Question

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

Labor (billions of hours per year) Real GDP (billions of 2000dollars)
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 GDPper hour of labor is at the subsistence level of $15. Then atechnological advance shifts the production function upward by 50percent at each level of labor.

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

b. What happens to labor productivity immediately following thetechnological advance?

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

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