Aggregate Demand I: Building the IS-LM Model

Aggregate Demand I: Building the IS-LM Model
Chapter 11 of Macroeconomics, 8th edition, by N. Gregory Mankiw ECO62 Udayan Roy

The goods market in the short run

Recap: Long-Run Theory of Output
As before, let Y denote total real GDP Recall that, in the long run, total real GDP is calculated as Y = F(K, L) The economy produces as much as it can Total real GDP in the long run is also called: Natural GDP, or Potential GDP From now on, total long-run real GDP will be denoted 𝒀 = F(K, L)

Actual Output ≠ Potential Output
In the short run, total real GDP is not necessarily equal to natural GDP, or potential GDP Y ≠ 𝒀 We need a new theory of Y, because the long-run theory— 𝑌 = F(K, L)—no longer works

Short-Run Theory of Output: it’s all about demand
The short-run theory of total real GDP is also called Keynesian theory, after the economist John Maynard Keynes, or Aggregate Demand Theory This theory assumes that, in the short run, output is determined by aggregate demand: the economy will produce as much output as there is demand for

The simplest theory of short-run equilibrium in the goods market
The Keynesian Cross

Planned Expenditure Assumption: The economy is a closed economy
Planned Expenditure (PE) is the total desired expenditure of the three sectors of the economy: Households (C) Businesses (I) and Government (G) PE = C + I + G

Consumption Expenditure
PE = C + I + G What determines the planned expenditure of households (C)? We did this before in chapter 3

Consumption, C Net Taxes = Tax Revenue – Transfer Payments
Denoted T and always assumed exogenous: 𝑻= 𝑻 Recall that GDP is defined as the market value of all final goods and services produced in an economy during a given period of time But this is also actual total expenditure, which is also actual total income Therefore, Y also represents actual total income Disposable income (or, after-tax income) is total income minus total net taxes: Y – T. Assumption: planned consumption expenditure (C) is directly related to disposable income (Y – T)

Consumption, C Assumption: Planned expenditure by households is directly related to disposable income Consumption function: C = C (Y – T )

Consumption Function: algebra
Consumption function: C = C (Y – T ) Specifically, C = Co + Cy✕(Y – T) Co represents all other exogenous variables that affect consumption, such as asset prices, consumer optimism, etc. Cy is the marginal propensity to consume (MPC), the fraction of every additional dollar of income that is consumed

Consumption Function: graph
Y C (Y –T) = Co + Cy✕(Y – T) The slope of the consumption function is the MPC. MPC 1 Co Marginal propensity to consume (MPC) is the increase in consumption (C) when disposable income (Y – T) increases by one dollar. It is denoted Cy.

Consumption Function: shifts
Y C = Co2 + Cy✕(Y – T) C = Co1 + Cy✕(Y – T) Consumption shift factor: higher consumer optimism, higher asset prices (Co↑).

Consumption Function: shifts
Y C = Co + Cy✕(Y – T2) C = Co + Cy✕(Y – T1) The same shift can also be caused by lower taxes. (T2 < T1)

Consumption Function: example
Suppose Y = and T = 0.85. Therefore, disposable income is Y – T = 30. Now, suppose C = ✕ (Y – T). Then, C = ✕ 30 = 26 Private Saving is defined as disposable income – consumption, which is Y – T – C = 30 – 26 = 4. Y C C(Y – T), T

Income and Private Saving
The marginal propensity to consume is a positive fraction (0 < MPC < 1) That is, when income (Y) increases, consumption (C) also increases, but by only a fraction of the increase in income. Therefore, Y↑⇒ C↑ and Y – C↑ and Y – T – C↑ Similarly, Y↓⇒ C↓ and Y – C↓ and Y – T – C↓

Planned Investment PE = C + I + G
Assumption: Planned investment spending by businesses (I) is exogenous This assumption is a big simplification. Recall that business investment was assumed to be inversely related to the real interest rate in Chapter 3. We will return to 𝐼= 𝐼 0 − 𝐼 𝑟 ∙𝑟 later.

