3. A worker chooses labor supply L to maximize his payoff: (1 t)wL 1 2 L 2 in which t is the tax rate, w is the wage per hour. The government chooses a tax rate t to maximize tax revenue R = tW L. (a) What is the labor supply L maximizing the payoff? (b) What is the government tax revenue R when the worker chooses the payoff-maximizing L? (c) Based on (b), draw the graph of R as a function of t if w = 10. (d) What is the optimal tax t that maximizes the tax revenue R? (e) Suppose the government cares about the worker's after-tax income and maximizes R + (1 t)wL. What is the new optimal tax? What is the relationship between wage and the tax?