Consider an economy in which the representative firm produces the final consumption good using the production function Y = zN, with z = 1.0. The economy is populated by a representative consumer whose utility function is given by U(C, l) = 1/3 C^1/2 + 2/3 l^1/2 . The total number of hours available to the representative consumer is h = 1. In this economy, the government finances G by taxing the income at a rate t.

1. Solve the consumer's problem by finding the optimal leisure (l ? ) and consumption (c ? ). [05 points]

2. How does increase in t affect the optimal leisure? Explain. [02 points]

3. Calculate the government revenue for t = 2/5, t = 1/2, t = 2/3, and t = 3/4. [03 points]

4. Find that optimal tax rate t ? that maximizes the revenue of the government. [05 points]