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.