In Romer's learning by doing model, assume the production function is [tex]Y = K^{0.50}(EL)^{0.50}[/tex], the saving rate is 20%, the depreciation rate is 2%, and the population growth is 2%. If the learning by doing function is [tex]E = 4\left(\frac{K}{L}\right)[/tex], then determine the growth rates:

A. The growth rate of capital per worker is 16% and the growth rate of output per worker is 4%.
B. The growth rate of capital per worker is 36% and the growth rate of output per worker is 6%.
C. The growth rate of capital per worker is 36% and the growth rate of output per worker is 36%.
D. The growth rate of capital per worker is 4% and the growth rate of output per worker is 16%.

Question

High School

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Answer :

The growth rate of capital per worker is 20% and the growth rate of output per worker is 6%.

In Romer's learning by doing model, the growth rate of capital per worker can be calculated using the formula:

Growth rate of capital per worker = (Saving rate - Depreciation rate) + Population growth rate

Substituting the given values:

Growth rate of capital per worker = (0.20 - 0.02) + 0.02 = 0.20

The growth rate of output per worker can be calculated using the learning by doing function:

Growth rate of output per worker = Learning by doing function

Substituting the given learning by doing function:

Growth rate of output per worker = 4(K/L) = 4(0.50) = 2

Therefore, the correct option is b. 36% and the growth rate of output per worker is 6%.

Learn more about calculating the growth rate of capital and output per worker in romer's learning by doing model here:

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