Could you please help me with question 4-9? I would be appreciate it!

Consider a static (one-period) economy. The technology that transforms labor N into output Y is given by Y : .erl\\f"'K1_cc with 0 1 and A > U are constants. Individuals are endowed with 1 unit of time. 1. Write down the rm's maximization problem and nd the optimal labor demand of the rm as a function of m, K, a, and z. Denote the labor demand by Nd. 2. Assuming that z = 1.5, K = 20, and a = 0.6, compute Nd when w = 1. Show all intermediate steps for partial credit. 3. Now plot the labor demand, making sure to label your axis and being as precise as possible (for example, show the point where w = 1 computed before). Feel free to draw it by hand or use Excel to do this. 4. Write down the maximization problem of consumers, specifying what are the endoge nous and what are the exogenous variables. Find the optimal labor supply of the household and denote it by as. What is n3 a function of? How does this compare with the benchmark case discussed in class? 5. What happens to the individual labor supply us when the wage rate to increases? An swer explaining how the income effect and the substitution effect affect consumption, leisure, and labor choices. 6. Let the aggregate labor supply be denoted by N 3. Assuming that V = 2 and A = 10, plot the aggregate labor supply, making sure to label your axis and being as precise as possible (for example, show the point where w = 1 computed before). Feel free to draw it by hand or use Excel to do this. 7. Dene a competitive equilibrium. Make sure to list all the variables that are deter- mined in equilibrium. 8. Plot the labor market equilibrium (e.g. putting demand and supply of labor in the same plot, and showing the equilibrium values of N\" and w'\") 9. Solve for the equilibrium allocations and prices. Show all intermediate steps for partial credit