Answer to Question #193982 in Microeconomics for Henderson

Question

The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components:

 (a) GH¢10 million for the land

(b) GH¢1/4 million per floor

(c) Specialized costs of GH¢10000x per floor.

 How many floors should the office complex contain if the average cost per floor is to be minimized?

Answer 1

4. Average cost per floor ATC is minimized if

$ATC = MC.$

$\frac{1}{4}=0.25$

$ATC = \frac{TC}{x }=\frac{ (10 + 0.25x)}{x }=\frac {10}{x }+0.25$

$MC = TC'(x) = 0.25$

$\frac{10}{x} + 0.25 = 0.25$

$\frac{10}{x} = 0.$

There is no root, so, there is no point, at which ATC is minimized.