Derivation of the Inflation Formula with Adaptive Expectations
The inflation rate under adaptive expectations can be determined through a derivation that incorporates the assumption that expected inflation equals the previous period's inflation (). The derivation proceeds in several steps: inflation is defined as the percentage increase in prices, which is equal to the increase in costs per unit of output. If wages are the only cost, this is equivalent to the percentage increase in wages. This wage increase is composed of expected inflation plus the bargaining gap. Finally, by substituting the previous period's inflation for expected inflation, we arrive at the formula . The full derivation is as follows:
\begin{align*} \text{inflation (%)} &\equiv \text{increase in prices (%)} \\ &= \text{increase in costs per unit of output (%)} \\ &= \text{increase in wages (%)} \; (\text{if wages are the only costs}) \\ &= \text{expected inflation (%)} + \text{bargaining gap (%)} \\ &= \text{last period's inflation} + \text{bargaining gap (%)} \\ \pi_t &= \pi_{t-1} + \text{gap}_t \end{align*}
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Figure 4.14: Causal Chain from Last Year's Inflation to This Year's Inflation
Derivation of the Inflation Formula with Adaptive Expectations
In an economy where wage and price setters form their inflation expectations based on the previous year's inflation rate, suppose the inflation rate last year was 4%. If the economy is currently experiencing a positive bargaining gap of 1.5%, what will be the inflation rate for the current year?
An economy is experiencing a persistent positive bargaining gap, and its participants (workers and firms) form their inflation expectations based on the inflation rate of the previous period. Arrange the following events to illustrate the correct causal chain that explains how inflation from one period influences the next.
Explaining Inflation Dynamics
Determinants of Current Inflation
In an economic model where expectations about future price increases are based on the most recently observed rate of price increases, the presence of a zero bargaining gap will cause the rate of price increases to immediately fall to zero.
Match each component of the inflation process with its specific role in determining the current period's inflation rate, assuming expectations are formed based on recent past experience.
The Dynamics of Persistent Inflation
In an economy where inflation expectations are based on the previous period's inflation rate, for the current inflation rate to be the same as the previous period's rate, the bargaining gap must be ____.
Policy Impact on Inflation Dynamics
An economy's inflation rate over four consecutive years is shown below. Assume that economic agents in this economy form their inflation expectations based on the actual inflation rate of the previous year.
- Year 1: 2.0%
- Year 2: 3.5%
- Year 3: 5.0%
- Year 4: 5.0%
Based on this data, which statement most accurately describes the state of the bargaining gap from the beginning of Year 2 to the end of Year 4?
Learn After
In an economic model, the rate of inflation is determined by the rate of increase in wages. This wage increase is, in turn, composed of two parts: the inflation rate that workers and firms anticipate, and a 'bargaining gap' that reflects the current state of the labor market. If this model ultimately expresses the current period's inflation (πt) as the sum of the previous period's inflation (πt-1) and the current bargaining gap, what logical assumption must have been made about how inflation expectations are formed?
A macroeconomic model derives the current inflation rate based on wage-setting behavior and how expectations are formed. Arrange the following statements to reflect the correct logical sequence of this derivation.
Inflation Forecasting in a Simplified Economy
In an economic model where the current inflation rate (πt) is determined by last period's inflation (πt-1) plus a 'bargaining gap', what condition is necessary for the inflation rate to remain stable from one period to the next?