Question

If P = 200 - 4Q, find the revenue-maximizing quantity.

Answer 1

Answer on Question #70349 - Economics - Microeconomics

Task: If $P = 200 - 4Q$, find the revenue-maximizing quantity.

Solution:

TR (total revenue) is defined as:

$$TR = PQ, \text{ so } TR = 200Q - 4Q^2$$

According to the theory, the necessary condition for any point of a function to be max is that $f(x) = 0$,

Hence the revenue-maximizing quantity is: $TR(q) = 0$.

$$TR(q) = (200Q - 4Q^2)' = 200 - 8Q = 0, \quad Q = 25$$

Answer: 25

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