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here were gonna look at contingent demand for inputs or a long-run conditional demand for inputs and this will be under the case of fix proportions production functions so here is a fixed proportions production function where output Q is the minimum of a times units of labor or B times units of capital fixed proportions production function means that output will occur at the vertex or kink of the isoquant this means that Q will equal a times L which will equal B times K the first thing we want to do is we want to solve for L and K so if Q equals a times L L is given by this expression and if Q equals B times K K is given by this expression step 2 total cost equals are the rental rate of capital times units of capital plus the wage times units of labour what were gonna do now is do some substitution for Al were gonna plug in Q divided by a and for K were gonna plug in Q divided by B so down here shows the result after making those substitutions the final step step 3 after making our