Consider an economy with the following Cobb-Douglas production function: Y=K^(1/3) * L^(2/3).

(a) Derive the equation describing labor demand as a function of the real wage and the capital stock.

(b) The economy has 1,000 units of capital and a labor force of 8,000 workers. Assuming that factor prices adjust to equate supply and demand, calculate the real wage, total output, and the total income earned by workers.

(c) Now, suppose that the new president, concerned about the welfare of the working class, passes a law setting a minimum wage that is 10 percent above the equilibrium wage you derived in part (b). What happens to the real wage, employment, output, and the total income earned by workers in this scenario? (no need to derive the numerical values)

(d) Does the president succeed in her goal of helping the working class? Explain why.