Answer to Question #171637 in Microeconomics for nadin

Question

if output is produced according to q=4l+6k the price of k is 12 and the price of l is 20 then the cost minimizing combination of k and l cable to produce 96 units of output is?

Answer 1

In this case we get the next equations:

q = 4l + 6k = 96,

TC = 20l + 12k = min.

Total cost is minimized when MPL/w = MPk/k.

MPL = q'(L) = 4,

MPK = q'(L) = 6.

So, 4/20 = 6/12, so the equation MPL/w = MPk/k can't be true in this case.

As Pk < Pl, then the cost is minimized, when only capital is used, so l = 0 and k = 96/6 = 16 units,

TC = 20×0 + 12×16 = 192.