Tau (τ) as the Expected Proportion of Time Unemployed

Two Formulations of the Reservation Wage Curve Equation

In a model where a worker's minimum acceptable wage (their reservation wage) is calculated as a weighted average of their utility when unemployed and their utility from other available jobs, consider the Nth worker in an ordered sequence of potential employees. The utility when unemployed is composed of both a market-wide benefit payment and a component unique to that individual. If the market-wide benefit payment for being unemployed increases, while all other factors (including the worker's unique utility and the value of other jobs) remain constant, how will the reservation wage for this Nth worker be affected?

Calculating a Worker's Reservation Wage

In the reservation wage model represented by the equation $w_N = \tau(b + \alpha_N) + (1-\tau)v$, a one-unit increase in a worker's individual unemployment utility ($\alpha_N$) will have a larger positive effect on their reservation wage ($w_N$) than a one-unit increase in the average utility from other jobs ($v$), if and only if the expected proportion of time the worker is unemployed ($\tau$) is greater than 0.5.

Analyzing Competing Effects on Reservation Wage

Match each component of the reservation wage equation, $w_N = \tau(b + \alpha_N) + (1-\tau)v$, with its correct economic interpretation. This equation models the minimum wage a worker will accept by weighting the value of being unemployed against the value of working elsewhere.

Evaluating the Real-World Applicability of the Reservation Wage Model

A worker's reservation wage ($w_N$) is determined by the equation $w_N = \tau(b + \alpha_N) + (1-\tau)v$, where $\tau$ is the expected proportion of time the worker is unemployed. In a scenario where a prolonged economic downturn causes the expected period of unemployment to increase dramatically, pushing the value of $\tau$ close to 1, which factor's influence on the reservation wage becomes minimal?

Consider the model for a worker's reservation wage, $w_N$, given by the equation: $w_N = \tau(b + \alpha_N) + (1-\tau)v$. In this model, under what condition will a worker's reservation wage ($w_N$) be strictly greater than the average utility from other available jobs ($v$)? (Assume the expected proportion of time unemployed, $\tau$, is greater than zero and less than one.)

Isolating an Individual-Specific Factor

Consider the reservation wage equation $w_N = \tau(b + \alpha_N) + (1-\tau)v$, which calculates the minimum wage ($w_N$) a specific worker will accept. In this model, a one-unit increase in the market-wide unemployment benefit ($b$) will have a greater effect on the reservation wage than an equivalent one-unit increase in that worker's personal, non-monetary utility from being unemployed ($\alpha_N$).

Tau (τ): Weight and Expected Proportion of Unemployment Time

The Comprehensive No-Shirking Wage Curve Equation