CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
The marginal revenue of a firm is MR = 100 − 4x (in ₹), where x is the number of units sold, and revenue is zero when nothing is sold. What is the demand (price) function p?
The demand function is p = 100 − 2x. Integrating marginal revenue gives R = 100x − 2x², with the constant zero because revenue is nil at zero sales. Dividing revenue by quantity x gives the price, 100 − 2x.
- Ap = 100 − 2xCorrect
- Bp = 100 − 4x
- Cp = 100x − 2x²
- Dp = 100 − x
Explanation
R(x) = ∫(100 − 4x)dx = 100x − 2x² + K, and R(0) = 0 gives K = 0. Price p = R/x = 100 − 2x. The option 100x − 2x² is the revenue function, not the price.
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