The Phillips curve captures the supply side short run relationship between inflation and unemployment is given by
a. Suppose job separation rate is 2% and job finding rate is 38%. Find the natural rate of unemployment for this economy.
b. Suppose that the slope of the Phillips curve is 0.6. Assuming that supply shock = 0, the expected inflation rate is 4% and actual unemployment rate is 8%, find the current inflation rate. Illustrate the Phillips curve graphically.
c. If natural rate of unemployment rises 2%, how does this affect the Phillips curve? Show this in your previous graph.
d. What will happen to the Phillips curve in case of negative supply shock and positive supply shock?
a. The natural rate of unemployment is given by the formula:
Natural rate of unemployment = job separation rate / (job separation rate + job finding rate)
Substituting the given values, we get:
Natural rate of unemployment = 0.02 / (0.02 + 0.38) = 0.05 or 5%
So the natural rate of unemployment for this economy is 5%.
b. The Phillips curve equation is:
Inflation = expected inflation rate + slope * (actual unemployment rate - natural rate of unemployment) + supply shock
Substituting the given values, we get:
Inflation = 4% + 0.6 * (8% - 5%) + 0
Inflation = 4% + 0.6 * 3% = 5.8%
So the current inflation rate is 5.8%.
To illustrate this on a graph, we plot the Phillips curve as a downward sloping curve, with inflation on the vertical axis and unemployment on the horizontal axis. The natural rate of unemployment is shown as a vertical line intersecting the Phillips curve. The point where the actual unemployment rate and the natural rate of unemployment intersect the Phillips curve gives us the current inflation rate.
c. If the natural rate of unemployment rises by 2%, then the Phillips curve shifts upwards by 2%. This is because the new natural rate of unemployment will intersect the Phillips curve at a higher inflation rate. We can show this graphically by shifting the vertical line representing the natural rate of unemployment upwards by 2%. The new intersection points between the Phillips curve and the actual unemployment rate line will give us the new inflation rate.
d. In case of a negative supply shock, the Phillips curve shifts upwards, indicating a higher inflation rate at every level of unemployment. This is because a negative supply shock reduces the aggregate supply, leading to higher prices and inflation. In case of a positive supply shock, the Phillips curve shifts downwards, indicating a lower inflation rate at every level of unemployment. This is because a positive supply shock increases the aggregate supply, leading to lower prices and inflation. We can show these shifts on the same Phillips curve graph by shifting the curve upwards or downwards accordingly.
The Phillips curve equation
The Phillips curve equation is a statistical model that demonstrates the inverse relationship between unemployment and inflation in an economy. The equation is given by:
Inflation = expected inflation rate + β (Unemployment - Natural rate of unemployment) + supply shock
where:
- Inflation is the rate of change in the general price level of goods and services over time
- Expected inflation rate is the rate of inflation that households and firms expect in the future
- β (beta) is the slope of the Phillips curve, which represents the strength of the relationship between unemployment and inflation
- Unemployment refers to the percentage of the labor force that is without work but actively seeking employment
- Natural rate of unemployment is the rate of unemployment that exists when the economy is in equilibrium, with no cyclical unemployment present
- Supply shock refers to changes in the availability or cost of key inputs such as labor, raw materials, or capital, which can shift the Phillips curve in the short run.
a. The natural rate of unemployment can be calculated using the formula:
Natural Rate of Unemployment = (Job Separation Rate) / (Job Separation Rate + Job Finding Rate)
In this case, the job separation rate is 2% and the job finding rate is 38%.
Natural Rate of Unemployment = 2% / (2% + 38%)
= 2% / 40%
= 0.05
Therefore, the natural rate of unemployment for this economy is 5%.
b. The Phillips curve equation can be written as:
Inflation Rate = Expected Inflation Rate + (Slope of the Phillips curve) * (Actual Unemployment Rate - Natural Rate of Unemployment)
Given that the slope of the Phillips curve is 0.6, the expected inflation rate is 4%, and the actual unemployment rate is 8%, the formula becomes:
Inflation Rate = 4% + (0.6) * (8% - 5%)
= 4% + (0.6) * (3%)
= 4% + (0.6) * (0.03)
= 4% + 0.018
= 4.018%
Therefore, the current inflation rate is 4.018%.
