3. Relationship Between Inflation and Unemployment. Okun's Law, The Phillips Curve.
Okun's law is an empirically observed relationship relating unemployment to losses in a country's production.
For every 1% increase in the unemployment rate, a country's GDP will be an additional roughly 2% lower than its potential GDP.
Mathematical statements of Okun's law is:
(Y* - Y) / Y* = ß (u - u*), where:
Y* - is potential output or GDP at full-employment
Y - is actual output
u*- is the natural rate of unemployment
u - is actual unemployment rate
ß - is the factor relating changes in unemployment to changes in output
Phillips curve is a historical inverse relationship between the rate of unemployment and the rate of inflation in an economy. Stated simply, the lower the unemployment in an economy, the higher the rate of inflation. While it has been observed that there is a stable short run tradeoff between unemployment and inflation, this has not been observed in the long run.
π = πe- ß (u - u*) + v
where π and πe are the inflation and expected inflation respectively, v - unexpected exogenous shocks to the world supply.
This equation, plotting inflation rate π against unemployment U gives the downward-sloping curve in the diagram that characterises the Phillips curve.
According to Okun's law π = πe+( Y* - Y ) / Y* + v
where v is also a Cost-push inflation, called "supply shock inflation," and ( Y* - Y ) / Y* - Demand-pull inflation.
In the diagram, the long-run Phillips curve is the vertical red line. Policymakers can reduce the unemployment rate temporarily, moving from point A to point B through expansionary policy. However, exploiting this short-run tradeoff will raise inflation expectations, shifting the short-run curve rightward to the "New Short-Run Phillips Curve" and moving the point of equilibrium from B to C. Thus the reduction in unemployment below the "Natural Rate" will be temporary, and lead only to higher inflation in the long run.