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The producer's input demand function is derived from underlying demand for the commodity which he produces. The demand can be derived from the first order condition i.e. pf1 = r1 & pf2 = r2.
The demand functions are homogeneous of degree 0. For x1, the input demand curves are obtained as a function of r1, keeping r2 and p fixed.
x1 = φ (r1, r2, p)
Example:
Let q = x1x2 & c = r1x1 + r2x2
∴ f1 = δq/δx1 = x2, f2 = δq/δx2 = x1
∴ pf1 = px2, pf2 = px1
We know, pf1 = r1 & pf2 = r2
∴ px2 = r1, px1 = r2
∴ x1/x2 = r2/r1
and x1 = r2/p = f(p, r2)
The producer's input demand function is derived from underlying demand for the commodity which he produces. The demand can be derived from the first order condition i.e. pf1 = r1 & pf2 = r2.
The demand functions are homogeneous of degree 0. For x1, the input demand curves are obtained as a function of r1, keeping r2 and p fixed.
x1 = φ (r1, r2, p)
Example:
Let q = x1x2 & c = r1x1 + r2x2
∴ f1 = δq/δx1 = x2, f2 = δq/δx2 = x1
∴ pf1 = px2, pf2 = px1
We know, pf1 = r1 & pf2 = r2
∴ px2 = r1, px1 = r2
∴ x1/x2 = r2/r1
and x1 = r2/p = f(p, r2)
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