1 a.
1  b & c)
Equation for APL = Q/H = 100*H
2/3
MPL is less than APL for all values of H.
2 a)
MPL = 3K
1/2
L
1/4
, so as L increases for some fixed value of K, the denominator is getting larger, so the
total expression is getting smaller.
Similar proof for MPK.
2 b)
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Total Product
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APL
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View Full DocumentMRTS =  MPL / MPK = (3/2) * (K/L)
2 c)
Let q =f(K,L) = 4K
1/2
L
3/4
The definition of IRS is that f(z*K,z*L)>z*f(K,L) for some z >1.
Let, K
’
=z*K and L
’
=z*L. Therefore, q
’
= f(z*K,z*L) = 4K
’
1/2
L
’
3/4
.
Rewriting q
’
leaves us with: q
’
= 4K
’
1/2
L
’
3/4
= 4(z*K)
1/2
(z*L)
3/4
= z
1.25
4K
1/2
L
3/4
= z
1.25
q.
Therefore, q
’
= z
1.25
q.
But since z>1 that means that z
1.25
> z. But this means q
’
= z
1.25
q > z*q.
This is just
saying that f(z*K,z*L)>z*f(K,L), which is the definition for IRS.
3)
False.
MRTS = MPL / MPK.
If MPL is constant, then MPK must also be constant otherwise the MRTS will
also change.
Similarly, if MPK is constant, then MPL must also be constant otherwise the MRTS will also
change.
Perfect substitutes require that MRTS will always be constant, no matter what choice of inputs
is used. Therefore, if only one of the marginal products is constant, it is not necessary that there are
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 Spring '09
 danbrown
 Economics, Microeconomics, Equals sign, tc, MPl

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