How does this new variable in the formula impact TFP growth? What happens if the country has higher average hours per worker? what happens if the country has lower average hours per worker?

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.14P
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Country Has Cobb-Douglas production function:

Y(it) = A(it) x K(it)1/3L(it)2/3

Where:

Y(it) = realGDP

K(it) = Capital

L(it) = No. workers employed in country (i) on date (t)

Suppose multiple countries share the same alpha = 1/3 but different levels of totalfactorproductivity (A(it)).

Now Instead of the above function the production function changes to:

Y(it) = A(it) x K(it)1/3 x (H(it)L(it))2/3

Y(it) = realGDP

K(it) = Capital

H(it) = Average hours worked p/worker (This is so the labour input is total hours opposed to employment)

L(it) = No. workers employed in country (i) on date (t)

These multiple countries share the same alpha = 1/3 but different levels of totalfactorproductivity (A(it)).

How does this new variable in the formula impact TFP growth?

What happens if the country has higher average hours per worker?

what happens if the country has lower average hours per worker?

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