Chapter 7: Equilibrium in the Flexible-Price Model

Chapter 7 1 Final Chapter 7: Equilibrium in the Flexible-Price Model J. Bradford DeLong Questions 1. When wages and prices are flexible, what economic forces keep total production equal to aggregate demand? 2. Why does the flow-of-funds through financial markets have to balance? 3. What are the components of savings flowing into financial markets? 4. What is a comparative statics analysis? 5. What are"supply shocks"? 6.. What are "real business cycles"? 7.1 Full-Employment Equilibrium Equilibrium and the Real Interest Rate

Chapter 7 2 Final The first section of Chapter 6 showed that, under the flexible-price full-employment classical assumptions, GDP and national income Y equal potential output Y*: Y = Y* The rest of Chapter 6 set out the determinants of each of the components of total spending. We saw that the exchange rate is a function of (a) the real interest rate differential between home and abroad, and (b) foreign exchange traders' opinions: ε = ε 0 ( r r f ) We saw the determinants of consumption spending: C = C 0 + C y (1 t) Y of investment spending: I = I 0 r and of net exports: ( ) ε 0 NX = X yf Y f ( ) ( X ε r) r f ( ) ( IM y Y) Fourth and last, we left the determination of government purchases to the political scientists: G = G These four components add up to aggregate demand, or total expenditure, written E when we want to emphasize that, conceptually at least, it is not quite the same as real GDP Y. However, the circular flow principle guarantees that in equilibrium aggregate demand will add up to real GDP Y: C + I + G + NX= E = Y

Chapter 7 3 Final However, the determinants of each of the components of total spending E seem to have nothing at all to do with the production function that determines the level of real GDP Y. How does aggregate demand add up to potential output? Can we be sure that all the output businesses think they can sell when they hire more workers is in fact sold? The answer is that in the flexible-price full-employment classical model of this section, the real interest rate r plays the key balancing role in making sure that the economy reaches and stays at equilibrium. If we look at all the determinants of all the components of total spending, we see that the components of total spending depend on four sets of factors: Factors that are part of the domestic economic environment (like consumers' and investors' baseline spending C 0 and I 0, and government purchases G). Factors that are determined abroad (like foreign real GDP Y f, and exchange speculators' view of the long-run fundamental value of the exchange rate ε 0 ). The level of real GDP Y itself (which is a determinant of consumption spending and imports). The real interest rate. Of all these factors, only one, the real interest rate, is a price determined by supply and demand here at home. So if market forces cause the components of total spending add up to real GDP, those market forces must work through the interest rate.

Chapter 7 4 Final To understand what makes aggregate demand equal to potential output, we need to look at the market in which the interest rate functions as the price: the market for loanable funds. When you lend money the interest rate is the price you charge and the price the borrower pays. Thus we need to look at the flow of loanable funds through the financial markets, the places where household savings and other inflows into financial markets are balanced by outflows to firms seeking capital to expand their productive capacity. The equilibrium we are looking for is one in which supply equals demand in the financial markets. According to the circular flow principle if financial markets are in equilibrium then the sum of all the components of spending is equal to real GDP. The Flow-of-Funds Through Financial Markets The circular flow principle ensures that if supply equals demand in the flow-of-funds through financial markets then aggregate supply (real GDP, Y, equal to potential output Y*) is equal to aggregate demand (the sum of all the components of total spending: C+I+G+NX). To see this, begin by assuming that real GDP is equal to potential output Y* and that the circular flow principle holds: real GDP is equal to aggregate demand: Y* = Y = C + I + G + NX Then rewrite this expression by moving everything except for investment spending I over to the left-hand side. Y* C G NX= I Now include taxes T in the left-hand side:

Chapter 7 5 Final (Y * C T) + (T G) NX = I Note that the right-hand side is simply investment, the net flow of purchasing power out of the financial markets as firms raise money to build factories and structures and boost their productive capacity. The left-hand side is equal to total savings: the flow of purchasing power into financial markets as households, the government, and foreigners seek to save by committing their money to buy valuable financial assets here at home (see Figure 7.1). Thus we see that whenever the circular flow principle holds, the supply and demand in the flow of funds through financial markets balances as well. The (Y*-C-T) inside the first set of parentheses are households' savings. Because national income is equal to potential output, Y* is just total household income. Take income, subtract taxes, subtract consumption spending, and what is left is household savings: the flow of purchasing power from households into the financial markets.

Chapter 7 6 Final Figure 7.1: The Flow-of-Funds Through Financia markets Private Savings: Y*-C-T Financial Markets Investment Demand Government Savings: T-G In ternational Savings: -NX The (T-G) inside the second set of parentheses are just government savings: the government's budget surplus (or government dissaving, the government s budget deficit, if G happens to be larger than T). They are the flow of funds from the government into the financial markets.

