The economy has grown by 4% per year over the past 30 years. During the same period, the labor force has grown by 1% per year and the quantity of physical capital has grown by 5% per year. Each 1% increase in physical capital per worker is estimated to increase productivity by 0.4%. Assume that human capital has not changed during the past 30 years. What is the growth rate of productivity?

Question

Quizplus · Accepted Answer

The Solow Growth Model states that economic growth is a function of physical capital, labor, and productivity. In this scenario, physical capital has grown by 5% and labor has grown by 1%, leading to a total growth in inputs of 6%. However, we need to account for the effect of physical capital on productivity. Each 1% increase in physical capital per worker increases productivity by 0.4%. Therefore, the effective growth in productivity is 5% * 0.4% = 2%.

Using the Solow Growth Model formula, we can calculate the growth rate of output as

Y = A*K^(1/3)*(L*H)^(2/3)

where Y is output, A is productivity, K is physical capital, L is labor, and H is human capital. We know that labor and human capital have not changed during the past 30 years, so we can focus on the growth in physical capital and productivity.

Over the past 30 years, physical capital has grown by 5% per year and labor has grown by 1% per year. Therefore, the effective growth rate of inputs is

(0.05*K/K) + (0.01*L/L) + (0*H/H) = 0.06

where we can assume that human capital (H) has not changed. We can rearrange this equation to solve for the growth rate of productivity (A):

A = Y/(K^(1/3)*(L*H)^(2/3))

Since the economy has grown by 4% per year over the past 30 years, we can assume that output (Y) has also grown by 4% per year. Plugging in the numbers, we get:

A = 0.04/(1.05^(1/3)*(1.01*1)^(2/3)) = 0.03

Therefore, the growth rate of productivity is 3%.

The Economy Has Grown by 4% Per Year Over the Past