Economics in the medium-run
• In developing the AD-AS framework, we
developed a model in levels- price levels, output
levels and interest rates.
• In the last lecture, we used the labour market
equations to derive the Phillips curve- a
relationship between growth in price level
(inflation) and unemployment.
• In this lecture we will complete the transition and
develop a model in growth- inflation, output
growth, money stock growth and unemployment.
Levels versus growth
• Levels
• When we were talking
in levels, our
variables are:
–
–
–
–
–
Interest rates
Output
Prices
Unemployment
Wages
• Growth
• When we are talking
in growth (percentage
change in levels), our
variables of interest
are:
–
–
–
–
Interest rates
Growth in Output
Growth in Prices
Unemployment
Okun’s Law
• Okun’s Law (named after an economist on
Kennedy’s Council of Economic Advisors)
states that there is a negative linear
relationship between growth in output and
changes in the unemployment rate.
– If economic growth is low, unemployment will
rise.
– If economic growth is high, unemployment will
fall.
Derivation of Okun’s Law
Y = Y (N/N) (L/L)
Y = (Y/N) (N/L) (L) = (Y/N) (1-u) L
Growth in Y = (Growth in Y/N) + (Growth in
L) – (Growth in u)
• Growth in Y/N has been 1.5% per year in
Australia. Growth in L has been 1.9% per
year in Australia.
(Change in ut) = gYt – 3.4%
Derivation of Okun’s Law
• Our best estimate of Okun’s Law is that:
ut – ut-1 = -0.5 (gYt – 3.4%)
• So if gyt > 3.4%, then unemployment rises, and if
gyt < 3.4%, then unemployment falls.
• In general:
ut – ut-1 = -β (gYt – g*Y)
• Intuition: The labour market is growing (in
numbers and productivity) every year. Output
must grow at least this fast, or the economy will
not absorb all of the labour.
Phillips curve
• The Phillips curve shows a linear relationship
between changes in the inflation rate and
changes in the unemployment rate:
πt - π te = - α (ut – un)
• If inflationary expectations are merely last year’s
inflation rate:
πt - πt-1 = - α (ut – un)
• Where we call 1/α the “sacrifice ratio”, as it
represents the number of percent-years of
unemployment required to reduce inflation by
1%.
What is a dynamic aggregate
demand?
• In developing the AD-AS framework, we
developed a static model for output and
introduced the RBA- treating the RBA as
though it had a “target price level”.
• But the natural rate of output is growing
over time and the RBA does not aim for a
price level- instead a target inflation rate.
• We want an AD relation in growth of output
and growth of prices.
Dynamic aggregate demand
• With our previous AD equations, we had
two forms:
– RBA controls money supply
Yt = Y((Mt/Pt), Gt, Tt)
– RBA controls interest rates
Yt = Y(it, Gt, Tt)
• We want to turn equations into “growth”
relations.
Growth relations
• Growth is the (Change in variable)/(Total
of variable). Let gx be the “growth of x”.
There are some simple rules we can
invoke for growth relationships:
A = BC then
gA = gB + gC
A = B/C then
gA = gB – gC
• You can prove this with some basic
calculus.
RBA controls money supply
• RBA controls money supply
Yt = Y((Mt/Pt), Gt, Tt) = (Mt/Pt) f(Gt, Tt)
• If we hold G and T constant, then they
drop out in a growth relation:
gYt = gMt – gPt
• But gP is just inflation, so we have:
gYt = gMt – πt
RBA controls interest rate
• RBA controls interest rates
Yt = Y(it, Gt, Tt) = Y*t / it
• Where Y* is the natural rate of output.
gYt = g*Y - git
• If the RBA follows an interest rate target
then the rule for the RBA might be
git = φ(πt – πT)
gYt = g*Y - φ(πt – πT)
Model in growth rates
• So we have three relations in growth rates:
Okun’s Law: ut – ut-1 = -β (gYt – g*Y)
Phillips curve: πt - π t-1 = - α (ut – un)
DAD: gYt = g*Y - φ(πt – πT)
• Or
DAD: gYt = gMt – πt
• Parameters: g*Y, un, πT , gMt
• Variables to be solved: gYt, ut, πt
• As these are growth models, we will typically be
solving for values of variables over time.
Solution of the model
• Unless we want to allow for a solution that
spirals away, ie. πt > πt-1 for all t, then we will
require that πt = πt-1.
• From our Phillips Curve, then ut = un for all t, so
through our Okun’s Law, gYt = g*Y for all t.
• Our DAD relations will then determine monetary
policy.
– πt = πT
– gMt = g*Y + πT
• So to maintain stability in our model, the path of
money supply is determined by our targets and
parameters.
What is the cause of inflation?
• In our solution, we have
– πt = gMt - g*Y
• Inflation simply depends on how much faster the
money supply grows than the natural rate of
output growth.
• This is what the book means by “Inflation is
always and everywhere a monetary
phenomenon.” Inflation in the medium-run does
not depend oil shocks or wages policy or
anything other than the rate of money creation.