Analyze the following scenario and predict the long-term outcome for the inflation rate.

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Inflation, defined as the percentage increase in prices, is equivalent to the rise in costs per unit of output. Assuming wages are the only cost, inflation equals the percentage increase in wages. This wage increase is composed of two parts: the expected inflation rate and the bargaining gap. When expectations are adaptive, meaning people expect this period's inflation to be the same as last period's, the formula becomes: $\pi_t = \pi_{t-1} + \text{gap}_t$. Here, $\pi_t$ is the inflation rate in the current period, $\pi_{t-1}$ is the inflation rate from the previous period, and $\text{gap}_t$ is the bargaining gap in the current period.

Inflation Formula with Adaptive Expectations

An economy is experiencing a period where wage demands consistently outpace productivity gains, creating a positive 'bargaining gap' of 2%. If the inflation rate last year was 3%, and people form their expectations about future inflation based on last year's rate, what will the inflation rate be this year?

Inflation Dynamics with a Persistent Bargaining Gap

Consider an economic model where this period's inflation (πt) is determined by last period's inflation (πt-1) and the current bargaining gap (gapt), according to the formula: πt = πt-1 + gapt. If an economy experiences a persistent positive bargaining gap (i.e., gapt > 0 for multiple consecutive periods), what is the resulting trajectory of the inflation rate over time? Explain your reasoning.

Inflation Dynamics with Adaptive Expectations

In an economy where inflation expectations are formed by looking at the previous period's inflation rate, a persistent positive bargaining gap will cause the inflation rate to stabilize at a new, higher level.

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