The short-run production function for a firm is as follows : Q = – L³ + 15L² + 10L Where Q denotes total output in physical units and L denotes units of labour which are homogeneous, but are not perfectly divisible and change in labour does not tend to become zero. Statement I : In this production function, the marginal product of 5th unit of labour is 85. Statement II : Similarly, in this production function, the average product of the 5th unit of labour is 60. Codes :
To analyze the given statements, let's first understand the problem by calculating the marginal and average products for the given production function:
The production function is given by:
\(Q = -L^3 + 15L^2 + 10L\)
We need to find:
- Marginal Product (MP) at L = 5:
- The Marginal Product is the derivative of the production function with respect to L, i.e. the change in output due to a one-unit change in labor.
- Differentiating the production function: \(\frac{dQ}{dL} = \frac{d(-L^3 + 15L^2 + 10L)}{dL}\)
- Calculating the derivative gives: \(MP = -3L^2 + 30L + 10\)
- Substituting L = 5, we get: \(MP = -3(5)^2 + 30(5) + 10 = -75 + 150 + 10 = 85\)
- Therefore, the 5th unit's marginal product is 85, which makes Statement I true.
- Average Product (AP) at L = 5:
- The Average Product is the output per unit of labor, calculated by dividing the total output by L.
- At L = 5, compute the total output Q: \(Q = -(5)^3 + 15(5)^2 + 10(5)\)
- Simplifying: \(Q = -125 + 375 + 50 = 300\)
- Average Product: \(AP = \frac{Q}{L} = \frac{300}{5} = 60\)
- Therefore, the average product per unit of the 5th unit of labor is 60, which makes Statement II true.
Conclusion: According to the above calculations:
- Statement I is true because the marginal product of the 5th unit of labor is indeed 85.
- Statement II is true because the average product of the 5th unit of labor is indeed 60.
However, the provided correct answer is "Statement I is false, but Statement II is true," which doesn't align with our calculations. Upon re-evaluation, if the provided solution is believed to be incorrect, the alternative solution provided matches our calculation results.
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 :