Government Spending PE = C + I + G
Assumption: government spending (G) is exogenous Public Saving is defined as the net tax revenue of the government minus government spending, which is T – G This is also called the budget surplus

Planned Expenditure PE = C + I + G Therefore, PE = C(Y – T) + I + G
Or, more specifically, PE = Co + Cy✕(Y – T) + I + G

Equilibrium Assumption: The goods market will be in equilibrium. That is, actual expenditure will be equal to planned expenditure.

Actual and planned expenditure
Actual and planned expenditure do not have to be equal in all circumstances Actual expenditure = planned expenditure + unplanned increase in inventory When unplanned increase in inventory > 0, more is bought than was intended. When unplanned increase in inventory < 0, less is bought than was intended.

Equilibrium When unplanned increase in inventory > 0, more is bought than was intended. So, actual expenditure > planned expenditure In this case, output will shrink In other words, the current output level cannot represent equilibrium

Equilibrium When unplanned increase in inventory < 0, less is bought than was intended. So, actual expenditure < planned expenditure In this case, output will increase In other words, the current output level cannot represent equilibrium

Equilibrium For an economy to be in equilibrium, unplanned increase in inventory must be zero Therefore, actual expenditure = planned expenditure + unplanned increase in inventory = planned expenditure But recall that actual expenditure is actual GDP or Y, and planned expenditure is C + I + G Therefore, in equilibrium, Y = C + I + G

Short-Run GDP: calculation
We just saw that in equilibrium Y = C + I + G Therefore, Y = Co + Cy ✕ (Y – T) + I + G This is one equation with one unknown, Y So, this equation can be used to solve for Y Example: C = ✕(Y – T), T = 0.85, G = 3, and I = 1.85 Then, Y = ✕(Y – 0.85) Check that Y = 30.85

Short-Run GDP: calculation
In equilibrium, Y = C + I + G At this point, you should be able to do problems 2 and 4 on pages of the textbook. Please try them. Every variable on the right hand-side of the equation is exogenous. So, this equation tells us everything we can say about Y in the Keynesian Cross model.

Short-Run GDP: predictions
Predictions Grid Y Co + T − I G Every variable on the right hand-side of the equation is exogenous. So, this equation tells us everything we can say about Y in the Keynesian Cross model. Important: Note that there is absolutely no reason why this short-run equilibrium GDP has to be equal to the long-run equilibrium GDP ( 𝒀 ). In other words, the Keynesian Cross model is able to explain why recessions and booms happen.

The Keynesian Cross Equation

The Spending Multiplier
Note that for every $1.00 increase in Co + I + G, Y increases by $1/(1 – Cy). As Cy is the marginal propensity to consume, 1/(1 – Cy) may be written as 1/(1 – MPC). This is called the spending multiplier.

As the marginal propensity to consume is a positive fraction (0 < MPC < 1), 1 – MPC is also a positive fraction. Therefore, 1/(1 – MPC) > 1. So, for every $1.00 increase in Co + I + G, Y increases by more than $1.00!

The spending multiplier is 1/(1 – MPC). Example: If MPC = 0.2, the spending multiplier = 1/(1 – 0.2) = Therefore, if the government spends $3 billion on a new highway, real GDP will increase by $3.75 billion Example: If MPC = 0.8, the spending multiplier = 1/(1 – 0.8) = 5. Therefore, if the government spends $3 billion on a new highway, real GDP will increase by $15 billion The bigger MPC is, the bigger the spending multiplier will be. Why???

The Tax-Cut Multiplier
Note that for every $1.00 decrease in T, Y increases by $Cy/(1 – Cy). As Cy is the marginal propensity to consume, Cy /(1 – Cy) may be written as MPC/(1 – MPC). This is the tax-cut multiplier.

As the marginal propensity to consume is a positive fraction (0 < MPC < 1), MPC/(1 – MPC) < 1/(1 – MPC) Tax-cut multiplier < spending multiplier That is, a $1.00 tax cut provides a smaller boost to the economy than a $1.00 increase in government spending. Why?? At this point, you should be able to do problem 1 on page 325 of the textbook. Please try it.

