L4 - IS-LM Model

Question 1

What are the 3 ways if expressing equilibrium in Keynesian cross?

Answer 1

•The first way: Output = aggregate demand:

Y=C+I+G

•The second way: Output = national income, hence:

C+S+T=Y=C+I+G

S+T=I+G

•The third way: Output = national product, hence:

C+I^r+G=Y=C+I+G

I^r(real)=I(desired)

Question 2

What does the Keynesian Model of Aggregate Expenditure and Model of Savings look like?

Answer 2

MPC +MPS = Y –> when there is no government

MPC+MPS = Y_D –> when there is government

Question 3

How can we derive the Aggregate Expenditure Equilibrium mathematically?

Answer 3

Y=C+I+G

C=a+bY_d=a+b(Y-T)

Where: T denotes lump-sum taxes. Therefore:

Y=a+bY-bT+I+G

or

Y=1/(1-b)∗(a-bT+I+G)

Where 1/1-b is the expenditure multiplier

Multiplier for government consumption: ∆Y/∆G=1/(1-b) and for taxes ∆Y/∆T=-b/(1-b)

Implication: balanced-budget multiplier

∆Y/∆G+∆Y/∆T=1/(1-b)+(– b/(1-b))=1

as the government wants taxes (revenue) and their expenditure to be equal, this multiplier demostrates that if they were to increase their taxes my £1 this will lead to an increase in expenditure by £1 leading to an increase in output by £1

Question 4

What does Mario Draghi say about the effect of Uncertainty and Monetary Stimulus on Aggregate Expenditure Equilibruim?

Answer 4

Mario Draghi –> President of the European Union

- Uncertainty –> US v China Trade War, Turkey and Syria War, Brexit - this is leading to uncertainty not only in the domestic country, but globally too –> this is causing people to save and investment fall as consumer and business confidence is falling causes a reduction in Aggregate Demand and Output

• Also if confidence is low, even if government introduce monetary and fiscal policies, their potency will be greatly effected by expectations (not stimulate AD)
• This is causing the economy to slow down especially in manufacturing where investment is needed the most right now

- Monetary Stimulus –> QE - increase liquidity in the economy, by buying securities from commerical banks so they have excess cash to provide low credit to consumers and business to spend more this can also be done via, lowering interest rates

Question 5

How can you derive the IS curve without government ?

Answer 5

Using S+T=I+G

• Assume we have no government - so no taxes or government spending so S=I
• When Keynes started creating the Investment-Savings model he believe that the money market/money supply has an effect on income, this is done via the interest rate –> he wanted to see how interest rates effected income and aggregate demand in the goods market

Investment Schedule:

• Investment is negatively related to interest rates –> as interest rates rise the cost of investment rises

Savings Schedule:

• We have a upwards savings function as savings increases with income, as investment is equal to savings, if investment has fallen there will be fall in savings due to an increase in interest rates –> thus income also falls

IS curve:

• by plotting the corresponding interest rates and income equilibrium points you will be able to connect the points and derive the negative gradient IS curve

Question 6

What factors affect the slope of the IS Curve without the government?

Answer 6

• When the Investment schedule is steep (interest elasticity of investment is low) –> investment has a low senstivity to interest rates meaning that a change in interest rate causes only a small change in investment spending
• This means that with a fall in interest rates we will only see a slight increase in savings and in turn, only a small increase in income
• This means that any form of monetary policy will have only a small impact of AD
• In turn monetary policy will have a larger impact if investment is more senstive to interest

Question 7

How do you derive the IS curve with the government?

Answer 7

Including the government now, we see equilibrium in the market occur at I + G = S + T

• We still derive the same result but adding the government sector shift the relative position of each curve –> the Investment Schedule shifts out because of the additional spending from the Goverment sector
• The savings function no longer depends on income as we have included taxes it is based on disposable income, as disposable income is less than normal due to taxes we save less for each level of interest thus the Savings Schedule moves in

Question 8

What causes a shift in the IS schedule?

Answer 8

• Any of the Autonomous factors
• Any changes in exogenous consumption (a), Taxes (T), Government Spending (G), Investment (I)
• A shift in G and I doesnt cause a shift in the Savings Function just movement up it –> just require more income based on the formula because we have increase a component of AD
• If Taxes increase there will be no shift in the Investment Schedule as there is no tax component –> as taxes take away from income however there will be a shift inwards of the Savings Schedule

Question 9

How can you derive the IS schedule algrebraically?

