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.Q3(b) in order to make output a function of K alone, after establishing that Hand K are proportional, should we also establish H=h*L to remove L from theequation? Or are we treating L and H as independent variables like we did forthe previous PSET and question 3(a) above.

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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

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

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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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.
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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In 1928, Charles Cobb and Paul Douglas published a study in which they modeled the growth of the US economy during the period 1899 to 1922. The function used to model production was of the form: (1) P(L, K) = 6LªK!-a where P is total production (monetary value of goods produced in the year); L, the amount of work (total number of person-hours worked in a year); and K, the amount of capital invested (monetary value of machinery, equipment and buildings). In these terms, the hypotheses made by Cobb and Douglas can be stated as follows: (i) If either labor or capital cancel each other out, so does production. (ii) The marginal productivity of labor is proportional to the amount of output per unit of work. (iii) The marginal productivity of capital is proportional to the amount of production per unit of сapital. 1. The output per unit of work is (a) Tick the alternative that, for some constant a, describes the hypothesis (ii) = aP·L. = a. P () aL L P = a. (b) If we keep K constant, K = K0,…
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