 # Motivation The Great Depression caused a rethinking of the Classical Theory of the macroeconomy. It could not explain: Drop in output by 30% from 1929.

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Topic 9: Aggregate Demand I (chapter 10)

Motivation The Great Depression caused a rethinking of the Classical Theory of the macroeconomy. It could not explain: Drop in output by 30% from 1929 to 1933 Rise in unemployment to 25% In 1936, J.M. Keynes developed a theory to explain this phenomenon. We will learn a version of this theory, called the ‘IS-LM’ model.

Context Chapter 9 introduced the model of aggregate demand and aggregate supply. Long run prices flexible output determined by factors of production & technology unemployment equals its natural rate Short run prices fixed output determined by aggregate demand unemployment is negatively related to output

Context This chapter develops the IS-LM model, the theory that yields the aggregate demand curve. We focus on the short run and assume the price level is fixed.

The Keynesian Cross A simple closed economy model in which income is determined by expenditure. (due to J.M. Keynes) Notation: I = planned investment E = C + I + G = planned expenditure Y = real GDP = actual expenditure Difference between actual & planned expenditure: unplanned inventory investment

Elements of the Keynesian Cross
consumption function: govt policy variables: for now, investment is exogenous: planned expenditure: Stress that much of this model is very familiar to students: same consumption function as in previous chapters, same treatment of fiscal policy variables. Note: In equilibrium, there’s no unplanned inventory investment. Firms are selling everything they had intended wanted to sell. Equilibrium condition:

Graphing planned expenditure
E =C +I +G Slope is MPC Why slope of E line equals the MPC: With I and G exogenous, the only component of (C+I+G) that changes when income changes is consumption. A one-unit increase in income causes consumption---and therefore E---to increase by the MPC. Recall from Chapter 3: the marginal propensity to consume, MPC, equals the increase in consumption resulting from a one-unit increase in disposable income. Since T is exogenous here, a one-unit increase in Y causes a one-unit increase in disposable income. income, output, Y

Graphing the equilibrium condition
planned expenditure E =Y 45º income, output, Y

The equilibrium value of income
planned expenditure E =Y E =C +I +G The equilibrium point is the value of income where the curves cross. Equilibrium income income, output, Y

The equilibrium value of income
planned expenditure E =Y E =C +I +G E<Y E>Y income, output, Y E>Y: depleting inventories: must produce more. E<Y: accumulating inventories: must produce less.

An increase in government purchases
Y E E =Y At Y1, there is now an unplanned drop in inventory… E =C +I +G2 E =C +I +G1 G Looks like Y>G …so firms increase output, and income rises toward a new equilibrium Explain why the vertical distance of the shift in the E curve equals G: At any value of Y, an increase in G by the amount G causes an increase in E by the same amount. At Y1, there is now an unplanned depletion of inventories, because people are buying more than firms are producing (E > Y). E1 = Y1 Y E2 = Y2

Why the multiplier is greater than 1
Def: Government purchases multiplier: Initially, the increase in G causes an equal increase in Y: Y = G. But Y  C  further Y  further C So the government purchases multiplier will be greater than one. Students are better able to understand this if given a more concrete example. For instance, Suppose the government spends an additional \$100 million on defense. Then, the revenues of defense firms increase by \$100 million, all of which becomes income to somebody: some of it is paid to the workers and engineers and managers, the rest is profit paid as dividends to shareholders. Hence, income rises \$100 million (Y = \$100 million = G ). The people whose income just rose by \$100 million are also consumers, and they will spend the fraction MPC of this extra income. Suppose MPC = 0.8, so C rises by \$80 million. To be concrete, suppose they buy \$80 million worth of Chevy Trailblazers. Then, General Motors sees its revenues increase by \$80 million, all of which becomes income to somebody - either GM’s workers, or its shareholders (Y = \$80 million). And what do these folks do with this extra income? They spend the fraction MPC (0.8) of it, causing C = \$64 million (8/10 of \$80 million). Suppose they spend all \$64 million on Hershey’s chocolate bars, the ones with the bits of mint cookie inside. Then, Hershey Foods Corporation experiences a revenue increase of \$64 million, which becomes income to somebody or other. (Y = \$64 million). So far, the total impact on income is \$100 million + \$80 million + \$64 million, which is much bigger than the government’s initial increase in spending. But this process continues, and the final impact on Y is \$500 million (because the multiplier is 5).

An increase in government purchases
Y E E =Y C even more C more C Y even more Y more G Y once Explain why the vertical distance of the shift in the E curve equals G: At any value of Y, an increase in G by the amount G causes an increase in E by the same amount. At Y1, there is now an unplanned depletion of inventories, because people are buying more than firms are producing (E > Y).

