3 Consider the production function of candles, with capital (K) and labour (L) as inputs:Qc = K0.1 L0.93.1 Show that both additional labour and additional capital increase production at a decreasingrate by computing and referring to some of the second derivatives of Qe.3.2 Now consider the production function of an additional product, electrical generators, de-fined by the following function: Qeg =K0.6 L0.4. Show, using the Jacobian derivativematrix of Qe and Qeg, how increasing capital by 10 units and decreasing labour by 5 units,would approximately change production of both goods. Start from an initial combinationof K = 100 and L = 50.3.3 Suppose that demand for capital and labour are in turn determined by the interest rate125,2r and wages paid to workers w, as follows: K =_8w and L =10r3Use the Jacobianderivative matrix of Qe and Qeg to calculate how production changes in response to anaQ.arincrease in interest rates:when r = 2 and w = 1000.

Since you have asked multiple questions, we will solve the first question for you. If you want any…

3 Consider the production function of candles, with capital (K) and labour (L) as inputs: Qe = Kº.1 L0.9_ 3.1 Show that both additional labour and additional capital increase production at a decreasing rate by computing and referring to some of the second derivatives of Qe.

3 Consider the production function of candles, with capital (K) and labour (L) as inputs: Qe = Kº.1 L0.9_ 3.1 Show that both additional labour and additional capital increase production at a decreasing rate by computing and referring to some of the second derivatives of Qe.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

3 Consider the production function of candles, with capital (K) and labour (L) as inputs:
Qc = K0.1 L0.9
3.1 Show that both additional labour and additional capital increase production at a decreasing
rate by computing and referring to some of the second derivatives of Qe.
3.2 Now consider the production function of an additional product, electrical generators, de-
fined by the following function: Qeg =
K0.6 L0.4. Show, using the Jacobian derivative
matrix of Qe and Qeg, how increasing capital by 10 units and decreasing labour by 5 units,
would approximately change production of both goods. Start from an initial combination
of K = 100 and L = 50.
3.3 Suppose that demand for capital and labour are in turn determined by the interest rate
125,2
r and wages paid to workers w, as follows: K =
_8w and L =
10r3
Use the Jacobian
derivative matrix of Qe and Qeg to calculate how production changes in response to an
aQ.
ar
increase in interest rates:
when r = 2 and w = 1000.

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