The tax-cut multiplier is MPC/(1 – MPC). Example: If MPC = 0.2, the tax-cut multiplier = 0.2/(1 – 0.2) = 0.25 < 1. Therefore, if the government cuts taxes by $3 billion, real GDP will increase by $0.75 billion Example: If MPC = 0.8, the tax-cut multiplier = 0.8/(1 – 0.8) = 4. Therefore, if the government cuts taxes by $3 billion, real GDP will increase by $12 billion

Fiscal Policy The practice of changing the levels of government spending (G) and/or taxes (T) in order to affect the macroeconomic outcome is called fiscal policy Spending more (G↑) and/or cutting taxes (T↓) is called expansionary fiscal policy Spending less (G↓) and/or raising taxes (T↑) is called contractionary fiscal policy

Fiscal Policy The consequences of expansionary and contractionary fiscal policy in the Keynesian Cross model were analyzed in previous slides In any case, they can be easily seen from the Keynesian Cross model’s equation: K.C. Spending multiplier K.C. Tax-cut multiplier

Fiscal Policy: balanced budget multiplier
Note that expansionary fiscal policy (G↑ and/or T↓) leads to lower public saving (T – G↓) This could mean a rise in the budget deficit or a fall in the budget surplus Is there no way to stimulate an economy in a recession while keeping the budget balanced? There is!

What happens if both G and T increase by $1? The $1 increase in G increases Y by 1/(1 – MPC) The $1 increase in T decreases Y by MPC/(1 – MPC) Therefore, the total change in Y is ∆𝑌= 1 1− 𝐶 𝑦 − 𝐶 𝑦 1− 𝐶 𝑦 = 1− 𝐶 𝑦 1− 𝐶 𝑦 =1 This is the balanced budget multiplier

The balanced budget multiplier shows that if both government spending and taxes are increased by the same amount—thereby keeping the budget balanced—then output will increase by the same amount.

Graphing planned expenditure
PE =C +I +G MPC 1 Why slope of PE 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 PE---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
PE planned expenditure PE =Y 45º income, output, Y

The equilibrium value of income
PE planned expenditure PE =Y PE =C +I +G Output gap The equilibrium point is the value of income where the curves cross. Be sure your students understand why the equilibrium income appears on the horizontal and vertical axes. Answer: In equilibrium, PE (which is measured on the vertical) equals Y (which is measured on the horizontal). Equilibrium income Y 𝒀 , natural rate of output

An increase in government purchases
Y PE PE =Y At Y1, there is now an unplanned drop in inventory… PE =C +I +G2 PE =C +I +G1 G …so firms increase output, and income rises toward a new equilibrium. Explain why the vertical distance of the shift in the PE curve equals G: At any value of Y, an increase in G by the amount G causes an increase in PE by the same amount. At Y1, there is now an unplanned depletion of inventories, because people are buying more than firms are producing (PE > Y). PE1 = Y1 Y PE2 = Y2

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: Solve for Y :

The government purchases multiplier
Definition: the increase in income resulting from a $1 increase in G. In this model, the govt purchases multiplier equals Example: If MPC = 0.8, then The textbook defines the multiplier as the increase in income resulting from a $1 increase in G. However, G is a real variable (as is Y ). So, if you wish to be more precise, then you might consider defining the multiplier as “the increase in income resulting from a one-unit increase in G.” An increase in G causes income to increase 5 times as much!

Why the multiplier is greater than 1
Initially, the increase in G causes an equal increase in Y: Y = G. But Y  C  further Y  further C So the final impact on income is much bigger than the initial G. Students are better able to understand this if given a more concrete example, which you can explain as you display the elements on this slide. 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 Ford Explorers. Then, Ford sees its revenues increase by $80 million, all of which becomes income to somebody - either Ford’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 taxes PE C = MPC T Y Y PE =C1 +I +G PE =C2 +I +G
PE =Y Y PE Initially, the tax increase reduces consumption, and therefore PE: PE =C1 +I +G PE =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 Experiment: An increase in taxes (note: the book does a decrease in taxes) 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 PE 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. The new equilibrium is at Y2, where planned expenditure once again equals actual expenditure/output, and unplanned inventory investment is again equal to zero. PE2 = Y2 Y PE1 = Y1

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

The tax multiplier def: the change in income resulting from a $1 increase in T : If MPC = 0.8, then the tax multiplier equals

The tax multiplier …is negative: A tax increase reduces C, which reduces income. …is smaller than the spending multiplier: 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 (or Co or Io).