Answer 9

I+G=S+T

Saving function:

S=-a+(1-b) Y_d=-a+(1-b)(Y-T)

•Investment function:

I=I(bar)-i₁r

•where i₁>0.

I(bar)-i₁r+G=-a+(1-b)(Y-T)+T

•Rearranging the equation we get:

Y=1/(1-b)(a+I(bar)+G-bT-i₁ r)

Question 10

What is the LM Curve?

Answer 10

Wh=B+M

• Keynes argued that you can hold your assets in either money assets or non-money assets ( for a simplification we just say bonds)
• Money assets are liquid e.g. currency, government securities and gives no interest
• non-money assets e.g. bonds, they are risky but earn interest
• Liquidity preference – Keyne’s term for the demand for money relative to bonds.
• if we have equilibrium in the bond market we will have equilibrium in the money market and vice versa –> you are getting your desired amount of both money and bonds, if for example you want to hold more money assets, this means there isnt enough money supply for you thus the money market isnt in equilibrium and the bond market isnt in equilibrium because you are demand more money so more bonds are being supplied than demanded
• Two ways of presenting the equilibrium. Walras Law – equilibrium in one market implies an equilibrium in another so we just look at one. We look at only one in the money.
• Equilibrium occurs when money supply equals money demand
• money supply is fixed by the policy maker so is vertical
• money demand is downwards slowly as it has a negative relationship with interest rates

Question 11

What are the Motives for demanding money?

Answer 11

Money demand (holding money):

1. Transaction Demand
2. Precautionary Demand
3. Speculative Demand

Question 12

What is Transaction Demand?

Answer 12

• This is the money held by people to buy goods and services
• It is said to be positively related to income as the more income we have the more transactions we are likely to make
• however when your receipt of money and expenditure of money are synchronised, ( you are receiving and spending money on the same day) –> their will be less incentive to hold money, thus less transactionary demand
• However if you hold it and gradually spend over the month till you get you next paycheck their is more need to hold money
• However their is an opportunity cost of holding money which is the interest rate, as you could be investing it –> so their is a negatively relationship between the interest rate and transactionary demand, thus as interest rises people want to hold less money

Question 13

What is Precautionary Demand?

Answer 13

• As we cannot predict all of our transaction, we hold money for these unforeseen events and emergencies
• their is a great similarity between transaction demand, one is known the other is not.
• this also means that it is postively related to income and negatively related to interest rates

Question 14

What is Speculative Demand?

Answer 14

• Because of the relationship between bond prices and the rate of interest
• in this model you can either hold money assets or bonds, as the rate of interest increases the price of decreases leading more people to hold them over money, thus if you are holding a bond and the interest rate falls you can make a captial gain –> it is this capital gain/loss on assets where the speculative part comes in
• in order for individual to determine whether bond prices will go up or down, people with have a notion of what they think the interest rate should be, thus if they think it will rise they will hold money, if it will fall they will hold bonds

Question 15

What does Speculative Demand look like on a graph?

Answer 15

Looking at an the individual graph first:

• above r_iⁿ (what people consider the normal rate of interest), people will hold bonds as people believe the interest rate will fall leading to a capital gain –> no speculative demand for money
• still will hold bonds between r_iⁿ and r_i^c (critical rate of interest where any change in price is offset by a change in interest) as even if interest rates rise they known their price of bond will fall, but as they are so close to r_iⁿ they believe the increase in interest rates will outway any capital loses
• Any point at or below r_i^c people believe interest will rise so everyone hold hold money

When combining all these points for every individual and plotting them on a graph we get the Aggregative Speculative demand for Money:

• At very low rates of interest we run into a liquidity trap –> people want to hold money as interest rates are well below r_i^c and everyone expects the interest rate to rise
• here the demand for money is very responsive to a change in interest rate, as any increase in interest will always lead to a greater capital losee
• but their is enough money supply for everyone to do so

Question 16

How can Total Demand be wrote mathematically?

