Statement (I): The elasticity of factor substitution is formally defined as the percentage change in the capital-labour ratio divided by the percentage change in the marginal rate of technical substitution. Statement (II): \(Q = K^{0.5} L^{0.3}\) is a production function where Q = output, K = units of capital and L = units of labour. This production function shows the application of increasing returns to scale. Codes:
Statement (I) is correct while statement (II) is incorrect.
This is a two-statement question, one testing a definition from production theory and the other a returns-to-scale calculation, so each is judged separately.
Statement (I) is correct. The elasticity of factor substitution measures how easily one input can be substituted for another along an isoquant as their relative prices change. It is formally defined as the percentage change in the capital-labour ratio (K/L) divided by the percentage change in the marginal rate of technical substitution (MRTS). A high value means the factors substitute easily; a low value means they are used in nearly fixed proportions.
Statement (II) is incorrect. For a Cobb-Douglas production function \(Q = K^{a}L^{b}\), the nature of returns to scale is decided by the sum of the exponents: if \(a+b>1\) there are increasing returns, if \(a+b=1\) constant returns, and if \(a+b<1\) decreasing returns. Here \(a+b = 0.5 + 0.3 = 0.8 < 1\), so the function shows decreasing returns to scale, not increasing returns as the statement claims.
So Statement (I) is correct while Statement (II) is incorrect.
Hence the correct code is that Statement (I) is correct while Statement (II) is incorrect.
Similar Questions
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 :
It costs a firm ₹ 90 per unit to produce product A, and ₹ 60 per unit to produce B individually. If the firm can produce both products together at ₹ 160 per unit of product A and B, this exhibits signs of:
Managerial economics is concerned with which combination of the following ?
(a) Investment Analysis and Decisions
(b) Production Behaviour and Cost Analysis
(c) Input Reward Analysis and Decisions
(d) Economic Environment Analysis
Code :
When P0 and P1 and Q0 and Q1 denote before and after change in the price and quantity respectively and in both the situations, total outlay remains the same, which of the following formulae give the similar value of the arc price - elasticity of demand ?
(a) \(\dfrac{Q_{0}-Q_{1}}{P_{0}-P_{1}}\times\dfrac{P_{0}+P_{1}}{Q_{0}+Q_{1}}\)
(b) \(\dfrac{Q_{0}-Q_{1}}{P_{0}-P_{1}}\times\dfrac{P_{0}}{Q_{1}}\)
(c) \(\dfrac{Q_{0}-Q_{1}}{P_{0}-P_{1}}\times\dfrac{P_{0}}{Q_{0}}\)
(d) \(\dfrac{Q_{0}-Q_{1}}{P_{0}-P_{1}}\times\dfrac{P_{1}}{Q_{1}}\)
(e) \(\dfrac{Q_{0}-Q_{1}}{P_{0}-P_{1}}\times\dfrac{P_{1}}{Q_{0}}\)
Code :
In case the producer's equilibrium shifts to a higher isoquant due to decrease in price of an input, the curve combining the successive equilibrium positions is known as :
Which one of the following statements is not correct ?
For the following two statements of Assertion (A) and Reasoning (R), indicate the correct code :
Assertion (A) : Ridge Lines in isoquant map set the limits for the positive productivities of the respective inputs used in the production process.
Reasoning (R) : Isoquants will slope positively if the use of an input is increased beyond the limit set by the ridge lines.
Code :
If a 100% scale-efficient plant has 92% technical efficiency and 88.5% allocative-efficiency, then its overall efficiency will be :
Law of Diminishing Return applies when the gaps among the successive ‘multiple-level of output’ isoquants:
Production function is not based on the assumption of the:
Important Questions from Production Function
For the following two statements of Assertion (A) and Reasoning (R) suggest the correct code:
Assertion (A): Low initial price regarded as the principal means for entering into mass market for some new products.
Reasoning (R): Firms generally enter into production of new products with excess capacity of the plant initially.
Code:
Indicate the correct code from the following types of the long run average cost curves on which the minimum average cost of production in long run can be determined:
(i) Long run average cost curve under normal production function
(ii) Long run average cost curve under linearly homogeneous production function
(iii) Planning curve
(iv) Envelope curve
Choose the correct answer from the code given below :
Which of the following is not an attribute of production function?
Which of the following is an example of non-durable goods?
What is constant along an isoquant?