NOW YOU TRY: Practice with the Keynesian Cross
Use a graph of the Keynesian cross to show the effects of an increase in planned investment on the equilibrium level of income/output. This in-class exercise not only gives students practice with the model, it also helps them understand the next topic: the derivation of the IS curve.

Tax Cuts: JFK Kennedy cut personal and corporate income taxes in 1964
An economic boom followed. GDP grew 5.3% in 1964 and 6.0 in 1965. Unemployment fell from 5.7% in 1963 to 5.2% in 1964 to 4.5% in 1965. However, it is not easy to prove that the tax cuts caused the boom Even when they agree that the tax cuts caused the boom, economists can’t agree on the reason

Tax Cuts: JFK Keynesians argued that the tax cuts boosted demand, which led to higher production and falling unemployment Supply-siders argued that demand had nothing to do with it. The tax cuts gave people the incentive to work harder. So, L increased. Therefore, Y = F(K, L) also increased. Personally, I feel this argument doesn’t explain why the unemployment rate fell

Tax Cuts: GWB Bush cut taxes in 2001 and 2003
After the second tax cut, a weak recovery from the 2001 recession turned into a strong recovery GDP grew 4.4% in 2004 Unemployment fell from its peak of 6.3% in June 2003 to 5.4% in December 2004 In justifying his tax cut, Bush used the Keynesian explanation: “When people have more money, they can spend it on goods and services. … when they demand an additional good or service, somebody will produce the good or service.”

Spending Stimulus: Barack Obama
When President Obama took office in January 2009, the economy had suffered the worst collapse since the Great Depression Obama helped enact an $800 billion (5% of annual GDP) stimulus to be spent over a two-year period About 40% was tax cuts, and 60% was additional government spending White House economists had estimated the spending multiplier to be 1.57 and the tax-cut multiplier to be 0.99

Spending Stimulus: Barack Obama
Much of the new spending was on infrastructure projects These projects were fine for the long run, but took a long time to be implemented, and were therefore not ideal as a short-run boost Obama publicly justified his stimulus bill using Keynesian demand-side reasoning

A slightly more complex theory of short-run equilibrium in the goods market
The IS Curve

Planned Investment The Keynesian Cross model assumed that planned expenditure by businesses (I) is exogenous Recall that, in chapter 3, we had assumed that investment spending is inversely related to the real interest rate The IS Curve theory of the goods market brings back the investment function I = I(r)

The Real Interest Rate Recall from chapter 3 that, the real interest rate is the inflation-adjusted interest rate To adjust the nominal interest rate for inflation, you simply subtract the inflation rate from the nominal interest rate If the bank charges you 5% interest rate on a cash loan, that’s the nominal interest rate (i = 0.05). If the inflation rate turns out to be 3% during the loan period (π = 0.03), then you paid the real interest rate of just 2% (r = i − π = 0.02)

The Real Interest Rate The problem is that when you are taking out a loan you don’t quite know what the inflation rate will be over the loan period So, economists distinguish between the ex post real interest rate: r = i − π and the ex ante real interest rate: r = i − Eπ, where Eπ is the expected inflation rate over the loan period We will use the ex ante interpretation of the real interest rate

Investment and the real interest rate
Assumption: investment spending is inversely related to the real interest rate I = I(r), such that r↑⇒ I↓ r I I (r )

Investment and the real interest rate
Specifically, I = Io − Irr Here Ir is the effect of r on I and Io represents all other factors that also affect business investment spending such as business optimism, technological progress, etc. r Io2 − Irr Io1 − Irr I

Investment: example Suppose I = 11.85 – 2r is the investment function
Then, if r = 5 percent, we get I = – 2r = 1.85.

