Dyanamic Aggregate Demad and supply

Question 1

What are some of the functions of this model?

Answer 1

• Expresses monetary policy in terms of nominal interest rates
• Allows monetary policy to implicitly adjust to meet nominal interest rate target
• allows monetary policy to respond to the state of the economy.

Question 2

How do we represent specific time periods?

Answer 2

• By using subscript ‘t’
• For example output produced in this current period will be referred to as Yt.
• Output in the subsequent period is Yt+1
• Output in prior period is Yt-1

Question 3

How do we deal with forward looking variables?

Answer 3

• By factoring in expectations
• this is done through the use of the expectations variable- Et
• The ‘t’ in ‘Et’ represents all the information known and used when the expectation was made.

Question 4

What is the equation for output?

Answer 4

Yt=Y̅-α(rt-ρ)+εt
Y̅: Natural output, output increases with this is because output increases with increasing living standards.
rt: real interest rate. when this increases demand and therefore output decreases as saving seems more attractive than borrowing.
εt- Demand shock. positive e.g. surge of activism. negative e.g. oil shock.
ρ- When εt=0 and rt=ρ then Y=Y̅ so ρ is referred to the natural rate of interest.

Question 5

What is the equation for fisher’s equation?

Answer 5

rt=it-EtΠt+1
it: nominal interest rate
EtΠt+1: tomorrows inspected rate of inflation
rt- is the ex ante real interest rate, this is the expected real interest rate.
ex poste interest rate- rt=it-Πt+1, however the true value of Πt+1 can only be known after the fact, i.e. only in time period t+1.

Question 6

What is the equation for inflation?

Answer 6

Π=Et-1Πt+Φ(Yt-Y̅ t)+vt
inflation is dependent on yesterdays’ expectation of today’s inflation. vt is positive in adverse conditions e.g. oil price shocks of 1970s. vt

Question 7

What is the extrapolation equation for inflation?

Answer 7

EtΠt+1=Πt
Today’s expectation of tomorrow’s inflation.
This implies that : Et-1Πt=Πt-1, yesterday’s prediction of today’s inflation. Πt is a predetermined value.

Question 8

What is the equation for nominal interest rate?

Answer 8

it=(EtΠt+1)+p+θΠ(Πt-Πt*)+θY(Yt-Y̅ t)
We know from the extrapolation equation that EtΠt+1=Πt
so we sub that in the equation.
it=Πt+θΠ(Πt-Πt*)+θY(Yt-Y̅ t)
it-Πt=θΠ(Πt-Πt*)+θY(Yt-Y̅ t)
it-Πt is the ex poste real interest rate
rt=θΠ(Πt-Πt*)+θY(Yt-Y̅ t)

Question 9

What is the equation for dynamic aggregate supply curve and how is it derived?

Answer 9

π=πt-1+∮(Y-Y̅t)vt

It is derived from adaptive expectations and the phillips curve.

Question 10

What is the dynamic long run equilibrium?

Answer 10

This is based on a long run position around which the economy fluctuates around in the short run. There are no shocks so εt=vt=0.
π is stable but variables can grow over time which is why it is called dynamic

Question 11

How is the dynamic aggregate demand curve derived?and what is it?

Answer 11

It is derived from aggregate demand curve- Yt=-α(rt-ρ)+εt
We then replace all the endogenous variables until all that is left is inflation and output

Yt=-α(it-Etπt+1-ρ)+εt

Yt=Y̅t-α[(πt+ρ+θπ(πt-πt*)+θy(Yt-)+πt-ρ]+εt

This is then simplified to
Yt= Y̅t- (θπ/1+θy)(πt-πt*)+ (1/1++θy)εt

Question 12

What nominal interest rate parameters are in the Dynamic aggregate supply equation?

Answer 12

• θπ

- θy

Question 13

What variables do we consider changing in the dynamic macroeconomic model?

Answer 13

Exogenous ones: πt*Y̅t, vt and εt

Question 14

Why might Y̅t change?

Answer 14

• Increase in population
• Capital accumulation
• Technological processes

Question 15

What happens to dynamic aggregate model when Y̅t increases?

Answer 15

• Y̅t appears in both equations

- Inflation remains stable though, which means long run output grows.

Question 16

What happens when Vt is no longer 0 and increases?

Answer 16

• Vt is only present In the dynamic supply equation
• This causes inflation to rise by the full amount of the shock
• So the dynamic aggregate supply curve shifts upwards to reflect this change.
• This causes output to fall
• When shock disappears, inflation lowers and the supply curve falls but not all the way to its original longterm position due to adaptive expectations.

Question 17

What happens εt is no longer 0 and increases for five periods?

Answer 17

• Positive demand shock
• Appears in demand curve only
• Demand curve shifts to the right as it increases output
• this change in demand lasts the whole shock period but as soon as the shock is gone, demand curve shifts back
• At first, supply curve does not move and then from the second period it shifts upward each period which increases inflation in every period
• After the shock disappears, supply gradually begins to return to its original equilibrium. This is because expectations are slow to adjust.

Question 18

What happens to the dynamic aggregate demand curve when πt falls by 2%?
(Starting position is in the long run I.e. Where πt=πt.)

Answer 18

• πt is now bigger than π*t.
• as the model is no longer in equilibrium it aims to fix this.
• As π*t appears in the dynamic aggregate demand curve. The demand curve shifts backwards to a place where it still intercepts long run curve but also at a point where inflation is two less than its starting position.
• (Recall that π*t has a positive relationship with The demand curve)
• dynamic aggregate supply does not shift immediately
• in the subsequent periods the supply curve falls until it eventually reaches the new target for inflation and πt= π*t once again

Question 19

What equation previously studies is the Taylor rule?

Answer 19

it= πt+ρ+θπ(πt-πt*)+θy(Yt-)

Question 20

If inflation increases by one percent, according to the Taylor rule how much does nominal interest rates increase by and why ?

Answer 20

• nominal interest rates increases by (1+θπ)
• This is because inflation appears twice in the Taylor equation the first one has a 1:1 ratio with nominal interest rates.
• the second one is governed by θπ, which dictates the nominal interest rate’s sensitivity to this inflation.
• this means when inflation increases, nominal interest rate increases only by θπ%.

Question 21

What basically happens when the central bank changes nominal interest rate in response to a change in inflation?

Answer 21

They change real interest rate

Question 22

How does a positive θπ have a stabilising effect on inflation ?

Answer 22

• an increase in inflation is sufficient to induce a monetary response (change in it) which affects rt
• this increases real interest rates which reduces demand
• this is evident in the dynamic aggregate demand curve as we see demand fall when θπ increases

Question 23

What happens if θπ is in between -1 and 0?

Answer 23

The dynamic aggregate demand equation shows that if inflation increases by 1% whilst θπ was negative then then nominal interest rate increases by (1-θπ). This means the increase in inflation is greater than that of the nominal interest rate which decreases rt which causes demand to rise which generates more inflation. This is destabilising.

Question 24

What is the graphical implications of a negative value of θπ in the dynamic macroeconomic model ?

Answer 24

The demand curve would be upward sloping meaning output grows with inflation and inflation obviously spirals out of control.

Question 25

What is the Taylor principle ?

Answer 25

For inflation to be stable, the central bank needs to respond to a change in inflation with an even greater increase in nominal interest. In other words 1+θπ>1 or θπ>0