Chapter 7 7 Final Figure 7.2: Minus Net Exports Equals the Capital Inflow The Rest of the World Goods imported Dollars earned by foreigners: IM Dollars paid by foreigners for exports: GX Goods exported Excessof dollars earned by foreigners over dollars spent by foreigners on home-country exports: = (IM-GX) = - NX Foreigners savings committed to U.S. financial markets The only remaining use for these dollars is in financial markets to purchase shares in U.S. companies and U.S. property The last term--minus net exports, -NX--is the net flow of purchasing power that foreigners channel into domestic financial markets. As Figure 7.2 illustrates, minus net exports is the excess of dollars earned by foreigners selling imports into the home country over and above the amount of dollars foreigners need to buy our exports. If net exports are less than zero, foreigners have some dollars left over. They then have to do something with these extra dollars. Foreigners find dollars useful in only two ways. First, they are useful for buying our exports (but if net exports are less than zero there aren t enough exports to soak up all the dollars they earn). Second, dollars are useful for besides buying property here--land, stocks, buildings, bonds. So this last term is the net flow of purchasing power into domestic financial markets by foreigners wishing to park some of

Chapter 7 8 Final their savings here. (And when net exports are positive, this term is the net amount of domestic savings diverted into overseas financial markets). Box 7.1--Details: Financial Transactions and the Flow of Funds Notice that the relationship between the flow offunds into and out of financial markets is indirect. When the government runs a surplus the government does not directly lend money to a business that wants to build a new factory. Instead, when the government runs a surplus it uses the surplus to buy back some of the bonds that it has previous issued. The bank that owned those bonds then takes the cash and uses it to buy some other financial asset perhaps bonds that had been issued by a corporation. The chain of transactions within financial markets only comes to an end when some participant makes a loan to an investing company or buys a newly-issued bond or stock, and so transfers purchasing power to the company actually undertaking an investment. Similarly a household or a foreigners using financial markets to save rarely buys a newly-issued corporate bond or shares of stock that are part of an initial public offering that transfer purchasing power directly to a company undertaking investment. Instead they usually purchase already-existing securities, or simply deposit their wealth in a bank. The relationship between the flow-of-funds into and out of financial markets is indirect. Nevertheless it is very real.

Chapter 7 9 Final Flow-of-Funds Equilibrium We have established that the three terms on the left-hand side of the equation: (Y * C T) + (T G) NX = I are the three flows of purchasing power into the financial markets: private savings, government savings, and international savings. Added together they make up the supply of loanable funds. The demand for loanable funds is simply investment spending. And the price of loanable funds is the real interest rate, as Figure 7.3 illustrates. Figure 7.3: Equilibrium in the Flow-of-Funds Real Interest Rate r Plus -NX International Savings =Total Savings Equilibrium real interest rate T-G Plus GovernmentPrivate Savings Savings Y*-C-T Investment Demand Equilibrium level of investment Flow-of-Funds Through Financial Markets

Chapter 7 10 Final What happens if the flow-of-funds does not balance--if at the current long-term real interest rate r the flow of savings into the financial markets exceeds the demand by corporations and others for purchasing power to finance investments? If the left-hand side is greater than the right, some financial institutions--banks, mutual funds, venture capitalists, insurance companies, whatever--will find purchasing power piling up as more money flows into their accounts than they can find good securities and other investment vehicles to commit it to. They will try to underbid their competitors for the privilege of lending money or buying equity in some particular set of investment projects. How do they underbid? They underbid by saying that they would accept a lower interest rate than the market interest rate r. Thus if the flow of savings exceeds investment, the interest rate r falls. As the interest rate r fell, the number and value of investment projects firms and entrepreneurs found it worthwhile to undertake rises.

Chapter 7 11 Final Figure 7.4: Excess Supply of Savings in the Flow-of-Funds Market Real Interest Rate r Public Savings Plus Private Savings Plus International Savings Equals Total Savings Investment Demand Flow-of-Funds Through Financial Markets Legend: When the interest rate is such that there is an excess supply of savings: some savers are about to offer to accept a lower interest rate, and the interest rate is about to drop. The process will stop when the interest rate r adjusts to bring about equilibrium in the loanable funds market. The flow of savings into the financial markets will then be just equal to the flow of purchasing power out of financial markets, and into the hands of firms and entrepreneurs using it to finance investment. Solving the Model

Chapter 7 12 Final At what level of the real interest rate will the flow-of-funds through financial markets in equilibrium? At what level will the real interest rate be stable? To determine the flow-offunds equilibrium, look more closely at the supply and demand for funds. First, let s look at the determinants of the supply of private savings: Y * C T = (1 t (1 t)c y )Y * C 0 Second, let s look at the determinants of public savings: T G = ty * G _ Third, let s look at the determinants of international savings: NX = IM y Y r X yf Y f X ε ε 0 X ε r f These three added together make up the flow-of-funds supply of savings. Note that in Figure 7.3 the supply of savings is upward sloping: when the interest rate r rises, the total savings flow increases. An increase in the real interest rate attracts foreign capital into domestic financial markets. The flow-of-funds demand is simply the investment function: I = I 0 r Equilibrium is, of course, where the supply and demand curves cross--where the supply of savings is equal to investment demand. What is the equilibrium interest rate? It is the level at which the supply of savings is equal to investment demand. To get an explicit

