provide solution only to part c of the question. 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 scalarlarger 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? Discussthe meaning of each property intuitively and mathematically.tImagine that parents invest in the human capital of their children up to the pointwhere the marginal product of physical capital, Kt, is equal to the marginalproduct of human capital, Ht.b) What is the relation between Kt and Ht? Use this relation to write down totaloutput as a function of Kt only.In this economy, we will relax the assumption that every person is in the labourforce. Thus, the number of people, Nt, is different from the number of workers(some people do not work). Let It = Lt/Nt be the number of workers per capita(the fraction of the population that works). Let yt = Yt/Nt be output per capitaand kt = Kt/Nt be capital per capita. Finally, let n be the rate of population growthand YL be the growth rate of labour.c) Using the "effective production function" you derived in (b), write down outputper capita, yt, as a function of capital per capita, kt, labour per capita, lt, the levelof population Nt, and the level of technology, A.

a) Neoclassical Properties Analysis:1. Positive Output Elasticity: The production function exhibits…

c) Using the "effective production function" you derived in (b), write down output per capita, yt, as a function of capital per capita, kt, labour per capita, lt, the level of population Nt, and the level of technology, A.

c) Using the "effective production function" you derived in (b), write down output per capita, yt, as a function of capital per capita, kt, labour per capita, lt, the level of population Nt, and the level of technology, A.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

provide solution only to part c of the question.

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.
In this economy, we will relax the assumption that every person is in the labour
force. Thus, the number of people, Nt, is different from the number of workers
(some people do not work). Let It = Lt/Nt be the number of workers per capita
(the fraction of the population that works). Let yt = Yt/Nt be output per capita
and kt = Kt/Nt be capital per capita. Finally, let n be the rate of population growth
and YL be the growth rate of labour.
c) Using the "effective production function" you derived in (b), write down output
per capita, yt, as a function of capital per capita, kt, labour per capita, lt, the level
of population Nt, and the level of technology, A.

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