Suppose we know that output in the economy is given by the production function: YttKt1/2Lt1/2. If total factor productivity (A) is growing at a rate of 1.5% per year, the capital stock (K) by 2%, and the labor supply (L) by 1%,
a. Calculate long run growth in output per worker (Y/L) for this economy.
b.This economy has capital growing faster than labor. While labor growth is mostly driven by population dynamics, firms in an economy do have some control over how fast capital stock grows. Do you think an economy will continue to grow capital faster than labor indefinitely? Why or why not?
c. What would happen to the growth rate of output per worker if capital growth slowed to 0.5% a year while labor continued to grow at 1% (and TFP still grows at 1.5%)?
d. What long run growth rate do you think this economy will eventually move towards over time? Explain your answer.