CMA Foundation · Fundamentals of Business Economics and Management · Cost of Production
A firm's long-run total cost is LTC = 50Q - 8Q² + Q³ (Q in thousand units, cost in ₹ thousand). At what output does long-run average cost reach its minimum?
Minimum long-run average cost occurs at Q = 4 thousand units. Dividing LTC by Q gives LAC = 50 - 8Q + Q²; its derivative -8 + 2Q equals zero at Q = 4, and LAC is then ₹34 thousand, lower than at neighbouring outputs.
- AQ = 4Correct
- BQ = 8
- CQ = 6
- DQ = 3
Explanation
LAC = LTC/Q = 50 - 8Q + Q². Setting d(LAC)/dQ = -8 + 2Q = 0 gives Q = 4. The second derivative is 2, which is positive, so it is a minimum. Check: LAC at 4 = 50 - 32 + 16 = 34, and at 3 it is 35 and at 5 it is 35. Q = 8 results from wrongly using -8 + Q = 0.
Did you get it right without looking?
One question tells you little. A timed set on Cost of Production shows your real accuracy, how long you take and where you lose marks.
More Cost of Production questions
- The long-run average cost (LAC) curve is often described as an 'envelope curve'. This is because it:
- A factory produces 100 units at a total cost of ₹5,000 and 101 units at a total cost of ₹5,030. What is the marginal cost of the 101st unit?
- A firm has the total cost function TC = 200 + 10Q + 2Q². What is the marginal cost at Q = 5 using the derivative of TC?
- A firm's total fixed cost is ₹40,000 and its average variable cost is ₹12 per unit at every level of output. What is the average total cost …
- Which of the following is an example of an opportunity cost rather than an explicit accounting outlay for a firm that owns its factory build…
- Ramesh leaves a job paying ₹6,00,000 a year to run his own bakery, where he earns revenue of ₹9,00,000 and pays explicit costs of ₹5,50,000.…