Ujawa Conditions Analysis for Production Functions
This question asks to identify the condition that is NOT considered necessary for a well-behaved production function according to Hirofumi Ujawa.
Evaluating Potential Conditions
Let's examine the common requirements for production functions and how they relate to the options provided:
- Continuously Differentiable: Production functions are typically assumed to be continuously differentiable. This property is essential for using calculus-based methods to analyze marginal productivity and optimize economic decisions.
-
Zero Output at Zero Input: The condition that $f(x) = 0$ when $x = 0$ represents the basic principle that if no inputs are utilized, no output is produced. This is a fundamental requirement. Mathematically, this is expressed as:
$f(0) = 0$
-
Negative Second Derivative: For a production function with a single input, $f(x)$, the condition $f''(x) < 0$ signifies diminishing marginal returns. This assumption is standard in many economic models, suggesting that adding more of one input, holding others constant, eventually yields smaller increases in output. Mathematically:
$f''(x) < 0$
Identifying the Non-Required Condition
Based on standard economic assumptions and the structure of the question implying only one option is incorrect:
- Conditions 1 (Continuously Differentiable) and 2 ($f(0) = 0$) are fundamental requirements.
- Condition 3 (Negative Second Derivative) relates directly to the common assumption of diminishing marginal returns, often linked to concavity.
- Condition 4 (The function is concave) is a broader property that encompasses diminishing marginal returns.
Given the provided answer, the requirement that the function must be concave is identified as the condition *not* imposed by Ujawa in this context.
Conclusion: While concavity is a common assumption, it is presented here as the factor that is *not* required by Ujawa's conditions for a well-behaved production function.
Correct Answer: Option D: The function is concave
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 :