Chapter 7 13 Final expression for the interest rate, begin by writing out the determinants of all the pieces of savings: ((1 t (1 t)c y )Y * C 0 ) + ty * G _ + IM Y + X X Y f y yf X ε ε 0 X ε r f ( ) = I 0 r Group all the terms that depend on Y* on the left of the left-hand side, all the terms that are constant in the middle of the left hand side, all the terms that depend on international factors on the right of the left-hand side, and move all the terms with the real interest rate r over to the right-hand side: ( 1 ((1 t)c y IM y ))Y * C 0 + I 0 + G _ X yf Y f ε 0 r f ( ) = And divide by -( ) to determine the equilibrium real interest rate r: ( )r r = (C + I + 0 0 G_ ) + (X yf Y f ε 0 r f ) ( 1 ((1 t)c y IM y ))Y* ( ) Box 7.2 shows how to use this equation to find the equilibrium real interest rate given values for the parameters of this flexible-price model of the macroeconomy. Box 7.2--Example: Solving for and Verifying the Equilibrium Real Interest Rate Given the parameters of the flexible-price model and the value of potential GDP, it is straightforward to calculate the equilibrium real interest rate r by substituting the parameters into the formula: r = (C + I + 0 0 G_ ) + (X yf Y f ε 0 r f ) ( 1 ((1 t)c y IM y ))Y* ( ) For example, when parameter values are:

Chapter 7 14 Final Potential output Y* = $10,000 billion Baseline consumption C 0 = $3,000 billion Baseline investment I 0 = $1,000 billion Government purchases G = $2,000 billion The tax rate t = 25% The MPC C y = 0.67 The propensity to import IM y = 0.2 Abroad, X yf =0.1 and Y f = $10,000 billion Foreign exchange speculators long-run view ε 0 = 100 The sensitivity of exports to the exchange rate X ε = 10 The sensitivity of investment to the interest rate = 9000 The sensitivity of the exchange rate to the interest rate = 600 Then replacing each of the parameters with its value produces: r = ( ( ) ) 10000 ( 9000 + 600 10) (3000 +1000 + 2000) + (0.1 10000 +10 100) 1 (1 0.25) 0.67 0.2 r = (6000) + (2000) ( 0.7) 10000 15000 r = 1000 15000 =.0667 An equilibrium real interest rate of 6.67% per year. Is the economy in fact in equilibrium when the real interest rate is 6.67% per year? Yes. At that level of the interest rate:

Chapter 7 15 Final Private savings equal -$500 billion (yes, they are less than zero: households are drawing down their wealth in order to finance high current consumption), as you can see by substituting the parameters into the equation: Y * C T = (1 t (1 t)c y )Y * C 0 that determines private saving. Government savings equal $500 billion, as you can see by subtracting government purchases from taxes. The capital inflow from abroad minus net exports equals $400 billion, as you can see by substituting the parameter values and a real interest rate of 6.67% into the equation: NX = IM y Y r X yf Y f X ε ε 0 X ε r f that determines minus net exports. These three components of saving add up to $400 billion. And investment is equal to $400 billion. Thus the flow of funds through financial markets balances. Looking at the components of real GDP: Consumption spending equals $8,000 billion Investment spending equals $400 billion Government purchases equal $2,000 billion Net exports equal -$400 billion All these add up to $10,000 billion: the level of potential output

Chapter 7 16 Final Total spending aggregate demand is indeed equal to real GDP. 7.2 Using the Model Comparative Statics as a Method of Analysis The flexible-price, full-employment model we have built in the last two chapters gives us the capability to determine the level and composition of real GDP and national income. If we know the economic environment and economic policy, we can use the model to determine the equilibrium real interest rate, either by solving the algebraic equations or by drawing the flow-of-funds diagram and looking for the point where supply balances demand, or both. We can then calculate the equilibrium values of a large number of economic variables real GDP, consumption spending and investment spending, imports and exports, the real exchange rate, and more. In fact, three of the six key economic variables real GDP, the exchange rate, and the real interest rate come directly from the model. We will see how to calculate the price level and inflation rate in the next chapter, Chapter 8. In a flexible-price model like this one the unemployment rate is not interesting, for the economy is always at full employment. And we have seen that the stock market is proportional to and a leading indicator of investment spending. However, the model so far gives us the capability not just to calculate the current equilibrium position of the economy, but how that equilibrium will change in response to

Chapter 7 17 Final changes in the economic environment or in economic policy. To do so we use a method of analysis economists call comparative statics. We determine the response of the economy to some particular shift in the environment or policy in three steps. We first look at the initial equilibrium position of the economy without the shift. We then look at the equilibrium position of the economy with the shift. We then identify the difference in the two equilibrium positions as the change in the economy in response to the shift. Let's see how the model can be used to analyze the consequences of three disturbances to the economy: (a) changes in fiscal policy, in the government's tax and spending plans; (b) changes in investors' relative optimism; and (c) changes in the international economic environment. Changes in Fiscal Policy Suppose the economy is in equilibrium when policy makers decide to increase annual government purchases by the amount G as before, a capital Greek letter delta, stands for "change." Let s look at what happens to the components of aggregate demand one by one. First, the change in government purchases has no effect on consumption. Because potential output does not change, national income does not change. Neither national income, baseline consumption, the tax rate, nor the marginal propensity to consume shifts, so there is no effect on the consumption function:

