Question

The demand curve of a commodity is given by p = `(50 - x)/5`, find the marginal revenue for any output x and also find marginal revenue at x = 0 and x = 25?

Answer 1

Given that p = `(50 - x)/5`

Revenue, R = px

`= ((50 - x)/5)`x

`= (50x - x^2)/5`

`= 1/5` (50x – x²)

Marginal Revenue (MR) = `"d"/"dx"`(R)

= `"d"/"dx" 1/5 (50x - x^2)`

= `1/5 "d"/"dx" (50x - x^2)`

= `1/5 (50 - 2x)`

Marginal revenue when x = 0 is, MR = `1/5` (50 – 2 × 0)

`= 1/5 xx 50`

= 10

When x = 25, marginal revenue is MR = `1/5` (50 – 2 × 25)

`= 1/5 (50 - 50)`

= 0