Question

Revenue function ‘R’ and cost function ‘C’ are R = 14x – x² and C = x(x² – 2). Find the

1. average cost
2. marginal cost
3. average revenue and
4. marginal revenue.

Answer 1

R = 14x – x² and C = x(x² – 2)

C = x³ – 2x

(i) Average Cost (AC) = `"Total cost"/"Output" = ("C"(x))/x`

`= (x^3 - 2x)/x`

`= x^3/x - (2x)/x`

= x² – 2

(ii) Marginal Cost (MC) = `"dC"/"dx"`

`= "d"/"dx" (x^3 - 2x)`

`= "d"/"dx" (x^3) - 2 "d"/"dx" (x)`

= 3x² – 2

(iii) Average Revenue R = 14x – x²

Average Revenue (AR) =`"Total Revenue"/"Output" = ("R"(x))/x`

`= (14x - x^2)/x`

`= (14x)/x - x^2/x`

= 14 - x

(iv) Marginal Revenue (MR) = `"dR"/"dx"`

`= "d"/"dx" (14x - x^2)`

`= 14 "d"/"dx" (x) - "d"/"dx" (x^2)`

= 14(1) – 2x

= 14 – 2x