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CMA Foundation · Fundamentals of Business Economics and Management · Theory of Production

A Nagpur firm's production uses labour L with Q = 12L - L^2 (capital fixed). Using marginal product as the derivative of Q with respect to L, at what number of workers does total product reach its maximum?

Total product is maximum at 6 workers. Marginal product is 12 minus 2L, which becomes zero at L equal to 6. Output there is 36 units, higher than 35 units at either 5 or 7 workers, so adding more labour beyond 6 reduces total output.

  1. A12 workers
  2. B3 workers
  3. C6 workersCorrect
  4. D4 workers

Explanation

MP = dQ/dL = 12 - 2L. Setting MP = 0 gives L = 6. Check: Q at 6 = 72 - 36 = 36, while Q at 5 = 35 and at 7 = 35, so 6 is the maximum. Choosing 12 is the point where Q returns to zero.

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