Calculus in Economics

Question

The cost, in dollars, of producing x units of a certain item is given by

C(x)= 5x − 4sqrt(x-4).

 

Find the production level that minimizes the average cost per unit.

 

 

The number of units that minimizes the average cost is ____________.

Answer 1

Joaquin

Average cost per unit = C(x) / x = 5 - 4 √ (x-4) / x

If you plot this function, you will see that for x>4, it is strictly increasing.

So the cost per unit will be minimum when x=4.

(Another way is to solve D'(x) =0 when D(x) = C(x)/x. There will be no solution for this as it is strictly increasing, so that means the minimum value must be at the left end of the interval ie at x=4).

Mike