Question

The demand and supply functions under the pure market competition are pd = 56 − x² and ps = 8 + x²/3 respectively, where p is the price and x is the quantity of the commodity. Using integrals find Producer’s surplus.

Answer 1

p_d = p_s

⟹ 56 − x² = 8 + \(\frac{x^2}{3}\)

⟹ 4/3 x² = 48

⟹ x² = 36

⟹ x = 6 , -6 ; since x can’t be –ve, so x = 6

When x₀ = 6 ; p₀ = 20

Hence, Producer’s surplus = p₀x₀ − \(∫^6_0\) p_sdx

= 6 × 20 − \(∫^6_0\) (8 + \(\frac{x^2}{3}\) ) dx

= 120 – [48 + 24]

= 48 units