Question

What is the conditional demand function for an input? What is the unconditional demand function for an input? How do they differ in what they assume? How do they differ in their right-hand side variables?

Answer 1

Conditional input demand function for an input is function of output & all input prices.

Thus these demand function are conditional or dependent on level of output.

It shows the cost minimising level of input , to be used in production of a given level of output, for given input price level

unconditional input demand function, shows the profit maximizing level of inputs to be used in production process, based on the price level of output & the input prices.

Thus these don't depend on output level, hence unconditional demand functions..

Bcoz output level in the firms profit maximization problem is already optimized and this optimized output is itself a function of the prices - input & output, that are taken as given.

. In contrast, the cost minimization problem is being solved for a given output level which is not necessarily the optimized one that firm will eventually choose.

so conditional demand functions are arrived at via cost minimization .

while unconditional demand functions result via profit maximization

the two differ mainly in their assumption about y, for conditional, the output level is assumed to be given , no such assumption for unconditional.

Difference in right side variables.

For unconditional, only input prices & output

For conditional , only input & output prices