In a simple scenario with only two factors of production, suppose that capital’s share
of income is .4 and labor’s share is .6 and that annual growth rates of capital and
labor are 6 and 2 percent, respectively. Assume there is no productivity (technical)
change.
a. At what rate does output grow?
b. How long will it take for output to double? Show.
c. Now suppose productivity (technology) grows at a rate of 2 percent. Recalculate
your answers to a. and b. above.

Question

In a simple scenario with only two factors of production, suppose that capital’s share
of income is .4 and labor’s share is .6 and that annual growth rates of capital and
labor are 6 and 2 percent, respectively. Assume there is no productivity (technical)
change.
a. At what rate does output grow? 
b. How long will it take for output to double? Show. 
c. Now suppose productivity (technology) grows at a rate of 2 percent. Recalculate
your answers to a. and b. above.

anonymous · Answer

the rate of output growth = (0.4x6) + (0.6x2)= 2.4+1.2= 3.6% 
b. 70/3.6 = 19 yrs
c. 2 + 3.6%= 5.6%
d. 70/5.6 = 12.5 yrs