CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
The demand law for a product is p = 49 − x², where p is the price in ₹ and x is the quantity demanded. If the market price is ₹40, the consumer's surplus is:
Consumer's surplus is 18. It equals the integral of the demand function from 0 to 3 minus the amount actually spent. The integral is 147 − 9 = 138, and expenditure is 3 × 40 = 120, so the surplus is 138 − 120 = 18.
- A₹138
- B₹27
- C₹120
- D₹18Correct
Explanation
At p = 40, x² = 9, so x = 3. The integral of (49 − x²) from 0 to 3 is 147 − 9 = 138. Subtract the amount spent, 3 × 40 = 120, to get 18. The value 138 forgets to subtract expenditure, and 27 forgets the x³/3 term.
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