Answer 16

M_i=M_i¹+M_i²

(transaction demand + speculative demand)

Wh_i=M_i+B_i

Total demand for money:

M^d=L(Y,r)

M^d= c₀+c₁Y-c₂r,

c₁,c₂>0

Question 17

How do you derive the LM schedule?

Answer 17

• Money supply is fixed (usually by the central bank) thus is vertical
• at r₀ the money demand is M^d(Y₀) and their is equilibrium in the market when M₀^s=M^d(Y₀)
• When incomes rise money demand increases because we have a positive relationship between money demand and income, this causes the interest rate to rise
• as money supply is fixed, when money demand rises it is greater than money supply, to equilibriate this in the market interest rates must rise to lower the demand ( as transactionary and precautionary demand is negatively related to income) so we get a shift up M^d(Y₁) to the equilibrium point at B
• By plotting the the equilibrium points at various level of income and connecting them we get the LM schedule
• c₁/c₂ –> slope of the LM curve (rate of change)

Question 18

How does interest elasticity of money demand affect the slope of the LM curve?

Answer 18

• The slope of the LM curve depends of c₁
• at higher levels of c₁ money demand reacts greatly to a change in income this means their need to be an small shift in interest rates to equilibriate the market, this causes the money demand and the LM curve to be very flat as interest rates are sensitive to a change in demand
• at lower level of c₁ money demand isnt effected as greatly by an increase in income so the change in interest rate to accommodate any changes is very large as money is not sensitive to a change in interest rate, causing the money demand and LM curve to be alot steeper
• in the graphs below this occurs with the same change in income

Question 19

What are two extreme cases that effect the slpope of the LM curve?

Answer 19

When c₂ is 0:

• If c₂ ​is 0 the value of -c₂r = 0 giving the equation for money supply to be c₀ ​+c₁ Y –> we have no interest
• this means that money demand is not responsive to interest rates at all (only depends on income), meaning we only have one level of money demanded in the market
• This is because if income rose, there isnt nothing to equilibriate the market, thus their is only one level of money demand which is equal to money supply
• This gives us a vertical value fo LM

When c₂ ​is very high (c₂ ​–> ∞):

• Their is now a curve in the money demand curve
• This has a similar explanation to speculative demand, in that at low level of interest rates more money is demanded –> at low levels of income when income rises, only a small increase in interest is needed to equilibriate the market (money demand is very responsive to changes in interest rates) , but at at higher levels a larger change in interest rates are needed
• This curves a curved LM curve

Question 20

What can cause a shift in the LM curve?

Answer 20

Changes in Money Supply:

• The y-intercept in the LM contains the Money Supply, so that is money supply is shifting outwards the money market needs to equilibriate once more.
• If there is an increase in money supply interest rates will fall (holding income constant), this also causes the LM curve to shift outwards
• If the monetary authority wanted to maintain the same level of interest they would need to raise income

Change in Money Demanded:

• This is factors other than changes in income e.g. loss of confidence in bonds causing more people to hold money that have causes a shift in Money Demanded
• If this occurs, and we have a fixed money supply, where demand exceed supply the interest rate must rise
• This cause the LM curve to shift left towards to origin
• However, if the government would want to maintain the same level of income, they would have to implement policies to reduce income

Question 21

What does the IS-LM model tell us?

Answer 21

• At the intercept, there is equilibrium between the goods market (IS) and the money market (also in the bond market) (LM)

Points Above the LM schedule (A and B):

• Excess Money Supply, causes interest rates to fall

Points Below the LM schedule (C and D):

• Excess Money Demand, causes intereat rates to rise

Points Above the IS schedule (B and C):

• Excess Supply of Output, causes Income to fall

Points Below the IS schedule (A and D):

• Excess Demand for Output, causes income to rise
• Points on the LM curve mean that interest rates and income will equilibriate the money market but not the goods market, and for points on the IS curve, interest rates and income will equilibriate the goods market but not the money market

Question 22

How can the IS-LM model be expressed mathematically?

Answer 22

Question 23

What are the Fiscal and Monetary multipliers of the IS-LM curve?