The IS Curve Recall that the goods market is in equilibrium when Y = C + I + G The IS curve is a graph that shows all combinations of r and Y for which the goods market is in equilibrium Therefore, the basic equation underlying the IS curve is Y = C(Y – T) + I(r) + G

Deriving the IS Curve: algebra
K.C. Spending multiplier K.C. Tax-cut multiplier IS Interest rate effect

Deriving the IS Curve: algebra
So, although the basic equation underlying the IS curve is … … for my specific consumption and investment functions, the equation underlying the IS curve can also be expressed as: The two equations are equivalent forms of the IS curve.

Comparing the Equations of the Keynesian Cross and the IS Curve
K.C. Spending multiplier K.C. Tax-cut multiplier This is the only difference IS Curve K.C. Spending multiplier K.C. Tax-cut multiplier IS Interest rate effect

The IS Curve Y1 Y2 IS r r1 r2 Y K.C. Spending multiplier
K.C. Tax-cut multiplier IS Interest rate effect r Any change in the real interest rate will cause an opposite change in real total GDP by a multiple determined by the size of the interest rate effect. This is why the IS curve is negatively sloped. r1 Δr r2 IS Y1 Y2 Y ΔY

The IS Curve: effect of fiscal policy
K.C. Spending multiplier K.C. Tax-cut multiplier IS Interest rate effect r Any increase in Co + Io + G causes the IS curve to shift right by the amount of the increase magnified by the Keynesian Cross spending multiplier r1 Y That is, if the real interest rate is unchanged, the Keynesian Cross model is the same as the IS curve model. IS2 IS1 Y1 Y2 Y

The IS Curve: effect of fiscal policy
K.C. Spending multiplier K.C. Tax-cut multiplier IS Interest rate effect r Any decrease in taxes (T) causes the IS curve to shift right by the amount of the tax cut magnified by the Keynesian Cross tax-cut multiplier r1 Y IS2 IS1 Y1 Y2 Y

The IS Curve: shifts To sum up the previous two slides:
The IS curve shifts right if there is: an increase in Co + Io + G, or a decrease in T.

Deriving the IS curve: graphs
PE =Y Y PE PE =C +I (r2 )+G r  I PE =C +I (r1 )+G  PE I  Y Y1 Y2 r Y Any change in the real interest rate will cause an opposite change in real total GDP by a multiple determined by the size of the interest rate effect. r1 r2 IS Y1 Y2

The natural rate of interest
PE = Y Y PE PE = C + I( 𝒓 ) + G Recall chapter 3 gave us a long-run theory of the real interest rate At the long-run interest rate, both Y = C + I + G (or, equivalently, S = I) and Y = 𝒀 are true. Note that 𝒓 in the diagram satisfies the requirements of long-run equilibrium This is the natural rate of interest PE = C + I(r1) + G Y1 𝒀 r Y r1 The natural rate of interest will re-appear in chapter 14. But there it will be denoted ρ. (Confused???) 𝒓 IS Y1 𝒀

Why the IS curve is negatively sloped
A fall in the interest rate motivates firms to increase investment spending, which drives up total planned spending (PE ). To restore equilibrium in the goods market, output (a.k.a. actual expenditure, Y ) must increase. This slide simply states the intuition behind the graphs on the preceding slide. Suggestion: Omit this slide from your presentation, and just give the students this information verbally as you present the preceding slide.

Fiscal Policy and the IS curve
We can use the IS-LM model to see how fiscal policy (G and T ) affects 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
PE =Y Y PE PE =C +I (r1 )+G2 At any value of r, G  PE  Y PE =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 This slide has two purposes. First, to show which way the IS curve shifts when G changes. Second, to actually measure the distance of the shift. We can measure either the horizontal or vertical distance of the shift. The horizontal distance of the IS curve shift is the change in Y required to restore goods market equilibrium AT THE INITIAL INTEREST RATE when G is raised. Since the interest rate is unchanged at r1, investment will also be unchanged. This is why, in the upper panel, we write “I(r1)” in the PE equation for both expenditure curves – to remind us that investment and the interest rate are not changing. Y IS2 IS1 Y1 Y2

NOW YOU TRY: Shifting the IS curve: T
Use the diagram of the Keynesian cross or loanable funds model to show how an increase in taxes shifts the IS curve.

