ECO 301: Intermediate Microeconomics
Marco A Castaneda
Homework 4: Answers
1.
ANSWER
For the production function F(K,L) = 2K + L, we have the marginal products of
labor and capital are
MP
L
= 1
and
MP
K
= 2
The marginal rate of technical substitution is
2
1
MP
MP
MRTS
K
L
LK
=
=
This implies the isoquants are linear. Graphically, the solution to this problem is
as follows:
Y
Isoquants:
MP
L
/MP
K
= 1/2
w
L
/w
K
= 1/3
Isocost lines (b):
Isocost lines (a):
w
L
/w
K
= 2/3
10
5
X
5
10
15
20
a)
In this situation, we have
L
L
K
K
w
MP
10
1
15
2
w
MP
=
>
=
This means the marginal output per dollar is always greater for capital than it
is for labor. Therefore, only capital should be used in the production process.
The optimal quantity of capital can then be determined by the equation
q = 2K
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View Full DocumentTherefore, we have
q
w
K
w
L
K*
L*
C
10
15
10
5
0
75
20
15
10
10
0
150
b)
In this situation, we have
L
L
K
K
w
MP
5
1
15
2
w
MP
=
<
=
This means the marginal output per dollar is always greater for labor than it is
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 Spring '08
 Castaneda
 Microeconomics, wk, MPl, L*, wL L*

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