Show how imposing a lump sum tax on a consumer who has never faced it before affects outcomes. Do the same for a proportional (linear) income tax that raises the same revenues. Explain, by aid of both a graph and an explanation, why one of these will have larger welfare effects on the consumer for the same amount of tax revenue raised. You should clearly write down both budget constraints and explain why they have different slopes as part of this answer, possibly including the equations for the budget constraints