Answer 23

• As ΔY/ΔG is positive, any increase in Government spending there is an increase in output, this causes the IS schedule to shift right, causing not only output to increase but interest rate increase, which causes investment spending to fall –> so although output increases it is supressed by a fall in investment so the change is small in the IS-LM compared to just the IS curve
• As ΔY/ΔT is negative, so when taxes increase the IS shifts inwards, which not only causes output to fall but also interest rates as well, but as interest rates are falling this leads to an increase in investment spending thus leading to a small fall in output than just looking at the IS schedule
• As ΔY/ΔM^s is positive, when there is an increase in the money supply, there is an increase in income, which causes the LM curve to shift right also leading to interest rates falling, this causes the investment to also to rise.

Question 24

What was the cause of the U.S. Recession of 2001?

Answer 24

• There was a leftwards shift of the IS curve due to a decrease in Aggregate Demand
• The decline in the stock market, Y2K bubble, optimism started falling as the innovation in technology didnt occur like everyone expected - when stock prices are falling, our wealth is falling, consumption then falls thus AD falls
• Tobin’s q –> when we have a falling valuation of the stock market, the numerator of Tobin’s q is falling, this means expectations are falling so people are investing less
• The September 11 terrorist attacks on New York and Washington –> causes the greatest fall in the stock market since the Great Depression - uncertainty
• A number of accounting scandals at prominent corporations (Enron and WorldCom)–> business publishing false profits

Question 25

What was the Response to the U.S. Recession of 2001?

Answer 25

• The Fed adopted an expansionary monetary policy –> increased money supply, interest rates falls, so borrowing in cheaper and stimulates consumption and investments
• Congress passed a tax cut (disposable income increases), including an immediate rebate, and also passed an emergency spending measure to help rebuild New York and bail out the airline industry.

Question 26

What was the Spending Hypothesis that led to the Great Depression?

Answer 26

• Shock to the IS curve
• Asserts the Depression was largely due to an exogenous fall in the demand for goods and services—a leftward shift of the IS curve.
• • Evidence:
    
    • output and interest rates both fell, which is what a leftward IS shift would cause.
• •Stock market crash reduced consumption
  
  • Oct 1929–Dec 1929: S&P 500 fell 17%
  • Oct 1929–Dec 1933: S&P 500 fell 71%
• Drop in investment
  
  • Correction after overbuilding in the 1920s. –> there had been excess amounts of investment prior to the crash
  • Widespread bank failures made it harder to obtain financing for investment.
• Contractionary fiscal policy
  
  • Politicians raised tax rates and cut spending to combat increasing deficits.

Question 27

What was the Money hypothesis that led to the Great Depression?

Answer 27

• This was a shock to the LM curve
• Asserts that the Depression was largely due to the huge fall in the money supply. –> probably caused by rising unemployment and falling GDP
• Evidence: M1 fell 25% during 1929–1933.
• But, two problems with this hypothesis:
  
  • P fell even more, so M/P (real money balances - what money can actually buy) actually rose slightly during 1929–1931. –> actually meant people could by more things which means LM should shift right causing output to be higher
  • Nominal interest rates fell, which is the opposite of what a leftward LM shift would cause
  • These two contridicting hypothesis shows that the money hypothesis was subject to criticisms
• Asserts that the severity of the Depression was due to a huge deflation:
  
  • P fell 25% during 1929–1933.
• This deflation was probably caused by the fall in M, so perhaps money played an important role after all. –> if only P fell it would have been just a bad recession, but because M fell due to deflation, it let to the worse Economic Downturn in history

Question 28

When does deflation have a stabilising effect?

Answer 28

The stabilizing effects of deflation:

• decrease in P –> Increase in M/P –> LM shifts right –> Y increases

Pigou Effect:

• decrease in P –> increase in M/P
  
  • consumer’s wealth increases
  • increase in C
  • IS shifts right
  • Increase in Y

Question 29

When does expected deflation have a de-stabilising effect?

Answer 29

• The destabilising effect of expected deflation:
• Fall in expected π
  • increase in r for each value of i (nominal interest rate as nominal - (-π) leads to higher values of r)
  • I because I=I(r) –> higher r leads to a fall in investment
  • planned expenditure and AD falls
  • Income and Output fall

Question 30

(2) When does unexpected deflation have a de-stabilising effect?

