Question

. The demand equation faced by DuMont Electronics for its personal computers is given by P == 10,000 – 4Q.

(a) At what price and quantity will total revenue be maximized?

Answer 1

The price is maximized when the marginal revenue is equal to zero.

Therefore the first step is to compute the total revenue:

$\text{Total revenue=Price * Quantity}$

$\text{Total revenue} = (10,000 – 4Q)Q$

$\text{Total revenue} = 10,000Q – 4Q^2$

Find the marginal revenue from the total revenue function:

$\text{Marginal revenue} = 10,000 – 8Q$

Equate the marginal revenue function to be equals to zero:

$10,000 – 8Q=0$

$10,000 = 8Q$

$Q=\dfrac{10,000}{8}=1,250$

The revenue maximizing quantity is 1,250 units.

To get the revenue maximizing price substitute the revenue maximizing quantity to the demand function provided:

$P =10,000 – 4Q.$

$P =10,000 – 4\times 1,250$

$P=5,000$

The revenue maximizing price is $5,000.