Question

Find the marginal and average revenue functions associated with the demand function P= -0.3Q + 221

Answer 1

Answer:

Marginal revenue = R'(Q) = -0.6 Q + 221

Average revenue = -0.3 Q + 221

Step-by-step explanation:

As per the question,

Functions associated with the demand function P= -0.3 Q + 221, where Q is the demand.

Now,

As we know that the,

Marginal revenue is the derivative of the revenue function, R(x), which is equals the number of items sold,

Therefore,

R(Q) = Q × ( -0.3Q + 221) = -0.3 Q² + 221 Q

∴ Marginal revenue = R'(Q) = -0.6 Q + 221

Now,

Average revenue (AR) is defined as the ratio of the total revenue by the number of units sold that is revenue per unit of output sold.

$Average\ revenue\ = \frac{Total\ revenue}{number\ of\ units\ sold}$

Where Total Revenue (TR) equals quantity of output multiplied by price per unit.

TR = Price (P) × Total output (Q) = (-0.3Q + 221) × Q = -0.3 Q² + 221 Q

$Average\ revenue\ = \frac{TR}{Q}$

$Average\ revenue\ = \frac{-0.3Q^{2}+221Q}{Q}$

∴ Average revenue = -0.3Q + 221