates in response to low inflation would carry the economy down and to the right along the monetary policy reaction function, increasing real GDP. If real GDP is greater than potential output, inflation might rise over time, and the central bank raising interest rates in response to high inflation would carry the economy up and to the left along the aggregate demand curve, reducing real GDP Aggregate Supply Output and the Price Level Inflation is an increase in the general, overall price level. An increase in the price of any one particular good--even a large increase in the price of any one particular good--is not inflation. Inflation, then, is an increase in the price of just about everything. Together, the

46 Chapter Final prices of all or nearly all goods and incomes rise by approximately the same proportional amount. Whenever real GDP is greater than potential output, inflation is likely to be higher than people had previously anticipated. Thus inflation is likely to accelerate. Conversely, whenever the level of real GDP is below potential output, then inflation is likely to be lower than people had previously anticipated. The inflation rate is likely to fall toward zero--and perhaps prices will begin to fall in deflation. Economists call this correlation between real GDP (relative to potential output) and the rate of inflation (relative to its previously-expected value) the short-run aggregate supply curve. One way to write theshort-run aggregate supply curve is as: Y Y* Y* = θ P Pe P e That is, the proportional deviation of real GDP Y from potential output Y* is equal to the parameter θ (the Greek letter theta ), which represents the slope of the short-run aggregate supply function, times the proportional deviation of the price level P from its anticipated level P e. But since the inflation rate π is simply the proportional rate of change of the price level, we can replace the expression ((P-P e )/P a ) with the actual inflation rate π minus the expected inflation rate π e : Y Y* Y* = θ ( π π e ) Figure plots this version of the short-run aggr4eaget supply curve.

47 Chapter Final Figure 11.19: Output Relative to Potential and the Inflation Rate Inflation Rate Expected Inflation Output Relative to Potential than Potential Output Legend: When production is higher than potential output, prices will be higher businesses, consumers, and workers had anticipated--and inflation will be higher than expected inflation. Whatever form of the aggregate supply function we use, we can combine it with the aggregate demand or monetary policy reaction function to and see not just the equilibrium level of real GDP but also the economy s price level and inflation rate will be, as Figure shows. The aggregate supply curve slopes upward because a higher

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