Question

For a given production function: Y = 10 + 0.6X (Where Y is wheat output and X is fertilizer input), the coefficient 0.6 is called as: 
• [(A).] MPP 
• [(B).] Slope 
• [(C).] Elasticity of production 
• [(D).] APP 
Choose the correct answer from the options given below: 
 

• (C) only.
• (D) only.
• (C) and (D) only.
• (A) and (B) only.

Hint:

For any linear production function (\(Y = a + bX\)):
- The MPP is constant and always equals the coefficient \(\mathbf{b}\).
- The Slope is constant and also equals \(\mathbf{b}\).
- This represents a production system showing constant marginal returns.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
A production function describes the technical and mathematical relationship between inputs (such as fertilizer) and outputs (such as wheat yield).
Analyzing the algebraic properties of this function allows us to determine productivity indicators like marginal and average products.
Key Formula or Approach:
For a linear production function of the form:
\[ Y = a + bX \] - The derivative of \( Y \) with respect to \( X \) represents the Marginal Physical Product (MPP):
\[ \text{MPP} = \frac{dY}{dX} = b \] - In coordinate geometry, the coefficient \( b \) represents the slope of the line (\( m \) in \( y = mx + c \)).

Step 2: Detailed Explanation:
Let us apply these formulas to the given production function:
\[ Y = 10 + 0.6X \] 1. Marginal Physical Product (MPP) - (A): Taking the first derivative of the output (\(Y\)) with respect to the input (\(X\)):
\[ \text{MPP} = \frac{dY}{dX} = \frac{d}{dX}(10 + 0.6X) = 0.6 \] This indicates that each additional unit of fertilizer input (\(X\)) increases the wheat output (\(Y\)) by a constant rate of 0.6 units. Thus, 0.6 represents the MPP.
2. Slope of the Function - (B): In a linear equation, the coefficient of the independent variable (\(X\)) represents the slope of the line.
Here, the slope is:
\[ \text{Slope} = \frac{\Delta Y}{\Delta X} = 0.6 \] Thus, 0.6 represents the slope of the production function.
3. Let us evaluate the other choices:
- Elasticity of Production (\(e_p\)) is calculated as:
\[ e_p = \frac{\text{MPP}}{\text{APP}} = \frac{0.6}{\text{APP}} \] Because APP changes as input \(X\) changes, the elasticity of production is not constant and does not equal 0.6.
- Average Physical Product (APP) is calculated as:
\[ \text{APP} = \frac{Y}{X} = \frac{10}{X} + 0.6 \] This also varies with \(X\), so APP does not equal 0.6.
Therefore, the coefficient 0.6 represents both the MPP and the Slope of the function.

Step 3: Final Answer:
The coefficient 0.6 is called the MPP and the Slope, matching Option (D).