If the supply function for a commodity is \( p=3+x^3 \). Then the producer's surplus, if 10 units of the goods are sold, is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 7,500
At \( x_0=10 \), the market price is
\( \displaystyle p_0=3+10^3=1003 \)
Producer's surplus is the revenue received minus the area under the supply curve:
\( \displaystyle PS=p_0x_0-\int_{0}^{x_0}S(x)\,dx \)
\( \displaystyle =1003\times 10-\int_{0}^{10}(3+x^3)\,dx \)
The integral is
\( \displaystyle \int_{0}^{10}(3+x^3)\,dx=\left[3x+\frac{x^4}{4}\right]_{0}^{10} \)
\( \displaystyle =30+2500=2530 \)
So
\( \displaystyle PS=10030-2530=7500 \)
CBSE Applied Mathematics (Class XII):
Producers Surplus
