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:

In a linear production function, the input coefficient is both the MPP and the slope.

Answer 1

The Correct Option is D

In the given linear production function, Y = 10 + 0.6X, the coefficient of the input variable X (fertilizer) represents the change in output (Y) for a one-unit change in input. This is the definition of Marginal Physical Product (MPP). In a linear function, this coefficient also represents the slope of the function when graphed.

Answer 2

Treat \( Y = 10 + 0.6X \) as a function and differentiate it with respect to \( X \): \[ \frac{dY}{dX} = 0.6 \] By definition, the marginal physical product (MPP) of an input is exactly this derivative, the rate of change of output per additional unit of input, so the coefficient 0.6 is the MPP. Since the function is linear, this same derivative is also, by definition, the slope of the line when \( Y \) is plotted against \( X \). Elasticity of production, in contrast, equals \( \frac{dY}{dX}\cdot\frac{X}{Y} \), a ratio that changes with \( X \) and \( Y \) and is not simply 0.6; average physical product (APP) equals \( \frac{Y}{X} = \frac{10}{X}+0.6 \), which likewise varies with \( X \). So only MPP and Slope match the constant coefficient 0.6, confirming (A) and (B) only, option (4).