Chapter 1. Chapter 7 – Problem 5

Step 1

Work It Out
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You must read each slide, and complete any questions on the slide, in sequence.

Question

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.)

bmoOsF/gFFCO1FxbuvZHJuHCZDZw/TVKhofeDGvmiSPsw43jynp1wtsGGoF3oKz9oknJH0LYoiHEvKm7Y5/TkuNTTAioqHnVn+ug4Pp5ClkzVy9q9LYKzaqtDUSkW218VNXvjdT/7tVrh2QIMiEGYwgN8FHo7bNVUo88+/urQv17EgTy1XeGVg==
Review text pages 53-56 and 58-61 in Chapter 3 for a discussion of demand for labor and the Cobb-Douglas production function.

Question

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 = yBhAQ+3VvjM=

Total Output = 86lkhjXE6cSvY4pmYMEsiw==

Total Amount Earned by Workers = 3N1zdPKp0pHkYn9M6ec4vQ==

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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Step 2

Question

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) = YKEOwYPXm3o=

Employment (rounded to then nearest whole number) = bGTmYVeVuDCcK6UMqQ58SQ==

Total Output (rounded to the nearest whole number) = VkJTVKvKAMDNzQsjWcxzmA==

Total Amount Earned by Workers (rounded to the nearest whole number) = u/dSXkG/+jziAcFc8A3D6g==

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.

Question

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Congress does not succeed in helping the working class. Although employed workers now earn a higher wage, fewer workers are employed. The difference between the labor supply of 10,000 workers and employment of 8,227 workers represents unemployment of 1,773 workers. And for those workers who still have jobs, total earnings are now lower, reflecting lower output for the economy.

Question

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The analysis is not very useful in considering the effects of actual minimum-wage laws because in countries adopting a minimum wage, it is almost always below the equilibrium wage for the economy. For subgroups of the labor force, such as teenagers where the equilibrium wage likely is very low, the analysis presented here may be somewhat more relevant.
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