Question

Suppose the cost function is given as C = 135 + 75Q – 15Q2 + Q3. Prepare a cost schedule (table) showing the TFC, TVC, TC, AFC, AVC, MC, and ATC. Is this cost function a short run or a long run cost function? Why? Draw the cost curves on the basis of cost data obtained from the cost function.

Answer 1

TFC$=$ production which is not variable during short run. It remains fixed.

TFC$=$ TC$-$ TVC

$=$ 135

TVC $=$ cost that is variable. It changes with change in the quantity produced or change in output.

TVC$=$ TC$-$ TFC

$=$ 75Q$-$ 15Q$^{2}$ $+$ Q$^{3}$

TC$=$ is total cost that is related to production.

$=$ 135 $+$ 75Q $-$ 15Q$^{2}$ $+$ Q$^{3}$

AFC $=$ $\frac{TFC}{Q}$ It changes with change in quantity as the output changes but the fixed cost remains the same.

$=$ $\frac{135}{Q}$

AVC $=$ $\frac{TVC}{Q}$ It is the average of total variable cist and is U_shaped.

$($ 75$-$ 15Q $+$ Q$^{3}$ $/$ Q

$=$ 75$-$ Q $+$ Q$^{2}$

MC $=$ is additional cist incurred due to producing one extra unit of a product MC $=$ TC$_n$ $-$ TC$_{n-1}$

$=$ 75 $-$ 30Q $+$ 3Q$^2$

ATC $=$ is defined as to ta cost divided by total quantity.

ATC$=$ $\frac{TC}{Q}$ Or AVC $+$ AFC

$=$ $($ 135 $+$ 75Q $-$ 15Q$^2$ $+$ Q$^{3}$ $)$ $/$ Q

$=$ 135 $+$ 75 $-$ 15Q $+$ Q$^2$

Cost curves on the basis of cost data obtained from the cost function.

A short run cost function because there is some quantity of an input which remains fixed.

The cost curve will show a U shaped average cost and a sloping marginal cost as shown above