Consider the production function modelled by the following equation: 1-α Y₁ = AK (BH₂) LE where Kt is capital, Ht is human capital, Lt is the number of workers, B is a scala larger than 0, A is the (constant) level of technology, 0 < a <1 and 0 <ɛ

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Chapter1: Making Economics Decisions
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Consider the production function modelled by the following equation:
Y₁ = AK₁-α(BH₂)ªL₹
where Kt is capital, Ht is human capital, Lt is the number of workers, B is a scalar
larger than 0, A is the (constant) level of technology, 0 < a <1 and 0 <ɛ<1.
a) Does this production function satisfy all the neoclassical properties? Discuss
the meaning of each property intuitively and mathematically.
t
Imagine that parents invest in the human capital of their children up to the point
where the marginal product of physical capital, Kt, is equal to the marginal
product of human capital, Ht.
b) What is the relation between Kt and Ht? Use this relation to write down total
output as a function of Kt only.
Q3(b) in order to make output a function of K alone, after establishing that H
and K are proportional, should we also establish H=h*L to remove L from the
equation? Or are we treating L and H as independent variables like we did for
the previous PSET and question 3(a) above.
Transcribed Image Text:Consider the production function modelled by the following equation: Y₁ = AK₁-α(BH₂)ªL₹ where Kt is capital, Ht is human capital, Lt is the number of workers, B is a scalar larger than 0, A is the (constant) level of technology, 0 < a <1 and 0 <ɛ<1. a) Does this production function satisfy all the neoclassical properties? Discuss the meaning of each property intuitively and mathematically. t Imagine that parents invest in the human capital of their children up to the point where the marginal product of physical capital, Kt, is equal to the marginal product of human capital, Ht. b) What is the relation between Kt and Ht? Use this relation to write down total output as a function of Kt only. Q3(b) in order to make output a function of K alone, after establishing that H and K are proportional, should we also establish H=h*L to remove L from the equation? Or are we treating L and H as independent variables like we did for the previous PSET and question 3(a) above.
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