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what is the conditional and unconditional input demand for a production firm with z = min...

what is the conditional and unconditional input demand for a production firm with
z = min ( q1/alpha, q2/beta)
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Answer #1

For conditional input demand function of this fixed proportion production function: -

Z = min (q1/alpha,q2/beta)

Here q1 and q2 are inputs and alpha and beta are constants.

Z = q1/alpha; q1 = Z*alpha

Z = q2/beta; q2 = Z*beta

Lets assume w1 and w2 are prices of factors q1 and q2 respectively.

Total Cost (TC) = w1*q1 + w2*q2 = w1*Z*alpha + w2*Z*beta

Conditional demand for q1 is partial derivative of Total cost with respect to w1

Conditional demand for q2

So Conditional demand of (q1,q2) = (Z*alpha, Z*beta)

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