Q.4
ICAR 2024Shift 1 MCQ (Single Correct) +4 −1
English हिन्दी

For a production function: $Y = 10 + 0.6X$ (Where $Y$ is wheat output and $X$ is fertilizer input), the coefficient 0.6 is called:

(A) . MPP
(B) . Slope
(C) . Elasticity of production
(D) . APP

Choose the correct answer from the options given below:

एक उत्पादन फलन के लिए: $Y = 10 + 0.6X$ (जहाँ $Y$ गेहूं का उत्पादन है और $X$ उर्वरक इनपुट है), गुणांक 0.6 कहलाता है:

(A) . सीमांत भौतिक उत्पाद (MPP)
(B) . ढाल (Slope)
(C) . उत्पादन की लोच (Elasticity of production)
(D) . औसत भौतिक उत्पाद (APP)
EXPLANATION Rural Financial Institutions: Cooperative Banks, Commercial Banks, RRBs, NABARD, Microfinance and KCC

Given the linear production function:

$$Y = 10 + 0.6X$$

The first derivative with respect to input $X$ is the slope of the production curve:

$$\text{Slope} = \frac{dY}{dX} = 0.6$$

By definition, Marginal Physical Product (MPP) is the rate of change of output with respect to input:

$$\text{MPP} = \frac{dY}{dX} = 0.6$$
Hence, the coefficient 0.6 represents both the Slope (B) and the Marginal Physical Product (MPP, A). Why (C) and (D) are not 0.6: Elasticity of production ($E_p$) = $\frac{dY}{dX} \times \frac{X}{Y} = 0.6 \times \frac{X}{10 + 0.6X} \neq 0.6$. Average Physical Product (APP) = $\frac{Y}{X} = \frac{10}{X} + 0.6 \neq 0.6$. Therefore, (A) and (B) only is the correct answer.

दिए गए रैखिक उत्पादन फलन:

$$Y = 10 + 0.6X$$

इनपुट $X$ के सापेक्ष प्रथम अवकलज (First derivative) उत्पादन वक्र की ढाल (Slope) को दर्शाता है:

$$\text{Slope} = \frac{dY}{dX} = 0.6$$

सीमांत भौतिक उत्पाद (MPP) की परिभाषा के अनुसार, यह इनपुट में परिवर्तन के सापेक्ष आउटपुट में परिवर्तन की दर है:

$$\text{MPP} = \frac{dY}{dX} = 0.6$$
अतः गुणांक 0.6 सीमांत भौतिक उत्पाद (MPP - A) और ढाल (Slope - B) दोनों को व्यक्त करता है। (C) और (D) क्यों नहीं हैं: उत्पादन की लोच ($E_p$) = $\frac{dY}{dX} \times \frac{X}{Y} = 0.6 \times \frac{X}{Y}$ (चर है, स्थिर 0.6 नहीं)। औसत भौतिक उत्पाद (APP) = $\frac{Y}{X} = \frac{10}{X} + 0.6$ (चर है)। अतः केवल (A) और (B) सही हैं।
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