Could you please help with 3.2 and 3.3. 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 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: QegK0.6 L0.4. Show, using the Jacobian derivativematrix of Q. 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 rater and wages paid to workers w, as follows: K8wand L125r2Use the Jacobian10r3derivative matrix of Qc and Q to calculate how production changes in response to anegincrease in interest rates:when r= 2 and w = 1000.aQegar

The production function is the mathematical expression of the technological relationship between…

3 Consider the production function of candles, with capital (K) and labour (L) as inputs: Qc = K0.1L0.9 .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 Qc. .2 Now consider the production function of an additional product, electrical generators, de- fined by the following function: Qeg K0.6L0.4 Show, using the Jacobian derivative matrix of Qc 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 Suppose that demand for capital and labour are in turn determined by the interest rate r and wages paid to workers w, as follows: K Use the Jacobian derivative matrix of Qc and Qeg to calculate how production changes in response to an 8w 10r3 and L= 125r² vw. increase in interest rates: ƏQc Ər ƏQeg Ər when r = 2 and w = 1000. =

3 Consider the production function of candles, with capital (K) and labour (L) as inputs: Qc = K0.1L0.9 .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 Qc. .2 Now consider the production function of an additional product, electrical generators, de- fined by the following function: Qeg K0.6L0.4 Show, using the Jacobian derivative matrix of Qc 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 Suppose that demand for capital and labour are in turn determined by the interest rate r and wages paid to workers w, as follows: K Use the Jacobian derivative matrix of Qc and Qeg to calculate how production changes in response to an 8w 10r3 and L= 125r² vw. increase in interest rates: ƏQc Ər ƏQeg Ər when r = 2 and w = 1000. =

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

Could you please help with 3.2 and 3.3.

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 Q. 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
r and wages paid to workers w, as follows: K
8w
and L
125r2
Use the Jacobian
10r3
derivative matrix of Qc and Q to calculate how production changes in response to an
eg
increase in interest rates:
when r
= 2 and w = 1000.
aQeg
ar

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