. 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 n\". 1iWhat is n\" a function of? How does this compare with the benchmark case discumed in class? . What happens to the individual labor supply a\" when the wage rate to increases? An swer explaining how the income e'ect and the substitution effect aifect consumptionI leisureI and labor choices. . Let the aggregate labor supply be denoted by N\". Assuming that y = 2 and A = 1!], 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. . Dene a competitive equilibrium. Make sure to list all the variables that are deter mined in equilibrium. . Plot the labor market equilibrium [e.g. putting demand and suppl},r of labor in the same plot, and showing the equilibrium values of N" and as") . Solve for the equilibrium allocations and prices. Show all intermediate steps for partial credit. 1 Competitive Equilibrium Exercise (45 points) Consider a static (one-period) economy. The technology that transforms labor N into output Y is given by Y = =N*Kl-@ with 0 > 1 and A > 0 are constants. Individuals are endowed with 1 unit of time. 1. Write down the firm's maximization problem and find the optimal labor demand of the firm as a function of w, K, a, and z. Denote the labor demand by No. 2. Assuming that = = 1.5, K = 20, and a = 0.6, compute N 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