[3] IS-LM

Question 1

Three ways of expressing equilibrium in Keynesian cross
Show them algebraically

[[ THERE ARE RELEVANT COPIES OF DIGITAL CHAPTER ON LEARN. ]]

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=𝑰

Question 2

Graphically determine the equilibrium of AE

[use G, I, S, T graph as well]

Answer 2

Slide 4

Question 3

What is the equilibrium for Y with taxes?

Answer 3

𝑌=𝑎+𝑏𝑌−𝑏𝑇+𝐼+𝐺
or
𝑌=1/(1−𝑏)∗(𝑎−𝑏𝑇+𝐼+𝐺)

Question 4

What is the Gov Consumption Multiplier?
What is the Tax Multiplier?
What does this imply the Balanced-Budget Multiplier equals?

Answer 4

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

Question 5

When applying the model to the ECB, what are 2 key aspects brought to attention by Mario Draghi?
How do these 2 issues affect the model?

Answer 5

• Uncertainty
• Monetary Stimulus
  [look up in lec capture]

Question 6

Derive the IS curve [3 graphs]

Answer 6

slide 8

Question 7

What affects the slope of the IS curve? [2]

Answer 7

slope of the IS curve depends on 2 factors : 1. The sensitivity (elasticity) of investment and saving to changes in the interest rate [the interest sensitivity coefficient], 2. Size of the multiplier

Question 8

Derive the IS curve with Government?

Answer 8

slide 10

Question 9

What is the savings function? and Including gov?

What is the investment function? and Including gov?

Now put this into the keynsian cross equation?

Answer 9

𝐼+𝐺=𝑆+𝑇

Saving function:
𝑆=−𝑎+(1−𝑏) 𝑌_𝑑=−𝑎+(1−𝑏)(𝑌−𝑇)

Investment function:
𝐼=𝐼̅−𝑖𝑟

where 𝑖_1>0.
𝐼̅−𝑖𝑟+𝐺=−𝑎+(1−𝑏)(𝑌−𝑇)+𝑇

Rearranging the equation we get:
𝑌 = 1/(1−𝑏) * (𝑎+𝐼̅+𝐺−𝑏𝑇−𝑖𝑟)

Question 10

What factors shift the IS curve?

Answer 10

IS curve represents the goods market equilibrium.

Changes in autonomous consumer expenditure
 Changes in planned investment spending unrelated
to the interest rate
 Changes in government spending
 Changes in taxes
 Changes in net exports unrelated to the
interest rate

Question 11

3 Factors affecting the demand for money:

Answer 11

Transaction > to carry out transactions to purchase G&S [opp cost equal to the rate of interest] When R ^, demand for money falls

• Precautionary > Higher your income, the more money you can hold as a buffer
• Speculative > Bond prices and the rate of interest [neg relationship] As r increases, the price of the bond falls (as capital gain can be made) [assumes all bonds the same] With a higher interest rate, there is higher returns on other bonds so these are more attractive

Question 12

What is the Critical Rate of interest?

What are the implications for interest below the critical rate?

Answer 12

Critical Rate (rCi): any r below this means that consumers expect the r to rise and therefore the bond price to fall [so there losses outweigh any gain in interest]
So ppl are more willing to hold their money. As r falls, the demand for money (spec) rises exponentially

Question 13

What does very low r result in and why?

Answer 13

Very low rates of interest = liquidity trap = bc ppl are almost certain that the r will rise!

liquidity preference may become virtually absolute in the sense that almost everyone prefers holding cash rather than holding a debt which yields so low a rate of interest.

Question 14

Why is the money demand curve downwards sloping?

Answer 14

Md downwards sloping bc neg related to r. As Y inc, Md inc bc they have a posi relationship.

Question 15

What does the LM curve represent?

What is the slope of the LM curve?

Answer 15

LM curve represents equilibrium in the money markets (Md &Ms) for given levels of interest and National Income

The income sensitivity of demand for real money over the interest sensitivity of demand for real money.
c1/c2 = the slope of the LM curve.

Question 16

What does interest elasticity of money demand mean?

Answer 16

interest elasticity of money demand – means how sensitive Md is to changes in r

Question 17

High interest elasticity of Md;
Md is ______ ______ so a _____ change in r required to offset the increase in demand
This brings a ______ LM schedule.

Answer 17

very responsive
small
flatter

Question 18

What causes a movement along the LM?

What factors cause a shift in the LM?

