Provide solutions only to part d and e, but you may need to refer previous questions for solutions 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.Following Solow and Swan, assume there is no government and no net exports,that the depreciation rate of capital is the constant 8 > 0 and the savings rate isconstant 0 < s < 1.d) Derive the fundamental equation of Solow-Swan. How does the growth rate ofcapital depend on employment per person, It? Explain intuitively.e) Does the equation of the growth rate of capital depend on the growth rate ofpopulation, n, or the growth rate of employment? Explain intuitively.

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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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.3P

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