Hi! If you could please help answer this question and explain step-by-step the equations used in the solution, I would really appreciate it. Thank you so much!

1. The Labor Market:

Consider an economy with production function given by Y = AK0.5L 0.5 where A is the total factor productivity (TFP), K is the capital stock and L is the labor input. For simplicity assume capital is fixed and equal to 1. Assume A=200.

a. Write the firm's problem of choosing labor demand. Derive the demand for labor as a function of the real wage.

b. Assume labor supply is inelastic and fixed at L = 100. Find the equilibrium values of the wage and the employment level for this economy. Display graphically the labor supply and the labor demand curves. Carefully label your graph.

c. Suppose the economy faces a positive productivity shock and TFP is now A=300. Display graphically the new labor demand function. What are the equilibrium values of employment and the real wage?

d. Compute the total output when A=100 and when A=300. What is the output's growth rate? Compare that growth rate with the growth rate in A. How does the growth rate of output per capita compares to the growth rate in A? Explain carefully.

e. Now, suppose that Congress, concerned about the welfare of the working class, passes a law setting the minimum wage that is 10 percent above the equilibrium wage you just derived (in the case where A = 300). Assuming that Congress cannot dictate how many workers are hired at the mandated wage, what are the effects of this law? Specifically, calculate what happens to the real wage, the employment, the output, and the total amount earned by workers.

f. Does Congress succeed in its goal of helping the working class? Explain.

g. Do you think the analysis provides a good way of thinking about a minimum-wage low? Why or why not?