Question

Suppose that the equilibrium real federal funds rate is 2 percent and the target rate of inflation is 2 percent. Use the following information and the Taylor rule to calculate the federal funds rate target: Current inflation rate \(=4\) percent Potential \(\mathrm{GDP}=17.0\) trillion Real GDP \(=17.17\) trillion

Short answer

Based on the Taylor Rule, the calculated target for the federal funds rate in this scenario would be 5%.

Step-by-step solution

Determine the Inflation Gap

This is the difference between the current inflation rate and the target rate of inflation, calculated as: Inflation Gap = Current Inflation Rate - Target Inflation Rate = \(4\% - 2\% = 2% \)

Convert GDP to a Percentage Gap

The GDP gap is calculated as the percentage difference between Real GDP and Potential GDP: GDP Gap (%) = [(Real GDP - Potential GDP) / Potential GDP] * 100% = [ \( (17.17 \, trillion - 17.0 \, trillion) / 17.0 \, trillion ] * 100% = 1% \)

Use Taylor Rule to Calculate the Federal Funds Rate Target

The formula for the Taylor rule is: Federal Funds Rate Target = Equilibrium Real Rate + 1.5(Inflation Gap) + 0.5(GDP Gap) = \(2% + 1.5 * 2% + 0.5 * 1% = 5% \)

Key concepts

Federal Funds Rate

The federal funds rate is a critical tool used by the Federal Reserve (often referred to as the Fed) to influence the economy. It is the interest rate at which depository institutions trade federal funds—balances held at Federal Reserve Banks— with each other overnight. By manipulating this rate, the Fed can affect the money supply, which in turn has effects on inflation, employment, and overall economic growth.

The Federal Reserve sets a target for the federal funds rate based on its monetary policy objectives, which include maximum employment, stable prices, and moderate long-term interest rates. To achieve these objectives, the Fed uses open market operations and other tools to push the market towards the target rate.

Significance of the Federal Funds Rate in Monetary Policy

The federal funds rate indirectly influences longer-term interest rates, which affects consumer and business borrowing costs, including for mortgages, car loans, and capital investment. Changes in these rates can then influence economic activity and inflation. The fed funds rate serves as a benchmark for many other interest rates and is a pivotal indicator for both markets and the general economy.

Inflation Gap

The inflation gap is a measure that shows the deviation of the current inflation rate from a target inflation rate, set by a central bank, like the Federal Reserve in the United States. It's essentially the percentage by which the actual price level, as measured by a consumer price index or other metric, is above or below the target.

An inflation gap can signal overheating in the economy when too high, or a slack when too low. Central banks might strive for a certain level of inflation as a way to spur economic growth without causing excessive price increases. The inflation gap helps them gauge if their monetary policy needs adjusting to bring inflation towards the targeted level.

Calculating the Inflation Gap

To calculate the inflation gap, as indicated in the step-by-step solution, you subtract the target inflation rate from the current inflation rate. For example, with a current inflation rate of 4% and a target of 2%, the inflation gap would be 2%. This positive gap indicates that the current inflation is higher than what the Fed targets, prompting potential monetary actions to cool down the economy and bring inflation back to the target level.

GDP Gap

The GDP gap, or output gap, quantifies the difference between the actual output of an economy and its potential output. Potential output is the level of economic activity that an economy can sustain over the long-term without increasing inflation. It refers to the maximum amount of goods and services an economy can produce when it is most efficient—that is, all resources are employed at their highest and best use.

A positive GDP gap suggests an economy is operating above its potential, which can lead to inflationary pressures as the demand for goods and services outstrips supply. Conversely, a negative GDP gap implies underuse of resources and can be indicative of a recessionary environment with high unemployment.

Assessing the Economic Condition

To assess the current economic condition using the GDP gap, you compare the actual GDP to the potential GDP, as demonstrated in the provided problem: a real GDP of 17.17 trillion and a potential GDP of 17.0 trillion yields a 1% GDP gap. This small positive gap indicates that the economy is slightly above potential output, suggesting a relatively healthy economic climate but also the possibility of inflationary pressures.