Question

A monopolist faces the inverse demand curve p = 120 - 6q. At what level of output is his total revenue maximized?

1. 20

2. 5

3. 20

4. 15

5. 10

Answer 1

The inverse demand function is given as:

p = 120 - 6q

The total revenue is equal to the product of price and quantity. So,

TR = pq = (120 - 6q)(q)

TR = 120q - 6q²

To find the critical point, putting the first derivative of total revenue function equal to zero:

d(TR)/dq = 120 - 12q = 0

12q = 120

q = 10

Calculating the second derivative of the total revenue function:

d²(TR)/dq² = -12 < 0

Since the value of the second derivative is less than zero, the total revenue is maximum when 10 units are produced. So, the correct answer is 'Option E'.