Question

A monopolist's demand function is `x = 60 - p/5`. At what level of output will marginal revenue be zero?

Answer 1

Demand function, `x = 60 - p/5`   ...(i)

Total revenue function, R(x) = px

= 5(60 – x)x   ...[From (i)]    

= 5x(60 – x)

= 300x – 5x²

Then, MR = `d/dx(R(x))`

= `d/dx(300x - 5x^2)`

= 300 – 10x

Put MR = 0

`\implies` 300 – 10x = 0

`\implies` 10x = 300

`\implies` x = 30

Hence, the value of output is 30.