CA Foundation · Business Economics · Theory of Production and Cost
For the production function Q = 4L^0.6 K^0.6 (a Cobb-Douglas form), what type of returns to scale does the firm experience when all inputs are increased in the same proportion?
The firm has increasing returns to scale. In a Cobb-Douglas function the sum of the exponents decides this, and 0.6 + 0.6 = 1.2, which is greater than 1. So output rises more than proportionately when all inputs are scaled up together.
- AConstant returns to scale
- BDecreasing returns to scale
- CIncreasing returns to scaleCorrect
- DReturns cannot be determined without input prices
Explanation
In a Cobb-Douglas function, returns to scale depend on the sum of the exponents. Here 0.6 + 0.6 = 1.2, which exceeds 1, so doubling inputs raises output by more than double (2^1.2 ≈ 2.3 times). Constant returns would need a sum of exactly 1. Input prices are irrelevant to returns to scale.
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