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Question

Match the production functions List - I with the return to scale List - II.

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) \( Q = 40\,K^{0.3}L^{0.5} \)

Code :

This question was previously asked in
UGC NET 2015 Paper 1 Question Paper (27-Dec-2015)
The correct answer is

(a)-(i), (b)-(ii), (c)-(ii), (d)-(iii)

Option 4 — (a)-(i), (b)-(ii), (c)-(ii), (d)-(iii) is correct.

For a multiplicative (Cobb-Douglas) production function, the return to scale is judged by the sum of the exponents on the inputs. If the exponents add to more than 1, doubling all inputs more than doubles output (increasing returns); if they add to exactly 1, output doubles (constant returns); if they add to less than 1, output less than doubles (decreasing returns).

FunctionSum of exponentsReturns to scale
(a) 0.5+0.4+0.15+0.11.15 (>1)increasing (i)
(b) 0.5+0.51.0constant (ii)
(c) linear 100K+15Ldegree 1constant (ii)
(d) 0.3+0.50.8 (<1)decreasing (iii)

Function (c) is linear and homogeneous of degree one: scaling K and L by t scales Q by exactly t, so it too shows constant returns.

Takeaway: Add the input exponents — greater than, equal to, or less than one signals increasing, constant, or decreasing returns to scale.

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