Question 12.18: What total revenue will a firm earn if it charges a price of......

As we have established that the integral of this form of MR function will not have a constant of integration then

TR = \int MR dq = \int (960 − 0.15q²)dq = 960q − 0.05q³

In this example we need to use the TR function to find the price. Since TR = pq then p = TR/q and so

p =  \frac{1}{q} (960q − 0.05q³) = 960 − 0.05q²
0.05q² = 960 − p
q² = 19,200 − 20p
q = (19,200 − 20p) ^{0.5}

When p = 715 then

q = (19,200 − 14,300) ^{0.5} = 4,900 ^{0.5} = 70

and so total revenue will be

TR = pq = 715(70) = £50,050

If both MC and MR functions are specified then one can use integration to work out what the actual profit is at any given output, provided that TFC is specified.