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CA Foundation · Business Economics · Theory of Production and Cost

The total product of labour is given by TP = 12L + 6L² - L³, where L is the number of workers. At which number of workers does the marginal product (taken as the derivative dTP/dL) reach its maximum, and what is that maximum MP?

Marginal product is maximum at 2 workers and equals 24 units. Differentiating TP gives MP = 12 + 12L - 3L², and setting its slope 12 - 6L to zero gives L = 2. Substituting yields 12 + 24 - 12 = 24.

  1. AL = 2, MP = 24Correct
  2. BL = 3, MP = 21
  3. CL = 2, MP = 12
  4. DL = 4, MP = 12

Explanation

MP = dTP/dL = 12 + 12L - 3L². Its slope is 12 - 6L, which is zero at L = 2. Maximum MP = 12 + 24 - 12 = 24. Check: at L = 3, MP = 12 + 36 - 27 = 21, which is lower, and at L = 4, MP = 12 + 48 - 48 = 12, also lower.

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