Match the production functions of List-I with the return to scale in List-II: Indicate the correct answer:List-I (Production function) List-II (Return to scale) (a) \(Q = 10\,K^{0.5}L^{0.4}E^{0.15}M^{0.1}\) (i) increasing (b) \(Q = 12\,K^{0.5}L^{0.5}\) (ii) constant (c) \(Q = 100\,K + 15\,L\) (iii) decreasing (d) \(Q = 40\,K^{0.3}L^{0.5}\)
(a)-(i), (b)-(ii), (c)-(ii), (d)-(iii)
For a Cobb-Douglas production function the return to scale is judged by the sum of the exponents of the inputs: sum greater than 1 means increasing, equal to 1 means constant, and less than 1 means decreasing.
(a) The exponents sum to \(0.5 + 0.4 + 0.15 + 0.1 = 1.15 > 1\), so it shows increasing returns (i).
(b) The exponents sum to \(0.5 + 0.5 = 1.0\), so it shows constant returns (ii).
(c) \(Q = 100K + 15L\) is linear and homogeneous of degree one, so doubling both inputs doubles output - constant returns (ii).
(d) The exponents sum to \(0.3 + 0.5 = 0.8 < 1\), so it shows decreasing returns (iii).
Hence the correct match is (a)-(i), (b)-(ii), (c)-(ii), (d)-(iii).
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