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?

Explanation / Answer

new levels of real after 50% increase in gdp = 0.5 ----> 8(1+0.5) = 12 labour productivity = 12/0.5 = 25 1-----> 22.5 22.5/1 =22.5 1.5 21(1+0.5) = 31.5 31.5/1.5 = 21 2.0 26(1+0.5) = 39 39/2 = 19.5 2.5 30 = 45 45/2.5 = 18 3.0 33 = 49.5 49.5/3 = 16.5 3.5 35 = 52.5 52.5/3.5 =15

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