Statement - II : In a hypothetical production function of the following form
Q = $− L^{3} + 15 L^{2} + 10 L$
Where, Q = Quantity of the product and L = No. of variable input (labour), the marginal physical productivity of labour is $− L^{2} + 15 L + 10$.
Code :
Statement I Analysis: Optimal Input Combination
Statement I concerns the condition for achieving an optimal input combination, typically referring to the least-cost method for production or profit maximization. This condition requires that the ratio of the marginal revenue product (MRP) of each input to its price must be equal across all inputs.
Mathematically, for two inputs like labour (L) and capital (K) with prices $P_L$ and $P_K$ respectively, and marginal revenue products $MRP_L$ and $MRP_K$, the condition is:
$ \frac{MRP_L}{P_L} = \frac{MRP_K}{P_K} $This equation can be rearranged to state that the ratio of the marginal revenue products equals the ratio of their prices:
$ \frac{MRP_L}{MRP_K} = \frac{P_L}{P_K} $Statement I correctly states that the "marginal revenue productivity ratio of the two inputs should be equal to their price ratio." Therefore, Statement I is true.
Statement II Analysis: Marginal Physical Productivity Calculation
Statement II provides a specific production function and claims a formula for the marginal physical productivity (MPP) of labour (L).
The given production function is:
$ Q = -L^3 + 15L^2 + 10L $Where $Q$ is the quantity of the product and $L$ is the number of variable input (labour).
The marginal physical productivity of labour ($MPP_L$) is found by taking the derivative of the total product ($Q$) with respect to labour ($L$):
$ MPP_L = \frac{dQ}{dL} $Calculating the derivative:
$ \frac{dQ}{dL} = \frac{d}{dL}(-L^3 + 15L^2 + 10L) $ $ \frac{dQ}{dL} = -3L^2 + (15 \times 2)L + 10 $ $ MPP_L = -3L^2 + 30L + 10 $The statement claims the MPP is $-L^2 + 15L + 10$. Comparing the calculated MPP ($−3L^2 + 30L + 10$) with the one stated in the question ($−L^2 + 15L + 10$), they are different.
Therefore, Statement II is false.
Conclusion
Based on the analysis, Statement I is true and Statement II is false.
Important Questions from Production Function
What is constant along an isoquant?
During the first stage of a total product curve, the total product is ______
Match List I with List II
LIST I
(Production Cost)
LIST II
(Underlying Meaning)
A.
Implicit Costs
I.
Change in the total cost per unit change in output.
B.
Marginal cost
II
Total increase in costs resulting from the implementation of a particular managerial decision.
C.
Incremental Cost
III.
Inputed value of inputs owned and used by the firm.
D.
Sunk Cost
IV.
The costs that are not affected by managerial decision.
Choose the correct answer from the options given below:
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 :