Here is a graphical representation of the Phillips curve:
Inflation Rate ^
|
+---------+---------+
| |
8% | |
| |
| |
| |
6% | |
| |
| |
| |
4% | |
| |
| |
| |
2% | |
| |
| |
+---------+---------+---------------> Unemployment Rate
5% 8%
c. If the natural rate of unemployment rises by 2%, it means that the new natural rate of unemployment will be 7% (5% + 2%).
This would shift the Phillips curve upwards, meaning that for any given actual unemployment rate, the corresponding inflation rate would be higher compared to the previous situation.
Here is the updated graph:
Inflation Rate ^
|
+---------+---------+
| |
8% | |
| |
| |
| |
6% | |
| |
| |
| |
4% | |
| |
| |
| |
2% | |
| |
| |
+---------+---------+---------+-----> Unemployment Rate
5% 7% 8%
d. In the case of a negative supply shock, the Phillips curve would shift upwards, meaning that for any given actual unemployment rate, the corresponding inflation rate would be higher compared to the previous situation. This is because negative supply shocks often lead to reduced output and increased costs, which can put upward pressure on prices.
In the case of a positive supply shock, the Phillips curve would shift downwards, meaning that for any given actual unemployment rate, the corresponding inflation rate would be lower compared to the previous situation. This is because positive supply shocks often lead to increased output and decreased costs, which can put downward pressure on prices.
a. To find the natural rate of unemployment, we need to use the formula in the Phillips curve model:
Natural Rate of Unemployment = Job Separation Rate / (Job Separation Rate + Job Finding Rate)
In this case, the job separation rate is given as 2% (0.02) and the job finding rate is given as 38% (0.38). Plugging these values into the formula:
Natural Rate of Unemployment = 0.02 / (0.02 + 0.38)
= 0.02 / 0.40
= 0.05 or 5%
Therefore, the natural rate of unemployment for this economy is 5%.
b. To find the current inflation rate using the information given, we need to use the Phillips curve equation:
Inflation = Expected Inflation + (Slope of Phillips Curve * (Actual Unemployment Rate - Natural Rate of Unemployment))
In this case, the slope of the Phillips curve is given as 0.6, the expected inflation rate is 4%, and the actual unemployment rate is 8%. Plugging these values into the equation:
Inflation = 4% + (0.6 * (8% - 5%))
= 4% + (0.6 * 3%)
= 4% + 1.8%
= 5.8%
Therefore, the current inflation rate is 5.8%.
To illustrate the Phillips curve graphically, you can plot the inflation rate on the y-axis and the unemployment rate on the x-axis. The Phillips curve will show a downward sloping curve, indicating the inverse relationship between inflation and unemployment.
c. If the natural rate of unemployment rises by 2%, it means the new natural rate of unemployment is 7% (5% + 2%). This will shift the Phillips curve upward and to the right, indicating a higher level of unemployment at any given inflation rate. The slope of the Phillips curve remains unchanged.
To show this on the previous graph, you can shift the Phillips curve upward by 2% from the original natural rate of unemployment.
d. In case of a negative supply shock, the Phillips curve will shift upward, indicating higher unemployment and inflation rates. This is because negative supply shocks, such as increased input costs or reduced productivity, lead to higher production costs and lower output levels.
In case of a positive supply shock, the Phillips curve will shift downward, indicating lower unemployment and inflation rates. Positive supply shocks, such as improved technology or increased productivity, lead to lower production costs and higher output levels.
To illustrate the Phillips curve with a negative or positive supply shock, you would need to shift the entire curve either upward or downward based on the direction of the shock.