Question

Based on a consulting economist’s report, the total cost function for Advance Electronics,
Inc. is
TC = 200 + 5Q –0.04Q2 + 0.001Q3
P.R. Swensen, president of the company, determines that knowing only this equation is
inadequate for decision-making. You have been directed to do the following:
i) Determine the level of fixed cost (if any) and equation for average total cost, average
variable cost, and average fixed cost.ii) Determine the rate of output that results in minimum average variable cost.
iii) If fixed costs increase to $500, what output rate results in minimum average variable
cost?

Answer 1

i) Total cost is the sum of total fixed cost of Total variable cost.

TC = TFC+TVC

Fixed cost is not dependent on quantity product where as variable cost is the function of quantity produces.

TC=FC+VC

Fixed cost = 200

$\frac{TC}{Q} = \frac{200+5Q-0.04Q^2+0.001Q^3}{Q} \\ = \frac{200}{Q} + 5 -0.04Q + 0.001Q^2 \\ \frac{VC}{Q} = \frac{5Q-0.04Q^2 + 0.001Q^3}{Q} \\ = 5 -0.04Q + 0.001Q^2 \\ \frac{FC}{Q} = \frac{200}{Q}$

ii) To determine the rate of output that min AVC

$\frac{∂(AVC)}{∂Q^*} = 0 \; for\; optimum \;Q^* \\ \frac{∂(AVC)}{∂Q^*} = -0.04 + 0.002Q = 0 \\ 0.04 = 0.002Q \\ Q^* = \frac{0.04}{0.002} = 20$

iii) Minimum AVC will not change if FC increases to $500 as fixed cost is invariant of output rate.