If the government pays a certain amount $b>0$ to every person who is not working, what is the impact of this subsidy on labour supply? How does it alter the reservation wage? Is your answer modified when payments are restricted to persons who are looking for a job?
My attempt: Suppose $A$ is an individual in the labour force. For an individual who is not in the labour force, there is no impact on labour supply. Therefore, it makes sense to apply the analysis to a person in the labour force.
In the income-leisure ($i$-$l$) diagram (of a week) for an individual $A$, without any government aid, let $w_R$ be the reservation wage. Suppose $G$ represents $A$'s other sources of income. Let $T=168$ be the number of hours in a week. Our analysis is done in the interval $[0,T]$ of the $l$-axis. We have the line $i=G+w(T-l)$ or $$i+wl=(wT+G).$$ At $l=T$ and $w=w_R$, $A$ is most happy (maximum utility) to not work at all. However, $w_R$ is the maximum wage rate at which $A$ doesn't work (by definition).
With the given government intervention, $A$'s original line shifts upward by $b$. $A$ comes to a higher utility point (than in previous case without government intervention) whether he is working or not. It is impossible to tell how the $w_R$ will be altered in this case. It is possible that if $A$ was working before, $A$ is not working now and vice-versa.
Am I correct?