Question

Determine whether the following production functions exhibit increasing, decreasing or constant returns to scale. a. Q...

Determine whether the following production functions exhibit increasing, decreasing or constant returns to scale.

a. Q = L + K

b. Q = 10KL

c. Q = L + K1/2L 1/2 + K

d. Q = 10K1/4L 1/4

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Homework Answers

Answer #1

a.
Q=L+K
mQ=m(L)+m(K)
mQ=m(L+K)
Constant returns to scale.
Since the value of m is same now
b.
Q=10KL
mQ=10(mK)(mL)
mQ=10m^(1+1)(LK)
mQ=m^2(10KL)
Increasing returns to scale.
Since the value of m is higher now
c.
Q = L + K1/2L1/2 + K
mQ=(mL)+(mK^0.5)(mL^0.5) +(mK)
mQ=m(L+K)+m(K^0.5L^0.5)
mQ=m(L + K1/2L1/2 + K)
Constant returns to scale
Since value of m is same now
d.
Q = 10K1/4L 1/4
mQ=10*(mK^0.25)(mL^0.25)
mQ=10m^0.5(K1/4L1/4)
Decreasing returns to scale
Since the value of m is lower now

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