4. In the economy of Cape Despair, the subsistence real wage rate is $15 an hour

Question

4. In the economy of Cape Despair, the subsistence real wage rate is $15 an hour. Whenever real GDP per hour rises above $15, the population grows, and whenever real GDP per hour of labor falls below this level, the population falls. The table shows Cape Despair's production function:

Labor (billions of hours per year) Real GDP (billions of 2000 dollars)
0.5 8
1.0 15
1.5 21
2.0 26
2.5 30
3.0 33
3.5 35

Initally, the population of Cape Despair is constant and real GDP per hour of labor is at the subsistence level of $15. Then a technological advance shifts the production function upward by 50 percent at each level of labor.

a. What are the initial levels of real GDP and labor productivity?

b. What happens to labor productivity immediately following the technological advance?

c. What happens to the population growth rate following the technological advance?

d. What are the eventual levels of real GDP and real GDP per hour of labor?

Explanation / Answer

4. In the economy of Cape Despair, the subsistence real wage rate is $15 an hour. Whenever real GDP per hour rises above $15, the population grows, and whenever real GDP per hour of labor falls below this level, the population falls. The table shows Cape Despair's production function:

Labor (billions of hours per year) Real GDP (billions of 2000 dollars)
0.5 8
1.0 15
1.5 21
2.0 26
2.5 30
3.0 33
3.5 35

Initally, the population of Cape Despair is constant and real GDP per hour of labor is at the subsistence level of $15. Then a technological advance shifts the production function upward by 50 percent at each level of labor.

a. What are the initial levels of real GDP and labor productivity?

Before the technological advance ,labor productivity ,which is defined as real GDP didvided by employment was $15 .00 an hour. Real GDP was $14 BILLION and 1.0 billion hours of lours were employed.

b. What happens to labor productivity immediately following the technological advance?

Immediately following the technological adavance ,real GDP rises to $ 22.5 billion and employment remains ar 1 billion hours. Labour productivity increases to $ 22.50 an hour

c. What happens to the population growth rate following the technological advance?

Real GDP per hoir exceeds the sunsidence level of $ 15. .00 so population growth increases

d. What are the eventual levels of real GDP and real GDP per hour of labor?

Eventually population growth will increase labour and productivity will return to its susbsistence level of $15.00 an hour.

Real GDP will increase to $52.5 billion. Lobiur employment will be 3.5 billion hours and labour productivity will be $15.00

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