Consider the following production function that is already written in per worker terms: y = Ak^α x h^1−α where h represents human capital per worker. Suppose we are given the following information: capital per worker in an economy has been growing at 1% per year, human capital per worker has been growing at 5% per year, and output per worker has been increasing at 1% per year. What is the rate of productivity growth? Assume that α = 1/3.

Question

03-02-2024
Business

High School

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Consider the following production function that is already written in per worker terms: y = Ak^α x h^1−α where h represents human capital per worker. Suppose we are given the following information: capital per worker in an economy has been growing at 1% per year, human capital per worker has been growing at 5% per year, and output per worker has been increasing at 1% per year. What is the rate of productivity growth? Assume that α = 1/3.

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snehashiwani51 snehashiwani51 · Answer 1 · 2024-09-04T04:59:00-04:00

To find the rate of productivity growth, we need to understand the components of the production function and how they are changing over time.

The given production function is: y = Ak^α x h^(1-α), where y represents output per worker, A is total factor productivity, k is capital per worker, h is human capital per worker, and α is a parameter with a value of 1/3. We are given the following information about the growth rates: Capital per worker is growing at 1% per year. Human capital per worker is growing at 5% per year. Output per worker is increasing at 1% per year.

To find the rate of productivity growth, we can start by considering the growth rate of output per worker. According to the production function, output per worker depends on capital per worker and human capital per worker. Since the growth rate of output per worker is given as 1% per year, this means that the combined growth rate of capital per worker and human capital per worker must also be 1% per year.

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