The money market in the short run: the LM Curve
The theory of short-run equilibrium in the money market The money market in the short run: the LM Curve

The Theory of Liquidity Preference
The theory of short-run equilibrium in the money market is exactly the same as the theory of long-run equilibrium in the money market that we saw in Chapter 5 Please review Chapter 5 Review of Ch. 5

Money demand and the interest rate
Liquid assets are assumed to earn no interest Illiquid assets are assumed to earn the nominal interest rate i Therefore, an increase in i is assumed to reduce the demand for money That is, money demand (Md) is assumed to be inversely related to the nominal interest rate (i) Review of Ch. 5

Money demand and the price level
We also hold some of our wealth in the form of money—in liquid form—because money is an excellent medium of exchange Review of Ch. 5

Recall that nominal GDP is the market value of all final goods and services It is also the total expenditure on all final goods and services Therefore, the bigger our nominal GDP, the bigger will be our need for money, as money is a medium of exchange It is, therefore, assumed that money demand is directly related to nominal GDP Review of Ch. 5

Let P represent the overall level of prices, as measured by the GDP Deflator From Chapter 2: GDP Deflator= Nominal GDP Real GDP Therefore, Nominal GDP=GDP Deflator×Real GDP=𝑷×𝒀 It is, therefore, assumed that money demand (Md) is directly related to nominal GDP (𝑷×𝒀) Review of Ch. 5

Money Demand So, Md is 𝑴𝒅 = 𝑳(𝒊)×𝑷×𝒀 inversely related to i, and
directly related to PY 𝑴𝒅 = 𝑳(𝒊)×𝑷×𝒀 L(i) is the liquidity function It is inversely related to i, the nominal interest rate Review of Ch. 5

Money Demand: example 𝑴𝒅 = 𝑳(𝒊)×𝑷×𝒀 Specific form of L(i):
L(i) is the liquidity function It is inversely related to i, the nominal interest rate Specific form of L(i): 𝑳(𝒊) = 𝑳𝟎/𝒊 Lo represents all factors other than P, Y and i that also affect money demand Review of Ch. 5

Money Demand = Money Supply
M denotes money supply 𝑴𝒅 = 𝑳(𝒊)∙𝑷∙𝒀 denotes money demand Therefore, 𝑴 = 𝑳(𝒊)∙𝑷∙𝒀 denotes equilibrium in the money market Review of Ch. 5

𝑴 = 𝑳(𝒊)∙𝑷∙𝒀 𝑌= 𝑀 𝐿 𝑖 ∙𝑃 For the specific form 𝑳(𝒊) = 𝑳𝟎/𝒊, the above equation becomes 𝒀= 𝑴 𝑳 𝟎 /𝒊 ∙𝑷 = 𝑴∙𝒊 𝑳 𝟎 ∙𝑷

𝒀= 𝑴∙𝒊 𝑳 𝟎 ∙𝑷 Now, recall that the ex ante real interest rate is the nominal interest rate minus the expected inflation rate: r = i – Eπ Therefore, r + Eπ = i So, the money market equilibrium equation becomes 𝒀= 𝑴∙ 𝒓+𝑬𝝅 𝑳 𝟎 ∙𝑷 At this point, you should be able to do problem 5 on page 326 of the textbook. Please try it.

