CMA Foundation · Fundamentals of Business Economics and Management · Cost of Production
A firm has the total cost function TC = 200 + 10Q + 2Q². What is the marginal cost at Q = 5 using the derivative of TC?
Marginal cost at Q = 5 is ₹30. Differentiating TC = 200 + 10Q + 2Q² gives MC = 10 + 4Q, since the fixed cost of 200 drops out. Substituting Q = 5 gives 10 + 20, which equals ₹30.
- A₹20
- B₹30Correct
- C₹40
- D₹110
Explanation
MC = dTC/dQ = 10 + 4Q. At Q = 5, MC = 10 + 20 = ₹30. The value ₹20 results from using only 4Q and ignoring the 10. ₹40 results from using Q = 7.5 incorrectly or not applicable; ₹110 is average cost at Q=5 (550/5) hence a different measure.
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