Question

Suppose you have the following information on the Fed’s and the European Central Bank’s (ECB) policy rules: Fed real interest rate =0.5 (inflation rate -2) ECB real interest rate= 0.2 * (inflation rate-2) +1

Graph these policy rules. If the inflation rate is 2 percent in each, what will be the real interest rate in the U.S. and the ECB area?

Some argue that Europe has a much lower tolerance for inflation than the United States. Can you tell—either from the diagram or from the equations—whether this is true?

Answer 1

Put Fed and ECB real interest rates on y-axis and inflation rate on x-axis.

Now, let us simplyfy the equations for policy rules so they are easier to graph.

Fed real interest rate = 0.5 (inflation rate -2) = -1 + 0.5 * inflation rate.

This can be graphed by using straight line with -1 as y-intercept and slope of 0.5 (the line, real interest rate, rises half as fast as inflation rate). It starts at -1 on y-axis and rises in y-axis direction 1 unit for a 2 unit increase in x-axis direction.

For ECB:

ECB real interest rate = 0.2 * (inflation rate -2) +1 = 0.2 * inflation rate - 0.4 + 1 = 0.6 + 0.2 * inflation rate

It can be grahed using a straight line with 0.6 as y-intercept and slope of 0.2 (the line, real interest rate, rises 1 units for every five units increase in inflatin rate). The line starts at 0.6 on the y-axis and rises 1 unit in y-axis direction for every 5 units increase in x-axis direction.

To say that Europe has lower tolerance for inflation than United States it to say that if inflation rises europeans are more raise real interest rates more than US would. This sensitivity is measured by the slopes of the two equations. The slope of 0.5 in United States is higher than 0.2 in Europe. Therefore, United States is more sensitive to inflation and less tolerant. Thus, we can conclude that it is not true that Europe has much lower tolerance for inflation than the United States.