EGs

Answer 18

KEY POINT: It is for the same level of income Y0. If the income changes then, causes a movement along the LM

Change in the Ms with the income held constant [outward shift of Ms causes LM to shift right and r must fall] eg : QE

Demand change results from change in anything apart from income eg: uncertainty = ^ Md, less demand for bonds

Question 19

Above LM:
Below LM:
Above IS;
Below IS:

Answer 19

Above LM = excess supply of money, so lower r to reduce supply
Below LM = excess demand for money, so have to increase r to reduce demand
Above IS = excess supply of output (exceeding demand), so have to reduce level of output or income
Below IS = excess demand for output (higher than 45 degree line)

Question 20

Equation for IS and LM?

What is the slope for each?

What does c1 and c2 represent?

Answer 20

𝐼𝑆: 𝑌=1/(1−𝑏) * (𝑎+𝐼̅+𝐺−𝑏𝑇−𝑖𝑟) ⇒ 𝑠𝑙𝑜𝑝𝑒 =−(1−𝑏)/𝑖_1

𝐿𝑀: 𝑟 = 𝑐0/𝑐2 − (𝑀0𝑠)/𝑐2 + 𝑐1/𝑐2 𝑌 ⇒ 𝑠𝑙𝑜𝑝𝑒=𝑐1/𝑐2

c1: Change in Money Demand when income changes
c2: Chagne in Money Demand when interest rate changes

Question 21

Express:

Spending ∆𝑌/∆𝐺=

Tax ∆𝑌/∆𝑇=

Monetary multiplier ∆𝑌/(∆𝑀𝑠 )=

algebraically
What does monetary multiplier also effect?

Answer 21

∆𝑌/∆𝐺=1/(1−𝑏+𝑖_1 𝑐_1/𝑐_2 )>0
∆𝑌/∆𝑇=(−𝑏)/(1−𝑏+𝑖_1 𝑐_1/𝑐_2 )<0
tax multiplier [also affects investment increases , so offsets the initial fall in output] (^ T, dec IS, Dec r, inc investment > offsets fall)

∆𝑌/(∆𝑀𝑠 ) = (𝑖_1/𝑐_2 )/(1−𝑏+𝑖_1 𝑐_1/𝑐_2 )=𝑖_1/((1−𝑏)𝑐_2+𝑖_1 𝑐_1 )>0
monetary multiplier [also affects investment]

Question 22

The U.S. Recession of 2001
Causes [3]
Responses [3]

Answer 22

CAUSES: Over optimism in technology and stocks not priced at their intrinsic value. [increases in comp ownership, from luxury to necessity]
Lower r, higher availability of capital, higher vol of speculative investment. Many Tech IPOs (Yahoo!) were successful developing interest in industry
Decline in stock market
9/11
Accounting scandals within big firms
RESPONSES: Expansionary M.P
Tax cuts and emergency spending measure to rebuild NY and bail out airline industry

Question 23

The Great Depression: what were the 2 Hypotheses of its causes

Answer 23

Spending Hypotheses

Money Hypotheses

Question 24

The spending hypothesis: Shocks to the ___curve

Asserts the Depression was largely due to an exogenous ___ in the ____ for goods and services—a ___ shift of the _____ curve.
Evidence: ___ and ____ ___ both fell, which is what a Leftward ___ shift would cause.
Stock market crash reduced ______
Oct 1929–Dec 1929: S&P 500 fell 17%
Oct 1929–Dec 1933: S&P 500 fell 71%
Drop in _____
Correction after overbuilding in the 1920s.
Widespread _____ failures made it harder to obtain _____ for investment.
______ fiscal policy
Politicians ______ tax rates and _____ spending to combat increasing deficits.

Answer 24

The spending hypothesis: A shock to the IS curve

Fall
Demand
Leftward
IS

output
interest rates
IS
Consumption
Investment
bank
financing
contractionary
Raised, cut

Question 25

The money hypothesis: A shock to the ___ curve Asserts that the Depression was largely due to the huge fall in the ___ _____. Evidence: M1 fell 25% during 1929–1933. But, two problems with this hypothesis: ___ fell even more, so M/P actually ____ slightly during 1929–1931. Nominal ____ _____ fell, which is the opposite of what a _____ ___ shift would cause. Asserts that the severity of the Depression was due to huge _____: P fell ____ during 1929–1933. This deflation was probably caused by the fall in M, so perhaps money played an important role after all.

Answer 25

``` LM money supply Price, rose interest rates leftward LM Deflation 25% ```

Question 26

What are The stabilizing effects of deflation? | step by step analysis

Answer 26

The stabilizing effects of deflation: ↓P , ^ (M/P), LM shifts right , ^Y [increase real money balances] ``` Pigou effect: ↓P, ^ (M/P ) consumers’ wealth ^ ^ C IS shifts right ^Y ```

Question 27

What are the destabilizing effects of expected deflation?

Answer 27

``` The destabilizing effects of expected deflation: Fall in E π [expected inflation] r ^ for each value of i I because I = I (r) planned expenditure and agg. demand ↓ income and output ↓ ```

Question 28

The destabilizing effects of unexpected deflation: _____-______ theory Who does this transfer purchasing power from and to? What shifts and which way? and only if what? Who is better off from redistribution of income?

