Consider an economy in which the representative consumer preferences are described by U(C, l) = 0.9 ln(C) + 0.1 ln(l). The total number of hours available to the representative consumer is h = 1, and the market real wage is w. The representative firm produces the final consumption good using the technology function Y = zN where N is the labour, and z = 2. Assume the government sets the level of its spending to G = 0.75 which has to be financed through a proportional tax t. 1.

Given the linear specification of the production function, what will be the equilibrium wage w ? . [03 points]

2. Find the Competitive Equilibrium allocation (t ? , l ? , N? , Y ? ). [07 points]

3. Find the the Pareto Optimal Allocation by solving the social planner's problem. [07 points]

4. What do you conclude? [03 points]