Question

A firm demand function for its output is p=400-0.5q. To maximize sales revenue,what price should be charged

Answer 1

Given the general form of Demand Function: P = f(Q),

Then the general form of Inverse Demand Function is: O = f^-1(P)

 Demand Curve: $P = 400 - 0.5 Q$

Driving Inverse Demand Curve:

$0.5 Q = 400 - P\\ Q =\frac{ (400 - P ) }{ 0.5}\\ Q = 400 / 0.5 - P / 0.5$

Inverse Demand Curve: Q = 800 - 2P

We can see that at Price $200, the total revenue is maximized at TR = $80,000

=> To maximize sales revenue, firm should charge price of $200