Skip to content
3.6 · Q6

Q.If the supply function is p=4−5x+x2p = 4 - 5x + x^2, find the producers' surplus when the price is 18.

Andaman Nicobar CbseNCERTSubjective· 3mImportance★★★★★
92% · 54/59 Questions
🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

At price p0=18p_0=18 the supply p=4−5x+x2p=4-5x+x^2 gives x0=7x_0=7; the producers' surplus is p0x0−∫07p dx=6376≈₹106.17p_0x_0-\int_0^{7}p\,dx=\dfrac{637}{6}\approx\text{₹}106.17.

Producers' surplus: PS=p0x0−∫0x0p dx\displaystyle PS=p_0x_0-\int_0^{x_0}p\,dx.

  1. Given supply p=4−5x+x2p=4-5x+x^2, p0=18p_0=18.
  2. Quantity supplied: 18=4−5x+x2⇒x2−5x−14=0⇒(x−7)(x+2)=0⇒x0=718=4-5x+x^2\Rightarrow x^2-5x-14=0\Rightarrow(x-7)(x+2)=0\Rightarrow x_0=7 (positive root). …

Unlock everything free for 14 days

  • Full step-by-step solutions
  • Concept-first explanations
  • Methods, shortcuts & mistakes
  • PYQ mapping + timed mock tests

Full access for 14 days. No credit card required.