Chapter 7 18 Final Thus: C = C 0 + C y (1-t)Y C = 0 While the shift in government purchases has no direct effect on investment, there will be an indirect effect. Investment depends on the interest rate, and the interest rate will change as a result of the change in government purchases. So from the investment function: I = I 0 - r we can conclude that the level of investment spending will change by: I = r That is, the shift in investment spending will be equal to the sensitivity of investment to the interest rate times the shift in the equilibrium real interest rate. Nothing in the international economic environment changes. Nor does the level of potential output does not change. So looking at the net exports function: NX = X yf Y f ε 0 X ε r r f IM y Y it is clear that here as well, the only shift will be a proportional change in response to the shift in the equilibrium real interest rate: NX = ( X ε r) Finally, real GDP Y does not change because otential output does not change, and this is a full-employment model with real GDP is always equal to potential output:

Chapter 7 19 Final Y = Y* = 0 Putting all these pieces together, we have assembled the relevant components of aggregate demand in "change" form. We can see that as government purchases shift, the other components of aggregate demand will have to shift with it: Y = I + G + NX 0 = r + G X ε r Put the change in the real interest rate on the left-hand side of the equation and everything else on the right, we discover that the shift in government purchases means that the equilibrium real interest rate must change by: G r =

Chapter 7 20 Final Figure 7.5: Effect of an Increase in Government Purchases on the Flow-of-Funds Real Interest Rate r An increase in government purchases reduces public savings and shifts the supply-of-savings line to the left......generates an increase in the real interest rate......a fall in investment spending... Investment Demand Flow-of-Funds Through Financial Markets...and an increased inflow of capital from abroad. To understand this answer, look at the flow-of-funds diagram in figure 7.5. More government purchases means less government savings. This shortfall in savings creates a gap between investment demand and savings supply: the interest rate rises. The rising interest rates lowers the quantity of funds demanded for investment financing. The rising interest rate increases international saving flowing into domestic financial markets. The flow-of-funds market settles down to equilibrium at a new, higher equilibrium interest rate r with a new, lower level of investment. On the flow-of-funds diagram, the increase in government purchases and the consequent reduction in government savings has shifted the flow-of-funds supply curve to the left. The equilibrium position in the diagram has moved up and to the left along the investment curve.

Chapter 7 21 Final Once the change in the equilibrium interest rate has been calculated, determining what happens to the rest of the economy is straightforward. Simply substitute the change in the equilibrium interest rate back into the model's behavioral relationships, and so calculate the changes in the equilibrium levels of the components of GDP, and in the equilibrium level of the real exchange rate. There is no effect on the level of real GDP Y or on consumption spending C: Y = 0 C = 0 The change in government purchases G is just equal to itself: the change in government purchases was the trigger that shifted the economy s equilibrium position: G = G The change in investment spending is the interest sensitivity of investment times the change in the equilibrium real interest rate, which we already calculated above. I = r = G The changes in net exports and in the exchange rate are also equal to their sensitivities to the real interest rate times the change in the equilibrium real interest rate. NX= ε = X ε G X ε G The overall picture of the changes generated by the increase in government purchases is clear. The increase in government purchases has led to a shortfall in savings and a rise in real interest rates. The higher real interest rates have led to lower investment, and to an appreciation in the home currency: a lower level of ε. This exchange rate appreciation has

Chapter 7 22 Final led to a decline in net exports. The declines in net exports and in investment spending just add up to the increase in government purchases, so the level of GDP is unchanged and still equal to potential output--as we assumed it would be. Figure 7.6: The Interest Rate, the Exchange Rate, and the Capital Inflow Real Interest Rate Public Plus Private Savings Total Savings Real Interest Rate Investment Demand Exchange Rate as a Function of the Domestic Interest Rate Flow of Funds Exchange Rate Net Exports Net Exports as a Function of the Exchange Rate - NX = International Savings 0 Exchange Rate Legend: Why does a rise in the domestic interest rate increase the flow of savings into the loanable funds market? Start in the upper left panel of the figure above, where the total savings and investment demand curves cross to determine the equilibrium level of investment spending and real interest rate. That real interest rate then helps determine the real exchange rate, as shown in the upper right panel: the higher the real interest rate, the lower the real exchange rate. That real exchange rate then helps determine net exports, as shown in the lower right panel. And the value of net exports is the inverse of

Chapter 7 23 Final international savings, the capital inflow into the flow of funds. Thus the total savings curve slopes upward: the higher the interest rate, the lower the exchange rate, the lower net exports, the more international savings flowing into domestic financial markets. Note that the fall in investment is not as large as the rise in government purchases. The increase in government purchases reduced the flow of domestic savings into financial markets, but the increased flow of foreign-owned capital into the market partially offset this reduction. The extra savings from abroad kept the decline in investment from being as large as the rise in government purchases, as Figure 7.6 shows. Box 7.3 provides a numerical example of this process at work. Box 7.3--Example: A Government Purchases Boom Assume that the parameters of the model are: t = 0.33 = 9000 Tax rate of 1/3 of income. A 1 percentage point fall in the interest rate raises investment spending by $90 billion a year. C y =0.75A marginal propensity to consume of three-quarters. =10 With an initial value for the real exchange rate ε set at the traditional indexed value of 100, a 1 percentage point change in the interest rate difference vis-à-vis abroad generates a 10% shift in the exchange rate. X ε =600 A 1% change in the exchange rate leads to a $6 billion a year change in exports.

