Question

If the marginal revenue function for a commodity is MR = 9 – 4x². Find the demand function.

Answer 1

Marginal Revenue function MR = 9 – 4x²

Revenue function R = ${\displaystyle \int \text{MR} \text{d}x}$

R = ${\displaystyle \int (9-4x^2) \text{d}x}$

R = ${\displaystyle 9x-4\left(\frac{x^3}{3}\right)+\text{k}}$

When x = 0

R = 0

⇒ k = 0

∴ R = ${\displaystyle 9x-\frac{4x^3}{3}}$

⇒ px = ${\displaystyle 9x-\frac{4x^3}{3}}$  .......${\displaystyle (\text{p}=\frac{4x^2}{x})}$

p = ${\displaystyle \frac{(9x-\frac{4x^3}{3})}{x}}$

= ${\displaystyle 9-\frac{4x^3}{3}}$

∴Demand function = ${\displaystyle 9-\frac{4x^2}{3}}$