Answer 30

debt-deflation theory

• Decrease in P (if unexpected)
  
  • transfer purchasing power from borrowers to lenders–> borrowers are having to pay back relatively more expensive money, while lenders are receiving it
  • borrowers spend less and lenders spend more –> if borrowers’ propensity to spend is the same as lenders, it will not effect overall spending they will both offset each other –> no change in Y
  • if borrowers’ propensity to spend is larger than lenders’ (spending reduces a greater amount than a lender), then Aggregate Spending falls, the IS curve shifts left and Y falls

Question 31

Why is another Depression unlikely?

Answer 31

• Policymakers (or their advisers) now know much more about macroeconomics:
  
  • The Fed knows better than to let M fall so much, especially during a contraction (at the same time as deflation, falling employment and falling GDP).
  • Fiscal policymakers know better than to raise taxes or cut spending during a contraction. (especially when falling unemployment and falling growth) –> more concerned with balancing the budget than stimulating demand
• Federal deposit insurance makes widespread bank failures very unlikely –> Government back deposit held in central banks
• Automatic stabilizers make fiscal policy expansionary during an economic downturn –> consumption doesnt change signficantly

Question 32

How does expectations effect consumption?

Answer 32

When discussing theories of consumption and investment, it was clear that future plays an important role.

• Expectations affect consumption:
  
  • Directly through human wealth (After-tax labor income over working life) –> If you expect a increase in your future disposable income you would start spending more now
  • Indirectly through non-human wealth (The sum of financial wealth and housing wealth)
• Implications of expectations of the relation between consumption and income:
  
  • Consumption is likely to respond less than one-for-one in current income.
  • Consumption may move even if current income does not change.
• Investment is a function of future profits. Therefore future productivity, or interest rate will impact current investment. Expectations affect investment.

Question 33

What will happen to the IS model when we add Expectations to the Model?

Answer 33

• IS curve is much steeper than the IS considered thus far -> this is by how much the interest rate affect spending of income and the size of the multiplier (G and T) affects output.
• A decrease in the current real policy rate, given unchanged expectations of the future real policy rate, does not have much effect on private spending. –> as investment look at future periods not just this one just because their is a decrease now doesnt really effect what they would receive in the future
• The multiplier is likely to be smaller because a change in current income (temporary change income), given unchanged expectations of future income (permanent income), is unlikely to have a large effect on spending. –> only have a small change as people would save some of the extra income they received in this period and for the next one
• Given expectations, a decrease in the real policy rate leads to a small increase in output. The IS Curve is steeply downward sloping. Increases in government spending, or in expected future output, shift the IS curve to the right.
• Increases in taxes, in expected future taxes, or in the expected future real policy rate shift the IS curve to the left.

Question 34

How does Monetary Policy affect the IS model when including expectations?

Answer 34

The effects of monetary policy depends on its effects on expectations:

• If a monetary expansion leads to changes in expectations of future interest rates and output, then the policy effect on output may be large.
  
  • Additional shift in the IS curve –> so it shifts even more than it original would as we expect more output for the future
• But if expectations remain unchanged, the policy effects on output will be limited.

Question 35

What are Rational Expectations?

Answer 35

• You cannot measure expectations so how can you test the effectiveness of government policy based on expectations –> you assume expectations arent arbitrary

• Rational expectations: Expectations formed in a forward-looking manner.
• The last 40 years in macroeconomic research are often called the “rational expectations revolution.”–> lots of model are starting to use expectation in models
• Expectations was referred to as animal spirits by Keynes in the General Theory. –> firms investment based on how they felt about the market, or their ‘mood’, this is referred to as animal spirits

Question 36

What have Economist split Rational Expectations into?

Answer 36

• Economists have also assumed that people form static expectations (people expect the future to be like the present), and adaptive expectations (people “adapt” by revising their expectations over time).
• In the early 1970s, Robert Lucas and Thomas Sargent argued that people have rational expectations as they look into the future and do the best job they can in predicting it. –> they make an educated guess about the future based on the informaiton you have

Question 37

How can Fiscal Policy affect the IS model with expectations included?