Chapter 7 24 Final Suppose that there is a sudden increase in government purchases of $150 billion a year. This boom in spending increases the equilibrium real interest rate by one percentage point: r = G = $150 9000 + 600 10 = 150 15000 =.01 =1% As a result, the equilibrium values of the other variables in the economy will change by: G = G = +$150 billion I = C = 0 NX= ε = G = 9000 $150 = $90 billion 9000 + 600 10 X ε (600 10) G = $150 = $60 billion 9000 + 600 10 10 G = $150 = 0.1 = 10% change 9000 + 600 10 In sum, the $150 billion increase in annual government purchases has shifted the economy's equilibrium by raising the real interest rates by 1%. Such an increase in the real interest rate carries with it a 10% fall in the exchange rate. The interest rate increase reduces investment spending by $90 billion a year. The exchange rate decline reduces net exports by $60 billion a year. Some additional insight into this example can be gained by looking at the flow of funds diagram in Figure 7.7. The increase in government spending shifts the supply of loanable funds curve to the left by $150 billion. Given the slopes of the loanable funds supply and the investment demand curves, the result of this

Chapter 7 25 Final leftward shift is a $90 billion fall in annual investment--and a 1% point rise in the real interest rate. Figure 7.7: Flow-of-Funds Diagram: An $150 Billion Increase in Government Purchases Real Interest Rate r An $150 billion increase in government purchases reduces public savings and shifts the supply-of-savings line to the left......generates a 1% increase in the real interest rate......a $90 billion fall in investment spending... Investment Demand Flow-of-Funds Through Financial Markets...and a $60 billion increased inflow of capital from abroad. Given this 1% point rise in the real interest rate, it is straightforward to determine the resulting change in the exchange rate, as shown in Figure 7.8, and thus the change in net exports.

Chapter 7 26 Final Figure 7.8: The Impact of a Change in the Domestic Interest Rate on the Exchange Rate Real Interest Rate r A 1% increase in the domestic real interest rate produces... Exchange Rate--the Value of Foreign Currency...an appreciation in the home currency: a 10% reduction in the exchange rate--that is in the value of foreign currency. What if this model economy had experienced not a change in government spending but a change in tax rates? A hint: the effects of a cut in tax rates are very similar but not quite identical to an increase in government spending. A tax cut increases household incomes, and they then divide their increased disposable income, spending some of the increase on consumption and saving the rest.

Chapter 7 27 Final Investment Shocks: Changes in Investors' Optimism Suppose the economy is in equilibrium, when domestic businesses become more optimistic about the future, and increase the amount they wish to spend on new plant and equipment. What would be the effect of this shift on the economy? It would produce a domestic investment boom--a rise I 0 in the value of I 0 in the investment equation: I = I 0 r While the increased optimism of investors increases investment, it is going to be associated with an increase in interest rates, so total investment spending will increease by an amount less than the rise in I 0 : I = I 0 r The increase in the domestic interest rate will change the exchange rate and net exports. But the other variables in the model will be unaffected. Government spending and consumption spending are unchanged; foreign income, foreign interest rates, and foreign exchange traders' long-run expectations are unchanged. Thus the changes in the national income identity are straightforward: I + NX = 0 ( I 0 r) + ( X ε r) = 0 For this to be true, the change in the equilibrium real interest rate must be: I r = 0

Chapter 7 28 Final Figure 7.9: The Flow-of-Funds Market in an Investment Boom Real Interest Rate r An investment boom shifts the demand for loanable funds line to the right... Total Savings...generates an increase in the real interest rate......a rise in investment spending... Flow-of-Funds Through Financial Markets...funded by an increased inflow of capital from abroad. Legend: An investment boom shifts the investment demand curve to the right. The new equilibrium in the flow of funds market has a higher real interest rate and a higher level of investment spending. Note that investment spending does not rise by the full amount of the shift in the investment demand curve. Higher interest rates crowd out some of the increase in investment spending. As Figure 7.9 shows, the investment boom has shifted the demand-for-loanable-funds curve to the right, and increased the equilibrium real interest rate. The increased equilibrium interest rate leads to no change in consumption spending or in government purchases. As Figure 7.10 shows, it leads to a fall in the exchange rate and in net exports. But nevertheless investment spending rises:

Chapter 7 29 Final C = 0 G = 0 ε = I 0 NX= X ε I 0 I I = I 0 0 = X ε I 0 Figure 7.10: The International Consequences of an Investment Boom Real Interest Rate Public Plus Private Savings Total Savings Real Interest Rate...the real interest rate rises... Investment demand shifts out... Flow of Funds...the inflow of foreign capital to fund domestic investment rises... Net Exports...the real exchange rate declines... Exchange Rate - NX = International Savings 0...net exports decline... Exchange Rate

Chapter 7 30 Final Legend: A change in business managers optimism that shifts the investment demand curve to the right triggers a rise in the real interest rate, a fall in the exchange rate, a fall in net exports, and in increase in foreigners funding of domestic investment. Thus the higher domestic interest rate pulls foreign funds into the country to finance higher desired domestic investment. 7.2.4 International Disturbances An Increase in Foreign Interest Rates Now consider a disturbance from abroad: an upward jump in the foreign real interest rate r f by an amount r f. This increase has an immediate impact on the exchange rate, changing it by: ε = ( r r t ) As a result, net exports shift by: NX = X ε ( r r t ) As net exports rise, the inflow of foreign funds to finance domestic investment falls. The supply of savings in the flow-of-funds diagram shifts to the left, and the domestic interest rate rises. Consumption spending and government purchases will not be affected by the rise in overseas interest rates, the fall in the exchange rate, and the rise in the domestic interest rate that it triggers. Nothing has happened to affect any of the determinants of consumption spending or government purchases. Investment spending, however, will be