Answer 28

Debt-Deflation theory: ↓P (if unexpected) transfers purchasing power from borrowers to lenders borrowers spend less, lenders spend more if borrowers’ propensity to spend is larger than lenders’, then aggregate spending falls, the IS curve shifts left, and Y falls [Redistribution of income between borrowers and lenders. In future, with deflation, you are paying back money with a larger purchasing power, so redistribution of income]

Question 29

Why another Depression is unlikely? [3]

Answer 29

1. 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. - Fiscal policymakers know better than to raise taxes or cut spending during a contraction. 2. Federal deposit insurance makes widespread bank failures very unlikely. 3. Automatic stabilizers make fiscal policy expansionary during an economic downturn.

Question 30

How Expectations affect Consumption? [2] What is I a function of? What does future Productivity & r depend on? What do we discount our cash flows using?

Answer 30

- Affect human wealth directly (after tax income over working life) - Indirectly through non-human wealth (sum of financial wealth and housing wealth) C is likely to respond less than one-for-one in current Y C may move even if current Y does Not change I is a func of future profits. Therefore future productivity/interest rate will impact current investment. We discount our cash flows using future r

Question 31

IS curve is much steeper than the IS considered thus far: A _____ in the current real policy rate, given unchanged expectations of the future real policy rate, does not have much effect on Private ____. The multiplier is likely to be ____ because a change in current ____, given unchanged expectations of future income, is unlikely to have a large effect on ____. Given expectations, a ____ in the real policy rate leads to a small increase in output. The IS Curve is steeply ____ sloping. Increases in ____ ______, or in _____ _____ _____, shift the IS curve to the right. Increases in t___, in e____ ______ _____, or in the e___ ____ ___ ____ ____ shift the IS curve to the left.

Answer 31

decrease, spending small, income, spending Decrease Downward government spending, expected future output taxes, expected future taxes, expected future real policy rate

Question 32

The effects of monetary policy depends on its effects on ______ Explain....

Answer 32

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. But if expectations remain unchanged, the policy effects on output will be limited.

Question 33

We can assume that expectations are _____ – we assume rational expectations of consumers and firms (are made based of _____-_____, considerate manner) Keynes referred to expectations as ‘____ _____’ Adaptive expectations – they ____ their expectations over time – r increases from 2% to 3%, you increase your expectations of future interest rates EV??

Answer 33

abitrary forward-looking animal spirits revise EV- this is not how epxectations are formed- look into the future and consider a whole range of possibilites

Question 34

Fall in Gov spending, IS shifts ___, giving a ___ in output – but this is only a SR effect. Incorporating _____ allows us to consider mid and long term effects Gov spending falling, expected fall in ___ ___, so ____ spending expected to _____ (mid term) (reverse ____ ____) In LR, by reducing deficit, gov doesn’t have to be stringent Expected future taxes fall, expected future ____ rises

Answer 34

inwards, fall expectations interest rates, private, rises, crowding out Output

Question 35

Deficit Reduction, Expectations, and Output The net effects of the three shifts in the IS curve depends on what about Policy Makers: [4, explain each one]

Answer 35

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. 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. 2. Composition 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. 3. Initial Situation 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. 4. Monetary Policy Even if monetary policy cannot fully offset the effect of an adverse shift in the IS curve, a decrease in the policy rate can help reduce the adverse effects of the shift on output.

Question 36

So far, we’ve been using the IS–LM model to analyze the ____ ____, when the price level is assumed to be ___. However, a change in__ would shift LM and would therefore affect Y. The ____ _____ curve captures this relationship between P and Y.

Answer 36

short run, fixed P aggregate demand

Question 37

Derive the AD curve?

Answer 37

slide 41

Question 38

Using Chain-analysis, how can The Fed can increase aggregate demand? [given price]

Answer 38

^ M shifts LM right | ↓r, ^i, ^Y at each value of P

Question 39

Expansionary fiscal policy (hG and/or iT) increases agg. demand: [Chain analysis]

Answer 39

↓T = ^C | IS shifts right = ^Y for each value of P

Question 40

SUMMARY

Answer 40

``` Derivation of IS-LM model IS-LM and effectiveness of policies Applications of IS-LM Role of expectations IS-LM and AD curve ```