Sum up changes in expenditure

Solving for Y equilibrium condition in changes because I exogenous
because C = MPC Y Collect terms with Y on the left side of the equals sign: Finally, solve for Y :

Algebra example Suppose consumption function: C= a+b(Y-T)
where a and b are some numbers (MPC=b) Use Goods market equilibrium condition:

Algebra example Solve for Y:
So if b=MPC=0.75, multiplier = 1/( ) = 4.

An increase in taxes E C = MPC T Y Y E =C1 +I +G E =C2 +I +G
E =Y Y E Initially, the tax increase reduces consumption, and therefore E: E =C1 +I +G E =C2 +I +G At Y1, there is now an unplanned inventory buildup… C = MPC T …so firms reduce output, and income falls toward a new equilibrium Suppose taxes are increased by T. Because I and G are exogenous, they do not change. However, C depends on (YT). So, at the initial value of Y, a tax increase of T causes disposable income to fall by T, which causes consumption to fall by MPC  T. Because consumption falls, the change in C is negative: C =  MPC  T C is part of planned expenditure. The fall in C causes the E line to shift down by the size of the initial drop in C. At the initial value of output, there is now unplanned inventory investment: Sales have fallen below output, so the unsold output adds to inventory. In this situation, firms will reduce production, causing total output, income, and expenditure to fall. E2 = Y2 Y E1 = Y1

Tax multiplier Define tax multiplier: how much does output fall for a unit rise in taxes: Can read the tax multiplier from the algebraic solution above: If b=0.75, tax multiplier = -0.75/( ) = -3.

Solving for Y eq’m condition in changes I and G exogenous
Final result:

The Tax Multiplier Question: how is this different from the government spending multiplier considered previously? The tax multiplier: …is negative: An increase in taxes reduces consumer spending, which reduces equilibrium income. …is smaller than the govt spending multiplier: (in absolute value) Consumers save the fraction (1-MPC) of a tax cut, so the initial boost in spending from a tax cut is smaller than from an equal increase in G.

A question to consider:
Using the Keynesian Cross, what would be the effect of an increase in investment on the equilibrium level of income/output. Note :This in-class exercise not only gives students practice with the model, it also helps them understand the next topic: the IS curve. Effect is just like rise in G previously.

Building the IS curve def: a graph of all combinations of r and Y that result in goods market equilibrium, i.e. actual expenditure (output) = planned expenditure The equation for the IS curve is:

Deriving the IS curve r  I  E  Y E =C +I (r2 )+G

Understanding the IS curve’s slope
The IS curve is negatively sloped. Intuition: A fall in the interest rate motivates firms to increase investment spending, which drives up total planned spending (E ). To restore equilibrium in the goods market, output (a.k.a. actual expenditure, Y ) must increase.

Fiscal Policy and the IS curve
We can use the IS-LM model to see how fiscal policy (G and T ) can affect aggregate demand and output. Let’s start by using the Keynesian Cross to see how fiscal policy shifts the IS curve…

Shifting the IS curve: G
E =Y Y E E =C +I (r1 )+G2 At any value of r, G  E  Y E =C +I (r1 )+G1 …so the IS curve shifts to the right. The horizontal distance of the IS shift equals Y1 Y2 r Y r1 Y IS2 IS1 Y1 Y2

Algebra example for IS curve
Suppose the expenditure side of the economy is characterized by: C = (Y-T) I = 100 – 100r G = 20, T=20 Use the goods market equilibrium condition Y = C + I + G Y = (Y-20) – 100r 0.25Y = 200 – 100r IS: Y = 800 – 400r or write as IS: r = Y

Graph the IS curve r 2 Slope = IS Y IS: r = Y

Slope of IS curve Suppose that investment expenditure is “more responsive” to the interest rate: I = 100 – 100r 200r Use the goods market equilibrium condition Y = C + I + G Y = (Y-20) – 200r 0.25Y = 200 – 200r IS: Y = 800 – 800r or write as IS: r = Y (slope is lower) So this makes the IS curve flatter: A fall in r raises I more, which raises Y more.

Building the LM Curve: The Theory of Liquidity Preference
due to John Maynard Keynes. A simple theory in which the interest rate is determined by money supply and money demand.

Money Supply The supply of real money balances is fixed: r M/P
interest rate We are assuming a fixed supply of real money balances because P is fixed by assumption (short-run), and M is an exogenous policy variable. M/P real money balances

Money Demand Demand for real money balances: L (r ) r M/P interest
rate L (r ) As we learned in chapter 4, the nominal interest rate is the opportunity cost of holding money (instead of bonds). Here, we are assuming the price level is fixed, so  = 0 and r = i. M/P real money balances

Equilibrium The interest rate adjusts to equate the supply and demand for money: r interest rate r1 L (r ) M/P real money balances

How the Fed raises the interest rate
To increase r, Fed reduces M r2 r1 L (r ) M/P real money balances

CASE STUDY Volcker’s Monetary Tightening
Late 1970s:  > 10% Oct 1979: Fed Chairman Paul Volcker announced that monetary policy would aim to reduce inflation. Aug 1979-April 1980: Fed reduces M/P 8.0% Jan 1983:  = 3.7% This and the next slide summarize the case study on pp The data source is given on the next slide. At this point, students have now learned different theories about the effects of monetary policy on interest rates. This case study shows them that both theories are relevant, using a real-world example to remind students that the classical theory of chapter 4 applies in the long-run while the liquidity preference theory applies in the short run. How do you think this policy change would affect interest rates?

