For the production function, Q = AL α Kβ A. The coefficient A shows managerial efficiency B. If α + β > 1, then the production function exhibits increasing returns to scale C. Marginal rate of technical substitution of L for K is given by βk/αL D. The marginal product of capital is given by βQ/K
A, B and D only
A is an efficiency/productivity parameter, and returns to scale depend on the sum of exponents: α + β > 1 implies increasing returns. Differentiation gives:
\(MP_L=\alpha Q/L,\quad MP_K=\beta Q/K,\quad MRTS_{LK}=\frac{\alpha K}{\beta L}.\)
Thus A,B,D are correct; C reverses the coefficient ratio.
Important Questions from Production Function - Teaching
Critical path indicates which one of the following?
Match the items of List - II with List - I ; and choose the correct code :
List - I
(Critical Control Standards)
List - II
(Critical Points
(a) Physical standards (i) Material cost per unit (b) Cost standards (ii) Labour hours per unit of output (c) Revenue standards (iii) Timing of production (d) Program standards (iv) Average sales per customer The relationship between rate of inputs of productive services and the rate of output is known as:
For the standard constant-returns Cobb–Douglas production function \(Q=AK^\alpha L^{1-\alpha}\), with \(A>0,\ K,L>0,\ 0<\alpha<1\), which statements are NOT properties?
A. Cobb‐Douglas production function is a homogeneous production function
B. Curves representing average and marginal productivity of inputs are not downward sloping
C. Marginal productivity of labour and capital in Cobb‐Douglas production function are functions of the capital‐labour ratio
D. Iso‐quants of Cobb‐Douglas production functions are positively sloped
Choose the correct answer from the options given below:
In the short‐run production function, which one of the following is CORRECT?
