Question

The Average Cost function is given by AC=1200-128Q+4Q².

a) Find the values of Q at which AC is zero. Hence explain why this AC function is always positive.

b) Find the minimum AC & the value of Q at which this occurs. Use it to make a sketch of the AC curve.

Answer 1

Solution1 Average cost is basically per unit cost, which can be obtain by diving quantity to total cost.

· AC = TC/ Q

As the total cost never be equal to zero because there always be some fixed cost in production, so average cost will never be equal to zero and it never touches any axis, hence it remains positive. So, we can conclude that Average cost never be equal zero and it will never be negative number because of positive effect of fixed cost.

(So, technically its vague to find the value of output when AC is zero)

Solution2. In order to find the minimum value of AC, where AC = MC, we have to first differentiate the equation

· AC^` = 8Q – 128

Let set AC^` = 0

· Q = 16

Let do double differentiation to check whether it is minimum or not

· AC^`` = 8 ……….. which is greater than 0, hence it is minimum

AC = 1200 – 128(16) + 4(16)²

AC = 176