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WELLESLEY COLLEGE
DEPARTMENT OF ECONOMICS
ECONOMICS 20103
JOHNSON
Problem
Set
#5
(due IN LECTURE Friday, October 24
th
)
1.
You are given the following production function for watches:
q
=
KL
 .8K
2
 .2L
2
Where
q
represents total watches produced,
K
represents units of capital
input, and L represents units of labor input.
a.
Suppose that
K = 10.
Graph the total product of labor curve and the average
product of labor curve.
Can these be on the same graph?
Why or why not?
What value of L maximizes the average product of labor?
How many watches
are produced at that point?
b.
Stay with
K = 10.
Graph the MP
L
curve.
At what point does the MP
L
= 0?
Put the AP
L
from (a) and the MP
L
on the same graph.
[Why can they be on the
same graph?].
Where do they intersect and why?
c.
Suppose
K jumps to 20.
How would your answers to (a) and (b) change?
d.
Does watch production exhibit CRS, IRS, or DRS?
Explain.
2.
Economists use a concept called the elasticity of substitution to describe how
quickly the MRTS changes (if at all) as we move around a given isoquant (thus
as we change the capital/labor ratio in producing the given amount of output on
the isoquant).
That elasticity is given by the following expression:
σ
=
%
∆
( K / L )
/
%
∆
MRTS
Or, equivalently:
σ
=
∂ ln ( K / L )
/
∂ ln MRTS
Calculate this elasticity of substitution for the following production functions.
Comment on whether the value of this elasticity implies that K and L are easily
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 Fall '08
 JOHNSON
 Economics

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