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.
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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:
$f(0) = 0$
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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
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?
- Match the stages of production with their corresponding characteristics :
(i) Stage-I (a) Total product declines, Marginal product is negative (ii) Stage-II (b) Total product increases at an increasing rate, marginal product positive (iii) Stage-III (c) Total product increases at a diminishing rate, marginal product is zero. - Neo-classical production function has which of the following characteristics ?
(a) Positive and diminishing marginal productivities of the factors
(b) Constant returns to scale
(c) Satisfies Inada conditions
Choose the correct answer from the code below :
