CA Foundation · Business Economics · Theory of Production and Cost
A production function is expressed as Q = 6L^0.5 K^0.5, where Q is output, L is labour and K is capital. If a firm in Rajkot uses 16 units of labour and 25 units of capital, what is the output?
Output is 120 units. Substituting L = 16 and K = 25 gives Q = 6 × 4 × 5 = 120, since the square root of 16 is 4 and the square root of 25 is 5. The constant 6 scales the product of those two values.
- A120Correct
- B240
- C60
- D132
Explanation
Q = 6 × √16 × √25 = 6 × 4 × 5 = 120. Check: √(16×25) = √400 = 20, and 6 × 20 = 120. The option 240 comes from wrongly multiplying by 2 (doubling the constant), and 60 comes from forgetting the constant 6.
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