Chapter 7 31 Final affected by the shift in the equilibrium domestic interest rate. As the economy responds to this shift, the changes in the national income identity will be: I + NX = 0 r X ε ( r r f ) = 0 Therefore the shift in the equilibrium domestic real interest rate r is: r = X ε r f From this change in the domestic interest rate and the value r f for the change in the foreign interest rate, we can calculate the shifts in the equilibrium values of the components of GDP and in the equilibrium real exchange rate. As we have seen, there are no changes in consumption spending or government purchases: C = 0 G = 0 Investment will fall by the sensitivity of investment spending to the interest rate times the change in the equilibrium real interest rate: I = X ε r f The shift in the exchange rate will be proportional to the difference between the shifts in the domestic and the foreign interest rates. And the shift in net exports will be proportional to the shift in the exchange rate.

Chapter 7 32 Final ε = NX= X ε r f + r f = r f X ε X ε r f r f = X ε r f Again, the quickest way to understand the shift in the economy s equilibrium is to use the flow-of-funds diagram. The rise in the foreign interest rate reduces the amount of capital foreigners want to devote to domestic investments. It shifts the flow-of-funds supply curve to the left, as Figure 7.11 shows. As a result, the economy s equilibrium moves up and to the left along the investment demand curve. The new equilibrium has a higher domestic interest rate and a lower value for investment. Figure 7.11: Flow-of-Funds: An Increase in Interest Rates Abroad Real Interest Rate r An increase in interest rates overseas reduces the funds that foreigners wish to place in U.S. financial markets, and shifts the total savings line to the left......generates an increase in the real interest rate......a fall in investment spending... Investment Demand Flow-of-Funds Through Financial Markets...and the higher interest rates at home pull some of the foreignowned capital back into the domestic market.

Chapter 7 33 Final Legend: A rise in foreign interest rates diminishes foreigners willingness to finance domestic investment, and shifts the flow of funds saving supply curve to the left. The economy s equilibrium moves up and to the left along the investment demand curve. The new equilibrium ha a higher real interest rate and lower investment spending. GDP remains equal to potential output. The domestic interest rate rises less than the change in the foreign interest rate, raising the real exchange rate as is shown in 7.12. Thus the economy's level of net exports grows by as much as the level of domestic investment shrinks.

Chapter 7 34 Final Figure 7.12: The Real Exchange Rate and Domestic Interest Rates Real Interest Rate r A rise in interest rates abroad makes foreign currency more valuable at any given level of the domestic interest rate......but the reduced capital inflow raises domestic interest ratess... Exchange Rate--the Value of Foreign Currency...and the higher domestic interest rates reduce the size of the increase in the equilibrium value of the foreign currency. Legend: A rise in foreign real interest rates raises the value of the exchange rate, but not by as much as one would expect from the change in foreign interest rates alone. Domestic interest rates rise as well, and partially offset the effect of changing foreign interest rates on the exchange rate. A Decline in Confidence in the Currency

Chapter 7 35 Final Suppose the economy is in equilibrium when there is a change in foreign exchange speculators' confidence in the currency and thus in the long-run value of the exchange rate ε 0. What will happen? The shift in the exchange rate will be: ε = ε 0 r because the exchange rate is affected not just by foreign exchange speculators beliefs but also by the domestic real interest rate, and the domestic interest rate will change because the change in the exchange rate will alter the flow of funds through financial markets. The change in net exports, and thus in the inflow of capital, will be proportional to the change in the exchange rate: NX = X ε ε 0 X ε r The changing domestic interest rate will shift the level of domestic investment spending sa well. Thus the relevant changes in the national income identity are: I + NX = 0 ( r) ε 0 X ε r ( ) = 0 This means that the change in the equilibrium domestic interest rate r is: r = X ε ε 0 Using this formula, we can calculate the shift in the equilibrium value of the components of real GDP, and the shift in the value of the exchange rate. Once again, consumption spending and government purchases are unchanged: C = 0 G = 0

Chapter 7 36 Final The change in investment spending is equal to the interest sensitivity of investment spending times the change in the real interest rate: I = X ε ε 0 The shift in the real exchange rate is generated both by the shift in foreign exchange speculators expectations and by the shift in the equilibrium real interest rate. And the shift in net exports is proportional to the shift in the real exchange rate: ε = NX= X ε ε 0 + ε 0 = ε 0 X ε X ε ε 0 ε 0 = X ε ε 0 Why has a decrease in foreign exchange speculators' long-run confidence--for that is what an increase in ε 0 is, a belief that the long-run value of the currency will be lower had these effects? The shift in confidence means that at current exchange and interest rates, foreign exchange speculators wish to pull their money out of the home currency; they are not happy using their money to finance domestic investment. Thus on the flow-of-funds diagram Figure 7.13 the savings supply curve shifts to the left. Once again, the equilibrium point moves up and to the left along the investment demand curve. Once again, the economy comes to rest at a point with a higher domestic interest rate and a lower value for investment. The equilibrium value of the exchange rate is higher, and so is the value of net exports. Box 7.4 provides a numerical example of this process.

