An economy initially has 200 units of physical capital per worker. Each year, it increases the amount of physical capital by 10%. According to the aggregate production function for this economy, each 1% increase in physical capital per worker, holding human capital and technology constant, increases output per worker by 0.25%. In three years' time, what is the level of physical capital per worker in this economy?

The capital growth as stated is compound growth. Since technology and human capital are constant, there is not expected changed in productivity factors relationship, so the formula for compound growth, in this case, is: capital per worker in 3 years' time = capital per worker * (1+ annual rate growth) ^ 3. Computing numbers would be: capital per worker in 3 years' time = 200*(1+10)^3= 266,2

JavierBardem JavierBardem · Answer 2 · 2025-01-27T13:48:00-05:00

Final answer:

The level of physical capital per worker in this economy would be 266.2 units after three years.

Explanation:

To find the level of physical capital per worker in this economy after three years, we need to calculate the compounded growth rate of physical capital per worker. Since the economy increases physical capital by 10% each year, after three years, it would have increased by 10% for each year. The compounded growth rate for three years is calculated as (1 + 0.1)^3 = 1.331. Therefore, the level of physical capital per worker in this economy after three years would be 200 units * 1.331 = 266.2 units.

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