Question

What is law of Variable Proportion ? How many stages of law of variable proportion are there ?

Hint:

The relationship between MP and AP is key to identifying the stages. Stage I ends where MP intersects AP at its highest point. Stage II ends where MP hits the x-axis (becomes zero).

Answer 1

Part 1: Law of Variable Proportions
The law of variable proportions, also known as the law of diminishing marginal product, is a short-run production concept. It states that if one factor of production (the variable factor, e.g., labor) is increased while all other factors (the fixed factors, e.g., capital and land) are held constant, then the total product (TP) will eventually increase at a diminishing rate and ultimately start to fall.
In other words, as the proportion of the variable factor to fixed factors is increased, the marginal product (MP) of the variable factor will eventually decline.
Part 2: Stages of the Law of Variable Proportions
There are three distinct stages in the law of variable proportions, which can be explained with the help of a diagram showing the relationship between Total Product (TP), Average Product (AP), and Marginal Product (MP). \begin{center} \begin{tikzpicture} \begin{axis}[ axis y line*=left, xlabel={Units of Variable Factor (Labor)}, ylabel={Total Product (TP)}, xmin=0, xmax=10, ymin=0, ymax=60, legend pos=outer north east, height=8cm, width=12cm ] \addplot[smooth, thick, blue, domain=0:8.5, samples=100] {20*x^2*exp(-0.5*x)}; \legend{TP} % Vertical lines for stages \draw[dashed, gray] (axis cs:2.7,0) -- (axis cs:2.7,48); \node at (axis cs:2.7, -5) {$L_1$}; \draw[dashed, gray] (axis cs:5.5,0) -- (axis cs:5.5,58); \node at (axis cs:5.5, -5) {$L_2$}; % Stage labels \node at (axis cs:1.35, 5) {Stage I}; \node at (axis cs:4.1, 5) {Stage II}; \node at (axis cs:7.5, 5) {Stage III}; \end{axis} \begin{axis}[ axis y line*=right, axis x line=none, ylabel={Average & Marginal Product (AP, MP)}, xmin=0, xmax=10, ymin=-10, ymax=40, legend style={at={(1.03,0.8)},anchor=west}, height=8cm, width=12cm ] \addplot[smooth, thick, red, domain=0:9, samples=100] {20*x*exp(-0.5*x)*(2-x)}; \addplot[smooth, thick, green, domain=0:9, samples=100] {20*x*exp(-0.5*x)}; \legend{MP, AP} \draw[dashed, gray] (axis cs:2.7,0) -- (axis cs:2.7,28); \draw[dashed, gray] (axis cs:5.5,0) -- (axis cs:5.5,15); \addplot[dashed,gray] coordinates {(0,0) (10,0)}; \end{axis} \end{tikzpicture} \end{center} \begin{itemize} \item Stage I: Stage of Increasing Returns (From origin to point L\(_1\)) \begin{itemize} \item TP increases at an increasing rate. \item MP increases, reaches its maximum, and then starts to decline. \item AP continuously increases and reaches its maximum at the end of this stage, where AP = MP. \item This stage ends when the average product is at its maximum. \end{itemize} \item Stage II: Stage of Diminishing Returns (From L\(_1\) to L\(_2\)) \begin{itemize} \item TP continues to increase, but at a diminishing rate, and it reaches its maximum at the end of this stage. \item MP continues to fall and becomes zero when TP is at its maximum. \item AP starts to fall but remains positive. \item A rational producer will always choose to operate in this stage, as it is the most efficient. \end{itemize} \item Stage III: Stage of Negative Returns (Beyond point L\(_2\)) \begin{itemize} \item TP starts to decline. \item MP becomes negative. \item AP continues to fall but remains positive. \item No rational producer would operate in this stage, as adding more variable input actually decreases the total output. \end{itemize} \end{itemize}