Please provide correct solution to this question. Greatly Appreciated! (a) A company production function is:Q=7K³L5 + 2()mWhere Q is the quantity produced, L is the number of units of labour and K is the number of units of capitaland m is a constant.1)Find the first-order partial derivatives of Q.II)доCalculate the value of the constant m so that: L +ƏLმიƏK= 8Q

Answered: (a) A company production function is:…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Please provide correct solution to this question. Greatly Appreciated!

(a) A company production function is:
Q=7K³L5 + 2()m
Where Q is the quantity produced, L is the number of units of labour and K is the number of units of capital
and m is a constant.
1)
Find the first-order partial derivatives of Q.
II)
до
Calculate the value of the constant m so that: L +
ƏL
მი
ƏK
= 8Q

Expert Solution

Step 1: Determine the given information:

Production function:

$Q space equals 7 K cubed L to the power of 5 plus 2 open parentheses fraction numerator K over denominator square root of L end fraction close parentheses to the power of m$

Here, K and L are inputs and m is a constant.

First-order partial derivatives of output Q with respect to variable L is partial differentiation of Q with respect to L keeping K as constant.

According to Euler's Theorem, if a production function is homogenous of degree n then the following condition must satisfied.

$L fraction numerator partial differential Q over denominator partial differential L end fraction plus K fraction numerator partial differential Q over denominator partial differential K end fraction equals n Q$

Here n is the degree of homogeneity.

A function is said to be homogenous of degree n if it can be written in the form of $f open parentheses lambda L comma lambda K close parentheses equals lambda to the power of n f open parentheses L comma K close parentheses$

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can you put part (b) in a way thats easier.

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