A firm uses only two inputs to produce its output. These inputs are perfect substitutes. Is it true that this firm must have the constant return to scale? If it is true, show the proof. If not, show a counter example.
True
General form of perfect substitute preferences
Q = aL + bK
a,b : Constant
Then MRTS = MPL/MPK = a/b
Then for all t > 1
Q(tL, tK) = atL + btK
= t*(aL + bK)
Q(tL, tK) = t*Q(L,K)
so it exhibits CRS
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