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CA Foundation · Quantitative Aptitude · Differential and Integral Calculus

The marginal revenue of a firm is MR = 40 − 6x, where x is the number of units sold, and revenue is zero when nothing is sold. The revenue function R(x) and the demand (price) function p are respectively:

Revenue is R = 40x − 3x² and price is p = 40 − 3x. Integrating MR gives 40x − 3x², with the constant zero because revenue is nil at zero sales. Dividing revenue by x gives the demand function 40 − 3x.

  1. AR = 40x − 3x², p = 40 − 3xCorrect
  2. BR = 40x − 6x², p = 40 − 6x
  3. CR = 40x − 3x², p = 40 − 6x
  4. DR = 40x − 3x² + 6, p = 40 − 3x

Explanation

R = ∫(40 − 6x)dx = 40x − 3x² + K, and R(0) = 0 gives K = 0. Price p = R/x = 40 − 3x. Check: dR/dx = 40 − 6x, matching MR. The option with p = 40 − 6x confuses MR with price.

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