Chapter 7 37 Final Figure 7.13: The Flow-of-Funds and a Decline in Exchange Rate Confidence Real Interest Rate r An increase in speculators' view of the "fundamental" long-run value of foreign currency reduces the flow of international savings into domestic financial markets......it generates an increase in the real interest rate......a fall in investment spending... Investment Demand Flow-of-Funds Through Financial Markets...and higher interest rates at home pull some foreignowned capital back into domestic financial markets. Legend: If foreign-exchange traders lose confidence in the long-run value of the domestic currency, the effects on the domestic economy are very similar to the effects of a rise in foreign interest rates. The value of the exchange rate rises, and the savings supply curve shifts to the left. Box 7.4--Example: The Effect of a Fall in Confidence in the Currency Suppose the parameters describing the economy are: t = 0.33 Tax rate of 1/3.

Chapter 7 38 Final = 9000 A 1 percentage point fall in the interest rate raises investment spending by $90 billion a year. C y =0.75 =10 A marginal propensity to consume of three-quarters. With an initial value for the real exchange rate ε set at the traditional indexed value of 100, a 1 percentage point change in the interest rate difference vis-à-vis abroad generates a 10% shift in the exchange rate. X ε =600 A 1% change in the exchange rate leads to a $6 billion a year change in exports. Suppose further that the initial value of the exchange rate ε is 100 and that longrun exchange rate expectations ε 0 is also 100. What happens if this economy is hit by a sudden loss in confidence in the long-run value of its currency, a rise in ε 0 from 100 to 120? Consumption does not change, and government purchases do not change, so the relevant changes in the national income identity are: Y* = 0 = I + NX The changes in investment and net exports are: I = r NX = X ε ε = X ε ε 0 X ε r With these particular parameter values: I = 9000 r NX= 600 ε = 600 0.20 600 10 r 0 = I + NX

Chapter 7 39 Final Substituting the values from the first two into the third: 0 = 9000 r + 600 0.20 600 10 r 0 = 120 15000 r r = 0.008 = 0.8% The real interest rate rises by eight-tenths of a percentage point. Thus investment falls by $72 billion and net exports rise by $72 billion: I = 9000 0.8 = 72 NX= 600 20 600 10 0.8 = +72 And the new equilibrium value of the real exchange rate is: ε = ε 0 + (r f r) = 120 +10 ( 0.8) = 112 Higher interest rates offset the loss of confidence in the currency, and so the exchange rate--the value of foreign currency--increases by a little more than half of the change in currency traders' expectations. The four cases we have analyzed here are not exhaustive. There are many other changes in the economic environment or in economic policy that the flexible-price is useful for analyzing. Think of these four as examples of how to proceed: identify the components of real GDP that are going to change, determine the change in the equilibrium real interest rate, and then use the change in the equilibrium real interest rate and the triggering shift in the economic environment to calculate the post-change state of the economy. Box 7.5--Policy: The Mexican and East Asian Financial Crises At the end of 1994, currency traders and international investors lost confidence in the Mexican peso. In the middle of 1997, currency traders and international

Chapter 7 40 Final investors lost confidence in virtually all the currencies of the rapidly-growing developing economies of East Asia. Sharp rises in real interest rates, falls in domestic investment, and declines in the value of the affected domestic currencies followed in both crises. Some commentators railed against these changes. From the right, the editorial page of the Wall Street Journal, for example, denounced the International Monetary Fund [IMF] and the U.S. Treasury for advising the affected countries that the values of their domestic currencies should depreciate--and the home-currency value of foreign currencies, the exchange rate, should rise. From the left, other economists denounced the IMF and the U.S. Treasury for advising countries to allow the real interest rate to rise. There are complicated and delicate issues involved in crisis management. But our analysis of the consequences of a collapse in foreign exchange trader confidence in the currency above should make us skeptical of both positions. Our analysis strongly suggests that both the Wall Street Journal which attacked the IMF from the right and the economists who attacked the IMF from the left were wrong. In our flexible-price model the fall in exchange-rate confidence and the resulting decline in international investment must lead to a rise in domestic interest rates and a fall in investment. There is no alternative equilibrium in which this does not happen. The fall in exchange-rate confidence and the decline in international investment must lead to a rise in the exchange rate and a rise in net exports. There is no alternative equilibrium in which this doesn't happen.

Chapter 7 41 Final There is a legend that King Canute s advisors told him that he was so powerful that he could command the tides to stop. Our analysis of the consequences of a collapse of exchange rate confidence suggests that unless confidence can be restored those who demand that such a crisis be resolved without a rise in the exchange rate and a rise in domestic interest rates are giving advice as good as that given to King Canute. 7.3 Supply Shocks So far we have assumed that the level of potential output is fixed. Whatever shocks have affected the economy, they have had no effect on aggregate supply, no effect on potential output. But there are shocks to a flexible-price full-employment economy that change aggregate supply. Supply shocks like the 1973 tripling of world oil prices reduce potential output. Inventions and innovations can be positive productivity shocks that increase the level of potential output. We can use the full-employment model of this chapter to analyze the effects on the economy of a supply shock. However, the effects of a supply shock are different in one important respect from the effects of the demand or international shocks we have analyzed above. In response to a supply shock the level of GDP does change--even in this, full-employment, chapter--because the level of potential GDP has changed. In each case, call the resulting supply-shock driven change in potential output Y*.

