Consider the introduction of a universal basic income (UBI) where all government benefits are eliminated but every adult receives UBI payment weekly, which is tax-free. To fund the UBI system, the GST will need to rise considerably, raising all prices. In real terms, the UBI payment will be $540 a week and real wages $30 an hour. Income tax will be levied on all real wage earnings at 50% (there will be no tax-free threshold).
You do not need to model the increase in the GST; instead, define all amounts in real terms (as given in the question above), such that C is real $ of consumption per week and wages and reservation wages are in real $ per week.