Answer 37

Looking at when trying to balance the budget with a deficit reduction

When account is taken of its effect on expectations, the decrease in government spending need not lead to a decrease in output

ΔG < 0 but ΔE(Y) < 0 (fall in output in the short-term)

but in the medium term –> Δ(r) < 0, ΔE(T) < 0 (fall in interest rate and taxes will lead to an increase in output)

• This happens because the government is reducing it deficit, if we change spending now output will fall (and as spending is the sum of both public and private it will also fall), to maintain output as a constant we need to increase firms spending (through a fall in interest rate)
• this will then be the opposite of crowding out –> as government spending is decrease, firm spending should increase
• in the long term by reducing their deficit the government no longer has to be so strict on their policies –> reduce taxes

Question 38

What is the net effect of the three shifts when a government is reducing their deficit on the IS curve when including expectations?

Answer 38

The net effect of the three shifts in the IS curve depends on:

1. Timing
2. Composition
3. Initial Situation
4. Monetary Policy

Question 39

How does timing have a net effect on the IS curve with a Deficit Reduction?

Answer 39

1.Timing

• Credibly backloading the deficit reduction program toward the future, with small cuts today and larger cuts in the future, is more likely to lead to an increase in output. ( as they no that a future fall in government spending and an decrease in taxes will increase their income even more so they will spend more now)
• The program’s credibility (the perceived probability that the government will do what it has promised when the time comes to it) decreases when the government announces the need for painful cuts in spending, and then leaving them to the future.

Question 40

How does Composition have a net effect on the IS curve with a debt reduction?

Answer 40

2.Composition (make up of taxes and government expenditure) –> how much spending falls and taxes increase

• If some government spending programs are perceived as “wasteful,” cutting these programs today will allow the government to cut taxes in the future.
• Expectations of lower future taxes and lower distortions could induce firms to invest today, thus raising output in the short run.

•See discussion in McManus, Ozkan, Trzeciakiewicz (2019, SJE) – show that expansionary contractions are possible, but unlikely to occur given the political situation.

Question 41

How does the Initial Situation have a net effect on the IS curve with a debt reduction?

Answer 41

•If government debt is increasing fast, then a credible deficit reduction program is more likely to increase output in the short run, as the program announcement may well reassure the people that the government has regained control of its budget.

Question 42

How does Monetary Policy have a net effect on the IS curve with a debt reduction?

Answer 42

•Even if monetary policy cannot fully offset the effect of an adverse shift in the IS curve, a decrease in the policy rate (expansionary monetary policy which will create outwards shift in monetary policy) can help reduce the adverse effects of the shift on output.

Question 43

Why is the Price Level fixed in the IS-LM Model?

Answer 43

• So far, we’ve been using the IS-LM model to analyse the short run, when the price level is assumed to be fixed to simplify the model –> if GDP had changed , was that a change in output, or just general price level of the economy, we fix P to look at purely real Output
• However a change in P would shift LM and therefore affect Y
• The AD curve captures this relationship between P and Y

Question 44

How do you calculate Real money balances?

Answer 44

Money Supply/Price level

this tells us what we can actual buy given the level of prices

• so if prices are high, you can purchase less goods, this decrease your income/wealth shifting the LM curve to the left for a lower level of income

Question 45

How can you derive the AD curve from the IS-LM model?

Answer 45

• when prices are low output and income are high
• however when prices rise, we demand less as our income has fallen, leading the LM curve to shift upwards, leading to a lower level of output at that price level

Question 46

How can Monetary Policy affect the AD curve?

Answer 46

• if money supply increases and prices are fixed our real money balance increases, this means we can spend more so in effect out income/wealth has increase leading us to great output, –> shifts the LM curve to the right and lowers interest rates
• lower interest rates lead to increase event spend which increase output at every level of P causing a rightwards shift of the AD curve

Question 47

How can Fiscal policy affect the AD curve?

Answer 47

• this is increasing government spending but lower taxes (increasing the deficit):
• When taxes fall consumption rises as we have more disposable income, this lead output to rise and their to be a shift right of the IS curve –> dampened by the increase in r which will lower investment
• output therefore increase for each value of P so AD shift right

Question 48

What causes shifts in the LM curve?

Answer 48

1. change in money demand –> through either interest rate or GDP
2. changes in the real supply of money
3. Changes in transaction technology e.g. credit cards
4. changes in the overall price level

Question 49

What causes shifts in the IS curve?

Answer 49

1. Changes in Fiscal Policy
2. Change in Consumer Savings Rates
3. Changes in Investment
4. Changes in Private Fixed Investment