A monopolist faces the inverse demand curve p = 120

Question

A monopolist faces the inverse demand curve p = 120 - 6q.At what level of output is his total revenue maximized?
A)20
B)5
C)20.
D)15
E)10

Quizplus · Accepted Answer

Total revenue (TR) is maximized where marginal revenue (MR) equals zero. The inverse demand curve is given by $p = 120 - 6q$. Total revenue is $TR = p \times q = (120 - 6q)q = 120q - 6q^2$. To find MR, differentiate TR with respect to q: $MR = \frac{d(TR)}{dq} = 120 - 12q$. Setting MR = 0 to maximize TR, we get $0 = 120 - 12q$, which simplifies to $q = 10$.