Question

Consider the cost function of Bamburi Cement Ltd given by Total cost (TC) = 4q2(squared)+ 16. Find the variable cost, fixed cost, average cost, average variable cost, average
fixed cost and the marginal cost for Bamburi Cement Ltd. ( 10 marks)

Answer 1

We are given $TC = 4q^2 + 16$

Variable Cost (VC):

Variable costs are costs that vary with the level of output. Hence, they are deduced from the TC function by isolating the component affected by output (q).

$\therefore \space VC = 4q^2$

Fixed Costs (FC):

Fixed costs are costs not affected by level of production. They are constant at all production levels. Fixed costs are, thus, the independent component of the total cost.

$\therefore \space FC = 16$

Average Cost (AC):

$AC = \dfrac {TC}{q}$

$= \dfrac {4q^2 + 16}{q}$

$= 4q +\dfrac {16}{q}$

Average Variable Cost (AVC)

$AVC = \dfrac {VC}{q}$

$= \dfrac {4q^2}{q}$

$= 4q$

Average Fixed Cost (AFC):

$AFC = \dfrac {FC}{q}$

$= \dfrac {16}{q}$

Marginal Cost (MC):

$MC = \dfrac {d}{dq}(TC)$

$= \dfrac {d}{dq}(4q^2 + 16)$

$= 8q$