DSE 2020 Question 9: Budget constraint and consumer equilibrium

A household with an endowment of $1$ unit of time maximises $u=\ln c+b\ln(1-l)$, where $c$ is consumption and $l\in[0,1]$ is time spent working, financing consumption from labour income $c=wl$ with $w$ the wage per unit of labour time. If the market wage rate rises, the household's equilibrium labour supply