Answer to Question #259402 in Microeconomics for Sansan Juliansyah

Question

If a firm's demand function is p=100-q,what quantities need to be sold to bring in a total revenue of

Answer 1

Complete Question

A firm faces the demand schedule q = 400 - 2p - p². What price does it need to charge to sell 100 units?

If a firm's demand function is P = 100 - q, what quantities need to be sold to bring in a total revenue of £100

Solution:

Q =400 – 2p – p²

Q = 100 units

100 = 400 – 2p – p²

P = 16.35

The firm needs to charge a price of 16.35 to sell 100 units.

Demand function: P = 100 – q

TR = P $\times$ Q

100 = (100 – q) q

100 = 100q – q²

100q – q² – 100 = 0

-q² + 100q – 100 = 0

Solve through quadratic equation:

Q = 98.99 units

The quantities needed to be sold to bring in total revenue of £100 = 98.99 units