Please can I get some explanations on this question. Especially when ln was added to find the elasticity. What is the elasticity of substitution, o, of the CES production function below?dPq = (alº + bK°)Assume d and p are positive constants and 0 Solving foras a function of the absolute value of the marginal rate of technical substitution, MRTS,1(MRTS) )K(Properly format your expression using the tools in the palette.)%DLaTaking the log of both sides,1InIn+ In|MRTS|Substituting this in for Inand taking the derivative,din(K/L)O =din MRTS|1Ina+ In MRTS|din MRTS|11 -

Elasticity is defined as the degree or measure of the change in a variable due to fluctuation in…

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What is the elasticity of substitution, o, of the CES production function below? q = (alº + bk°) P Assume d and p are positive constants and 0

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Please can I get some explanations on this question. Especially when ln was added to find the elasticity.

What is the elasticity of substitution, o, of the CES production function below?
d
P
q = (alº + bK°)
Assume d and p are positive constants and 0<a<1 and 0<b<1. Also assume capital is measured on the vertical axis and labor on the
horizontal axis.
The elasticity of substitution is the percentage change in the capital-labor ratio divided by the percentage change in the MRTS:
d(K/L)
K/L
d(K/L) MRTS
%D
DMRTS
DMRTS K/L
MRTS
The elasticity of substitution can be written as a logarithmic derivative:
din(K/L)
din|MRTS| '
which is possible because din(K/L) = d(K/L)/ (K/L) and din|MRTS| = d|MRTS|/MRTS.
The marginal rate of technical substitution (MRTS) as a function of Labor (L) and capital (K) is
p-1
a
MRTS =
E. (Properly format your expression using the tools in the palette. Hover over tools to see keyboard

Solving for
as a function of the absolute value of the marginal rate of technical substitution, MRTS,
1
(MRTS) )
K
(Properly format your expression using the tools in the palette.)
%D
L
a
Taking the log of both sides,
1
In
In
+ In|MRTS|
Substituting this in for In
and taking the derivative,
din(K/L)
O =
din MRTS|
1
In
a
+ In MRTS|
din MRTS|
1
1 -

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