Question

Explain the Law of Variable Proportions with the help of total product and marginal product curves.
OR
Explain the law of supply with the help of a supply schedule and supply curve.

Hint:

To remember the slopes: Demand curve is Downward sloping. Supply curve slopes upwards, like a Slide you climb up.

Answer 1

Step 1: Statement of the Law:
The Law of Variable Proportions (or the Law of Diminishing Marginal Returns) states that in the short run, when some factors of production are fixed and one factor is variable, as we increase the quantity of the variable factor, the Total Product (TP) initially increases at an increasing rate, then at a diminishing rate, and finally starts to decline. Consequently, the Marginal Product (MP) of the variable factor first increases, reaches a maximum, then falls, becomes zero, and finally becomes negative.

Step 2: Explanation of the Three Stages:
The law operates in three distinct stages: \begin{enumerate} \item Stage I: Increasing Returns to a Factor. In this stage, the Total Product (TP) increases at an increasing rate, and the Marginal Product (MP) of the variable factor increases. This is due to better utilization of the fixed factor and increased efficiency of the variable factor. \item Stage II: Diminishing Returns to a Factor. In this stage, the Total Product (TP) continues to increase but at a diminishing rate, and the Marginal Product (MP) falls but remains positive. This stage ends when TP is at its maximum and MP is zero. This is the rational stage of production for a firm. \item Stage III: Negative Returns to a Factor. In this stage, the Total Product (TP) starts to decline, and the Marginal Product (MP) becomes negative. This is because the quantity of the variable factor is too high in relation to the fixed factor, leading to overcrowding and inefficiency. \end{enumerate}

Step 3: Explanation with Diagram:
The relationship between TP and MP and the three stages can be shown with the help of the following diagram: \begin{center} \begin{tikzpicture}[scale=1] % Upper panel for TP \begin{scope}[yshift=4cm] \draw[->] (0,0) -- (8,0) node[right] {Units of Variable Factor}; \draw[->] (0,0) -- (0,4) node[above] {Total Product (TP)}; \draw[thick, color=blue] (0,0) .. controls (1,1) and (2,3.5) .. (2.5,3.8); % Increasing returns \draw[thick, color=blue] (2.5,3.8) .. controls (3.5,4.3) and (4.5,4.5) .. (5,4.5); % Diminishing returns \draw[thick, color=blue] (5,4.5) .. controls (5.5,4.4) and (6.5,4) .. (7,3.5); % Negative returns \node[above] at (3.5, 4.5) {TP}; \draw[dashed] (2.5, 3.8) -- (2.5, -2); \draw[dashed] (5, 4.5) -- (5, -2); \node at (1.25, -0.5) {Stage I}; \node at (3.75, -0.5) {Stage II}; \node at (6, -0.5) {Stage III}; \node at (2.5, 3.8) [circle,fill,inner sep=1pt]{}; \node at (5, 4.5) [circle,fill,inner sep=1pt]{}; \node[above] at (2.5,3.8) {Point of Inflection}; \node[above] at (5,4.5) {Max TP}; \end{scope} % Lower panel for MP \begin{scope}[yshift=0cm] \draw[->] (0,0) -- (8,0) node[right] {Units of Variable Factor}; \draw[->] (0,-1) -- (0,3) node[above] {Marginal Product (MP)}; \draw[thick, color=red] (0,0) .. controls (1.5,2.5) and (2,2.5) .. (2.5,2); \draw[thick, color=red] (2.5,2) .. controls (3.5,1) and (4,0.5) .. (5,0); \draw[thick, color=red] (5,0) .. controls (5.5,-0.2) and (6.5,-0.5) .. (7,-0.8); \node[above] at (3.5, 1.5) {MP}; \draw[dashed] (2.5, 2) -- (2.5, 2); \node at (2.5, 2) [circle,fill,inner sep=1pt]{}; \node at (5, 0) [circle,fill,inner sep=1pt]{}; \end{scope} \end{tikzpicture} \end{center}

Solution (Law of Supply):

Step 1: Statement of the Law:
The Law of Supply states that, other things being equal (ceteris paribus), there is a direct relationship between the price of a commodity and its quantity supplied. This means that as the price of a commodity increases, its quantity supplied by producers also increases, and as the price decreases, the quantity supplied also decreases. This is primarily due to the profit motive; a higher price makes it more profitable for firms to produce and sell more.

Step 2: Supply Schedule:
A supply schedule is a table that shows the quantity of a good that a producer is willing and able to supply at different prices over a given period of time. \begin{center} Supply Schedule for Good X\[\begin{array}{|c|c|} \hline Price per unit (Rupees) & Quantity Supplied (units) \\ \hline \text{10} & \text{100} \\ \hline \text{20} & \text{200} \\ \hline \text{30} & \text{300} \\ \hline \text{40} & \text{400} \\ \hline \end{array}\]The schedule clearly shows that as the price increases from Rupees10 to Rupees40, the quantity supplied increases from 100 to 400 units.

Step 3: Supply Curve:
A supply curve is a graphical representation of the supply schedule. It plots the relationship between price and quantity supplied. \begin{center} \begin{tikzpicture} \draw[->] (0,0) -- (5,0) node[right] {Quantity Supplied}; \draw[->] (0,0) -- (0,5) node[above] {Price}; \draw[thick, color=green] (1,1) -- (4,4) node[right] {SS (Supply Curve)}; \draw[dashed] (1,1) -- (1,0) node[below] {100}; \draw[dashed] (1,1) -- (0,1) node[left] {10}; \draw[dashed] (2,2) -- (2,0) node[below] {200}; \draw[dashed] (2,2) -- (0,2) node[left] {20}; \draw[dashed] (3,3) -- (3,0) node[below] {300}; \draw[dashed] (3,3) -- (0,3) node[left] {30}; \fill (1,1) circle (2pt); \fill (2,2) circle (2pt); \fill (3,3) circle (2pt); \fill (4,4) circle (2pt); \end{tikzpicture} \end{center} In the diagram, the supply curve SS slopes upwards from left to right, indicating the direct relationship between price and quantity supplied.

Step 4: Final Answer:
The Law of Supply describes a direct relationship between price and quantity supplied. This is demonstrated by a supply schedule, which shows higher quantities supplied at higher prices, and a corresponding upward-sloping supply curve.