Question 12.16: If a firm spends £650 on fixed costs what is its total cost ......

We know that for any cost function

\int MC dq = TC

Therefore

\int (82 − 16q + 1.8q²)dq = TC
82q − 8q² + 0.6q³ + TFC = TC

We are told that TFC = 650 and so

TC = 650 + 82q − 8q² + 0.6q³

If one is given a firm’s marginal revenue function then one can integrate this to find the total revenue function. For example, if

MR = 360 − 2.5q
TR = \int MR dq = 360q − 1.25q² + C

When q is zero, TR must also be zero. Thus C = 0 and so

\int MR dq = 360q − 1.25q² = TR            (1)