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 the GDP per hour of labor falls below this level, the population falls. The table shows Cape Despair's production function:
Labor Real GDP
(billions of hr per yr) (billions of 2000 dollars)
Initially, 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?
a) We are told that the population is constant, so GDP/h must be $15. This occurs when Labor = 1 and GDP = 15
This solution analyzes how the equilibrium between Cape Despair's GDP and population responds to a technological advance that increases labor productivity by 50%.