This is now

```{math}

:label: lake_lamda

:label: endogenous_lake_lambda

\lambda

= \gamma \mathbb P \{ w_t \geq \bar w\}

For each specification $(c, \tau)$ of government policy, we can solve for the

worker's optimal reservation wage.

This determines $\lambda$ via {eq}`lake_lamda` evaluated at post tax wages,

This determines $\lambda$ via {eq}`endogenous_lake_lambda` evaluated at post tax wages,

which in turn determines a steady state unemployment rate $u(c, \tau)$.

For a given level of unemployment benefit $c$, we can solve for a tax that balances the budget in the steady state