Consider the following Preference function u(C, 1)=4log(C +1)+1 and his production function is given by 2F (K, Nd)=2K (N), with z = 1 and K = 23. Suppose that G = 1 and h = 8. Let w be the wage rate. 1. Write the utility maximization problem. 2. Given π, w and T, derive the labor supply N'(w). 3. Write the profit maximization problem. 4. Given w, derive the labor demand Nd (w). 5. Suppose w=4 and T = 1. How much is excess supply of or demand for labor (if any) and how does w respond to that? 6. Find the equilibrium. 7. Write the problem that a social planner solves. 8. Explain the condition that a social planner uses in item 7 to find the solution, and discuss whether the allocation in item 6 satisfies the condition.