Formula

Reservation Wage as an Average Over a Planning Horizon

To calculate an individual's reservation wage, one must determine the total expected value of their reservation option over a specific planning period. This calculation relies on averages because key factors, such as the exact duration of unemployment and the precise wage of a future job, are uncertain. The value is composed of two parts: the utility received during the expected period of unemployment (e.g., b + aM for j weeks) and the utility from the new job they expect to find for the remainder of the period (e.g., v for h - j weeks). The reservation wage (wrw_r) is then defined as the average of this total value, calculated by dividing it by the total length of the planning horizon (h). This is expressed by the formula:

wr=j(b+aM)+(hj)vhw_r = \frac{j(b+a^M) + (h-j)v}{h}

Where:

  • jj is the expected number of weeks unemployed.
  • b+aMb+a^M is the weekly utility while unemployed (unemployment benefit plus individual-specific utility).
  • hjh-j is the remaining number of weeks in the planning horizon, spent employed.
  • vv is the net utility from the new job.
  • hh is the total length of the planning horizon in weeks.

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Updated 2026-05-02

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