Assuming that Tis the transfer income financed by income tax. The income tax rate is t. For example if t = 1/2 , then half of your wage income goes to the government. So the individual solves

max c x l

s.t.

c = w(1-l)(1-t)+T

So the worker earns labor income net of taxes and transfers.

1) Solve this with Lagrangian.

2) Taxes reduce labor supply. Try to plot the labor supply with respect to taxes. Show all your work