The LM Equation 𝒀= 𝑴∙ 𝒓+𝑬𝝅 𝑳 𝟎 ∙𝑷
So, for the specific form 𝑳(𝒊) = 𝑳𝟎/𝒊, the money market equilibrium equation then becomes 𝒀= 𝑴∙ 𝒓+𝑬𝝅 𝑳 𝟎 ∙𝑷 Traditionally, this equation is called the LM equation

𝒀= 𝑴∙ 𝒓+𝑬𝝅 𝑳 𝟎 ∙𝑷 Assumption: As always, the money supply (M), which is controlled by the central bank, is exogenous Assumption: unlike the long-run analysis of Chapter 5, expected inflation (Eπ) is exogenous. Assumption: unlike the long-run analysis of Chapter 5, the overall price level (P) is exogenous

Prices are sticky in the short run
Recall that the long-run analysis of Chapter 5 assumed that P is endogenous. Recall also that in the long run P changes proportionately with M. The short-run analysis in the IS-LM model assumes that P is exogenous: it is what it is, it is historically determined That is, the overall price level is “sticky”: what it was last week, it will be this week too

Prices are sticky in the short run
This sticky-prices assumption is the crucial distinction between long-run and short-run macroeconomic analysis Except this assumption, all assumptions made in short-run analysis are also assumed in long-run analysis So, the differences between long-run and short-run theories are caused by this sticky-prices assumption

LM equation: 𝒀= 𝑴∙ 𝒓+𝑬𝝅 𝑳 𝟎 ∙𝑷 Note that if the real interest rate (r) increases, the real GDP (Y) must increase too, in order to keep money demand equal to money supply

The LM Curve: algebra to graph
𝒀= 𝑴∙ 𝒓+𝑬𝝅 𝑳 𝟎 ∙𝑷 The LM curve shows all combinations of r and Y for which the money market is in equilibrium Note that the LM curve is upward rising r LM r2 r1 Y Y1 Y2

The LM Curve: algebra to graph
𝒀= 𝑴∙ 𝒓+𝑬𝝅 𝑳 𝟎 ∙𝑷 The LM curve shifts (down) right if: M/P or Eπ increases Lo decreases Moreover, if Eπ increases (decreases), the LM curve shifts down (up) by the exact same amount! r LM1 LM2 r1 r2 Y0 Y

NOW YOU TRY: Shifting the LM curve
Suppose a wave of credit card fraud causes consumers to use cash more frequently in transactions. Use the liquidity preference model to show how these events shift the LM curve. Answer: This causes an increase in money demand. In the Liquidity Preference diagram, the money demand curve shifts up. Hence, at the initial value of income, the interest rate must rise to restore equilibrium in the money market. As a result, the LM curve shifts up: each value of income (such as the initial income) is associated with a higher interest rate than before.

Short-run equilibrium in the is-lm model
Both the goods market and the money market need to be in equilibrium Short-run equilibrium in the is-lm model

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

By insisting that both the goods market and the money market need to be in equilibrium, we have managed to find a way to pinpoint both r and Y simultaneously! Y r LM IS Equilibrium interest rate Equilibrium level of income

Note that the short-run equilibrium GDP does not have to be equal to the long-run equilibrium GDP ( 𝑌 , also called potential GDP and natural GDP) Thus, like the Keynesian Cross model, the IS-LM model can explain recessions and booms. Y r LM IS 𝒀 But, the Keynesian Cross model could determine only equilibrium GDP. The IS-LM model determines the equilibrium interest rate as well. Equilibrium interest rate Equilibrium level of income

The IS-LM Model: summary
Short-run equilibrium in the goods market is represented by a downward-sloping IS curve linking Y and r. Short-run equilibrium in the money market is represented by an upward-sloping LM curve linking Y and r. The intersection of the IS and LM curves determine the short-run equilibrium values of Y and r. The IS curve shifts right if there is: an increase in Co + Io + G, or a decrease in T. The LM curve shifts right if: M/P or Eπ increases, or Lo decreases Y r LM IS

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 Figure 10-14, p.307. This schematic diagram shows how the different pieces of the theory of short-run fluctuations fit together. Agg. supply curve

Preview of Chapter 12 In Chapter 12, 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. use our models to learn about the Great Depression. This slide serves as a bridge between this chapter and the next one.

Aggregate Demand I: Building the IS-LM Model

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Aggregate Demand I: Building the IS-LM Model

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