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Consider an economy with the following Cobb–Douglas production function:

Y = 4K1/4L3/4.

Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock. (Hint: Review Chapter 3.)

Labor Demand = ___________

Review text pages 53-56 and 58-61 in Chapter 3 for a discussion of demand for labor and the Cobb-Douglas production function.

The economy has 160,000 units of capital and a labor force of 10,000 workers. Assuming that factor prices adjust to equilibrate supply and demand, calculate the real wage, total output, and the total amount earned by workers.

Real Wage =

Total Output =

Total Amount Earned by Workers =

Review text pages 53-56 and 58-61 in Chapter 3 for a discussion of demand for labor and the Cobb-Douglas production function.
Review text pages 53-56 and 58-61 in Chapter 3 for a discussion of demand for labor and the Cobb-Douglas production function.
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      Consider an economy with the following Cobb–Douglas production function:

      Y = 4K1/4L3/4.

      Now suppose that Congress, concerned about the welfare of the working class, passes a law setting a minimum wage that is 5 percent above the equilibrium wage you derived in part (b). 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, employment, output, and the total amount earned by workers.

      Real Wage (rounded to one decimal place) =

      Employment (rounded to then nearest whole number) =

      Total Output (rounded to the nearest whole number) =

      Total Amount Earned by Workers (rounded to the nearest whole number) =

      Review text pages 53-56 and 58-61 in Chapter 3 for a discussion of demand for labor and the Cobb-Douglas production function. Review pages 189-192 in Chapter 7 for a discussion of wage rigidity and structural unemployment. Review the case study on The Characteristics of Minimum-Wage Workers in Chapter 7.

      Does Congress succeed in its goals of helping the working class?

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      Does this analysis provide a good way of thinking about a minimum-wage law?

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