Match the items of List - I with the items of List - II and find out the correct matching. Codes : (a) (b) (c)List - I List - II Production functions Name of the shapes of returns to scale (a) \(Q = 10.2\ K^{0.19}\ L^{0.88}\) (i) Constant Returns to scale (b) \(Q = 1.01\ L^{0.75}\ K^{0.25}\) (ii) Diminishing Returns to scale (c) \(Q = 0.84\ L^{0.63}\ K^{0.3}\) (iii) Increasing Returns to scale
(iii) (i) (ii)
For a Cobb–Douglas function \(Q = A K^{\alpha} L^{\beta}\), returns to scale depend on \(\alpha + \beta\): greater than 1 means increasing, equal to 1 constant, less than 1 diminishing returns to scale.
(a) \(0.19 + 0.88 = 1.07\) > 1, so (a) shows increasing returns to scale – (iii).
(b) \(0.75 + 0.25 = 1.00\) = 1, so (b) shows constant returns to scale – (i).
(c) \(0.63 + 0.3 = 0.93\) < 1, so (c) shows diminishing returns to scale – (ii).
The matching of the three production functions is therefore (a) – (iii), (b) – (i), (c) – (ii).
Hence, the answer is (iii) (i) (ii).
Similar Questions
Statement (A) : The isoquant curves are drawn convex to the origin due to diminishing technical rate of substitution.
Statement (B) : The lesser the convexity of the isoquant curve the greater the possibility of the complementarity of the two inputs.
Codes :
Important Questions from Production Function
- Match the stages of production with their corresponding characteristics :
(i) Stage-I (a) Total product declines, Marginal product is negative (ii) Stage-II (b) Total product increases at an increasing rate, marginal product positive (iii) Stage-III (c) Total product increases at a diminishing rate, marginal product is zero. - Neo-classical production function has which of the following characteristics ?
(a) Positive and diminishing marginal productivities of the factors
(b) Constant returns to scale
(c) Satisfies Inada conditions
Choose the correct answer from the code below : - Which one of the following is not an Hirofumi Ujawa condition for a well behaved production function ?
- Exponents of the Cobb-Douglas production represent :
- Given the production function $Q = 2 \cdot K^{1/3} \cdot L^{2/3}$, find the output level when 8 units of capital and 27 units of labour are used.
