The management of Acrosonic plans to market the ElectroStat, an electrostatic speaker system. The marketing department has determined that the demand for these speakers is , where p denotes the speaker's unit price (in dollars) and x denotes the quantity demanded. Find the marginal revenue function .

Question

The management of Acrosonic plans to market the ElectroStat, an electrostatic speaker system. The marketing department has determined that the demand for these speakers is  , where p denotes the speaker's unit price (in dollars) and x denotes the quantity demanded. Find the marginal revenue function  .

Quizplus · Accepted Answer

The marginal revenue (MR) function is the derivative of the total revenue (TR) function.

Since the demand function is given as:
x = 110 - 2p

We can rewrite it as:
p = 55 - 0.5x

Therefore, the revenue function is:
TR = p*x
TR = (55 - 0.5x)*x
TR = 55x - 0.5x^2

Taking the derivative of TR with respect to x gives us the marginal revenue function:
MR = 55 - x

Substituting the demand function into this, we get:
MR = 55 - (110 - 2p)
MR = -55 + 2p

Simplifying this, we get:
MR = 2p - 55

Therefore, the correct answer is (B).

The Management of Acrosonic Plans to Market the ElectroStat, an Electrostatic