Volcker’s Monetary Tightening, cont.
prediction actual outcome The effects of a monetary tightening on nominal interest rates prices model long run short run Liquidity Preference (Keynesian) Quantity Theory, Fisher Effect (Classical) sticky flexible Since prices are sticky in the short run, the Liquidity Preference Theory predicts that both the nominal and real interest rates will rise in the short run. And in fact, both did. (However, the inflation rate was not zero, and in fact it increased, so the real interest rate didn’t rise as much as the nominal interest rate did during the period shown.) In the long run, the Quantity Theory of Money says that the monetary tightening should reduce inflation. The Fisher Effect says that the fall in  should cause an equal fall in i. By January of 1983 (which is “the long run” from the viewpoint of 1979), inflation and nominal interest rates had fallen. (However, they did not fall by equal amounts. This doesn’t contradict the Fisher Effect, though, as other economic changes caused movements in the real interest rate.) i > 0 i < 0 8/1979: i = 10.4% 4/1980: i = 15.8% 1/1983: i = 8.2%

The LM curve Now let’s put Y back into the money demand function:
The LM curve is a graph of all combinations of r and Y that equate the supply and demand for real money balances. The equation for the LM curve is:

Deriving the LM curve L (r , Y2 ) L (r , Y1 ) r r LM Y1 Y2 r2 r2 r1 r1
(a) The market for real money balances (b) The LM curve L (r , Y1 ) M/P r r Y LM Y1 Y2 r2 r2 r1 r1

Understanding the LM curve’s slope
The LM curve is positively sloped. Intuition: An increase in income raises money demand. Since the supply of real balances is fixed, there is now excess demand in the money market at the initial interest rate. The interest rate must rise to restore equilibrium in the money market.

Deriving LM curve with algebra
Suppose a money demand: Where e describes the responsiveness of money demand to changes in income. And f describes responsiveness to interest rate. Suppose money supply: Use money market equilibrium condition:

Graph the LM curve r LM Slope = e/f Y (1/f)(M/P)
A steep LM curve (e/f large) means that a rise in output implies a big rise in interest rate to maintain equilibrium. Causes of this: Money demand is not very responsive to interest rate (f is small) Money demand is very responsive to output (e large)

How M shifts the LM curve
(a) The market for real money balances (b) The LM curve L (r , Y1 ) M/P r r Y LM2 Y1 LM1 r2 r2 r1 r1 We can think of the LM curve shift as a vertical shift: When the Fed reduces M, the vertical distance of the shift tells us what happens to the equilibrium interest rate associated with a given value of income. Or, we can think of the LM curve shifting horizontally: When the Fed reduces M, the horizontal distance of the shift tells us what would have to happen to income to restore money market equilibrium at the initial interest rate. (The graphical analysis would be a little different than what’s depicted on this slide.)

The short-run equilibrium
The short-run equilibrium is the combination of r and Y that simultaneously satisfies the equilibrium conditions in the goods & money markets: Y r LM IS Equilibrium interest rate Equilibrium level of income

The Big Picture Keynesian Cross IS curve IS-LM model
Explanation of short-run fluctuations Theory of Liquidity Preference LM curve Agg. demand curve Model of Agg. Demand and Agg. Supply Agg. supply curve

Chapter summary Keynesian Cross basic model of income determination
takes fiscal policy & investment as exogenous fiscal policy has a multiplied impact on income. IS curve comes from Keynesian Cross when planned investment depends negatively on interest rate shows all combinations of r and Y that equate planned expenditure with actual expenditure on goods & services

Chapter summary Theory of Liquidity Preference
basic model of interest rate determination takes money supply & price level as exogenous an increase in the money supply lowers the interest rate LM curve comes from Liquidity Preference Theory when money demand depends positively on income shows all combinations of r andY that equate demand for real money balances with supply

Chapter summary IS-LM model
Intersection of IS and LM curves shows the unique point (Y, r ) that satisfies equilibrium in both the goods and money markets.

Preview of Chapter 11 In Chapter 11, we will
use the IS-LM model to analyze the impact of policies and shocks learn how the aggregate demand curve comes from IS-LM use the IS-LM and AD-AS models together to analyze the short-run and long-run effects of shocks learn about the Great Depression using our models

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