ES200013 intermediate economics
Aggregate demand and the labour market
Aggregate demand
- Our analysis of AD builds on the IS-LM curve
- The IS curve is a negative relationship between output and the interest rate
- In the simple stylised IS relationship discussed in week 1, we assumed a linear
relationship between output and the nominal interest rate
- In this section
o We use the real interest rate rather than the nominal
o We assume a relationship between the log of output and the interest rate
- In week 1 IS was
o
o Where Y_ = C_ + I_ + G; this is exogenous
- We now make three changes
o Add a demand shock, e^d
o We use the real interest rate r rather than the nominal (i)
o We assume the relationship between log output and the interest rate
- We assume that the aggregate demand relationship is
o
- the equilibrium level is where output is Y = Y*
- the equilibrium real interest rate is r*
- there are no shocks in equilibrium
- so, in equilibrium AD is
o
- Subtracting log(Y*) from log(Y) gives
o
- This is the proportional difference between actual and equilibrium output
- We denote the gap output gap as ý = log(Y) – log(Y*)
- So
o 3
o If positive we are in an expansionary phase
, o If negative we are in a contractionary phase – (recession)
- Inflation is denoted as π
- Inflation in period t is the proportionate change in the price level compared to the
previous period π t = Pt-Pt-1/Pt-1
- It is approximately equal to the change in log price level
- So
o π t = log(Pt) – log(Pt-1)
o Or
o π t = Pt – Pt-1
o Where Pt = log(Pt) and Pt-1 = log(Pt-1)
- The real interest rate is defined as rt = it – Et x π t+1
- Where Et x Pi t+1 is the expected inflation rate in the next period
- For simplicity of notation, we will not use the time subscript so π t = π
- And r = i – π ^e, where π ^e = Et x π t+1 (expected inflation rate in the next period)
Aggregate demand and the labour market
Aggregate demand
- Our analysis of AD builds on the IS-LM curve
- The IS curve is a negative relationship between output and the interest rate
- In the simple stylised IS relationship discussed in week 1, we assumed a linear
relationship between output and the nominal interest rate
- In this section
o We use the real interest rate rather than the nominal
o We assume a relationship between the log of output and the interest rate
- In week 1 IS was
o
o Where Y_ = C_ + I_ + G; this is exogenous
- We now make three changes
o Add a demand shock, e^d
o We use the real interest rate r rather than the nominal (i)
o We assume the relationship between log output and the interest rate
- We assume that the aggregate demand relationship is
o
- the equilibrium level is where output is Y = Y*
- the equilibrium real interest rate is r*
- there are no shocks in equilibrium
- so, in equilibrium AD is
o
- Subtracting log(Y*) from log(Y) gives
o
- This is the proportional difference between actual and equilibrium output
- We denote the gap output gap as ý = log(Y) – log(Y*)
- So
o 3
o If positive we are in an expansionary phase
, o If negative we are in a contractionary phase – (recession)
- Inflation is denoted as π
- Inflation in period t is the proportionate change in the price level compared to the
previous period π t = Pt-Pt-1/Pt-1
- It is approximately equal to the change in log price level
- So
o π t = log(Pt) – log(Pt-1)
o Or
o π t = Pt – Pt-1
o Where Pt = log(Pt) and Pt-1 = log(Pt-1)
- The real interest rate is defined as rt = it – Et x π t+1
- Where Et x Pi t+1 is the expected inflation rate in the next period
- For simplicity of notation, we will not use the time subscript so π t = π
- And r = i – π ^e, where π ^e = Et x π t+1 (expected inflation rate in the next period)