Chapter 7 42 Final Oil and Other Supply Shocks In 1973 the world price of oil tripled. In response to the 1973 Arab-Israeli War, the Organization of Petroleum Exporting Countries exerted its market power to restrict the worldwide supply of oil and raise the price. Capital- and energy-intensive production processes that had made economic sense and been profitable with oil costing less than $3 a barrel became unproductive and unprofitable with oil costing $10 a barrel. Thus potential output fell because it was now more profitable to use technologies that economized on oil by intensively using other factors of production like labor, and so the efficiency of labor E in the production function fell. If we look at the changes in the national income identity: C + I + G + NX= Y * we will find them more complex than in the case of the demand shocks considered in the section above because the change in real GDP is not zero. If we expand the changes form of the national income identity by substituting for each component of GDP the equation for its determinants, we produce: ( C y (1 t) Y *) ( r) + ( X ε r IM y Y *) = Y * We can regroup and solve this equation for the change r in the equilibrium interest rate is:

Chapter 7 43 Final r = 1 C (1 t) + IM y y Y * A negative value for Y*--an adverse supply shock, one that lowers the level of potential output and GDP--generates an increase in the domestic real interest rate. Why? Because a fall in GDP due to an oil price increase or other adverse supply shock reduces incomes, and so reduces the flow of private savings into financial markets. (It is true that a decline in incomes carries with it a decline in consumption, and in net exports, but these declines do not match the decline in income, so domestic savings falls.) As Figure 7.14 shows, the fall in domestic savings shifts the savings supply curve to the left, raising the real interest rate and reducing investment. As before, the increase in the domestic real interest rate makes foreigners more willing to invest in the home country. It increases the flow of foreign savings (which partly offsets the leftward shift in the savings supply curve), reduces net exports, and lowers the exchange rate (lowers the value of foreign currency). By now must seem as though every shock that affects a full-employment economy does one of four things: It shifts the savings supply curve to the left (raising domestic interest rates and lowering investment). It shifts the savings supply curve to the right (lowering domestic interest rates and raising investment). It shifts the investment demand curve to the left (lowering investment and lowering domestic interest rates).

Chapter 7 44 Final Or it shifts the investment demand curve to the right (raising investment and raising domestic interest rates). If you think this, you are right. Every shock to the economy will have an impact on the flow of funds, and those are the four kinds of impact on the flow-of-funds a shock can have. Analyzing the effect of the shock on savings and investment is key to understanding its economy-wide impact. Outside the flow-of-funds, however, different kinds of shocks have other, less similar effects. Figure 7.14: Flow of Funds in Response to an Adverse Supply Shock Real Interest Rate r A reduction in potential output reduces incomes, and so reduces savings......it generates an increase in the real interest rate......a fall in investment spending... Investment Demand Flow-of-Funds Through Financial Markets...and the higher interest rates at home pull some foreignowned capital back into domestic financial markets.

Chapter 7 45 Final Legend: An adverse supply shock will diminish savings, raise the real interest rate, and lower investment. From the change in the level of GDP and the change in the interest rate, it is straightforward to calculate the effect of the supply shock on the other economic variables: C = C y (1 t) Y * 1+ IM I = I y C y (1 t) r Y * G = 0 1 + IM NX = X ε ε y C y (1 t) r Y * 1 + IM ε = ε y C y (1 t) r Y * An adverse supply shock--a negative value for Y*--leads to declines in consumption, investment, and net exports; it leads to an appreciation of the home currency, and thus to a reduction in the value of foreign currency--in the exchange rate. It also leads to a rise in the price level, and an acceleration of inflation. But that is covered in the next chapter, Chapter 8. Real Business Cycles

Chapter 7 46 Final The mid-twentieth century economist Joseph Schumpeter was the most powerful exponent of the belief that changes in technology were the principal force driving business cycles. Schumpeter saw technological progress as inherently lumpy. There were five-year periods during which a great deal of new technology diffused rapidly throughout the economy. These were booms. There were five-year periods during which the pace of technological innovation and diffusion was much slower. These were periods of relative stagnation. Schumpeter saw the key feature of the business cycle as the comovements of output, employment, investment, and interest rates: all were high together in a boom, all were low together (relative to trend) in a recession. It is easy to see how uneven invention and innovation patterns could generate such real business cycles business cycles driven by the fundamental technological dynamic of the economy. Suppose that the most common shift in technology involves (a) a sudden step up in the efficiency of labor, accompanied by (b) a sudden rise in investment demand as it becomes more profitable for a business to enlarge its capital stock. Such a shock has a supply component--an increase Y* in this year's potential output--and an investment demand component--an increase I 0 in this year's investment demand. How does the economy's full-employment equilibrium shift in response to such a combined shock? We simply add together the effects of a supply shock, outlined immediately above, and the effects of an investment boom driven by investors' increasing optimism, outlined in the previous section. The change in the equilibrium domestic real interest rate from a supply shock is: r = 1 C (1 t) + IM y y Y * The change from an investment demand shock is: