Question

How is the price and output of a commodity determined under perfect competition? Explain.
OR
Calculate Marginal Propensity to Consume and Average Propensity to Consume from the following data:
Income (Rupees)): 50, 100, 150
Consumption (Rupees): 60, 100, 120

Hint:

For perfect competition, remember: Industry is the price-maker, Firm is the price-taker. For MPC/APC calculations, always set up a table to keep your calculations organized and avoid errors.

Answer 1

Step 1: Understanding Perfect Competition:
Under perfect competition, there are a very large number of buyers and sellers of a homogeneous product. No single buyer or seller can influence the market price. Therefore, the industry is the price-maker, and the individual firm is the price-taker.

Step 2: Price Determination by the Industry:
The market price is determined by the collective forces of market demand and market supply. \begin{itemize} \item Market Demand: The total quantity of a commodity demanded by all consumers at different prices. The market demand curve is downward sloping. \item Market Supply: The total quantity of a commodity supplied by all firms at different prices. The market supply curve is upward sloping. \end{itemize} The equilibrium price is established at the point where market demand equals market supply.

Step 3: Output Determination by the Firm:
The individual firm has to accept the equilibrium price determined by the industry. At this price, the firm can sell any quantity it wants. Hence, the demand curve for the firm is a horizontal line parallel to the X-axis (perfectly elastic). For a perfectly competitive firm, Price (P) = Average Revenue (AR) = Marginal Revenue (MR).
The firm's objective is to maximize profit. A firm is in equilibrium (and maximizes its profit) when two conditions are met: \begin{enumerate} \item Marginal Revenue (MR) = Marginal Cost (MC). \item The MC curve must cut the MR curve from below. \end{enumerate}

Step 4: Explanation with Diagram:
\[\begin{array}{cc} \hline Industry & Firm \\ \begin{tikzpicture}[scale=0.7] \draw[->] (0,0) -- (5,0) node[below] {Quantity}; \draw[->] (0,0) -- (0,5) node[left] {Price}; \draw[thick, color=blue] (1,4) -- (4,1) node[right] {DD}; \draw[thick, color=green] (1,1) -- (4,4) node[right] {SS}; \draw[dashed] (2.5, 2.5) -- (2.5, 0) node[below] {$Q_e$}; \draw[dashed] (2.5, 2.5) -- (0, 2.5) node[left] {$P_e$}; \fill (2.5,2.5) circle (2.5pt) node[right]{E}; \end{tikzpicture} \\ \hline \begin{tikzpicture}[scale=0.7] \draw[->] (0,0) -- (5,0) node[below] {Output}; \draw[->] (0,0) -- (0,5) node[left] {Price, Cost, Revenue}; \draw[thick, color=red] (0, 2.5) -- (5, 2.5) node[right] {P = AR = MR}; \draw[thick, color=purple] (1,4) .. controls (2,1) and (3,1.2) .. (4,4) node[above] {MC}; \draw[dashed] (3.3, 2.5) -- (3.3, 0) node[below] {$q_e$}; \fill (3.3,2.5) circle (2.5pt) node[above]{e}; \end{tikzpicture} \end{array}\]In the left panel (Industry), the equilibrium price \(P_e\) is determined at point E, where the demand curve DD and supply curve SS intersect. In the right panel (Firm), the firm takes this price \(P_e\) as given. The firm produces \(q_e\) output, where its MC curve cuts the MR curve at point 'e', thus maximizing its profit.

Solution (Calculation of MPC and APC):

Step 1: Understanding the Concepts and Formulas:
\begin{itemize} \item Average Propensity to Consume (APC): The ratio of total consumption (C) to total income (Y). It shows the proportion of income that is consumed. \[ APC = \frac{C}{Y} \] \item Marginal Propensity to Consume (MPC): The ratio of the change in consumption (\(\Delta C\)) to the change in income (\(\Delta Y\)). It shows the proportion of additional income that is consumed. \[ MPC = \frac{\Delta C}{\Delta Y} \] \end{itemize}

Step 2: Organizing the Data and Calculations:
We will create a table to calculate the required values from the given data.\[\begin{array}{cc} \hline Industry & Firm \\ \begin{tikzpicture}[scale=0.7] \draw[->] (0,0) -- (5,0) node[below] {Quantity}; \draw[->] (0,0) -- (0,5) node[left] {Price}; \draw[thick, color=blue] (1,4) -- (4,1) node[right] {DD}; \draw[thick, color=green] (1,1) -- (4,4) node[right] {SS}; \draw[dashed] (2.5, 2.5) -- (2.5, 0) node[below] {$Q_e$}; \draw[dashed] (2.5, 2.5) -- (0, 2.5) node[left] {$P_e$}; \fill (2.5,2.5) circle (2.5pt) node[right]{E}; \end{tikzpicture} \\ \hline \begin{tikzpicture}[scale=0.7] \draw[->] (0,0) -- (5,0) node[below] {Output}; \draw[->] (0,0) -- (0,5) node[left] {Price, Cost, Revenue}; \draw[thick, color=red] (0, 2.5) -- (5, 2.5) node[right] {P = AR = MR}; \draw[thick, color=purple] (1,4) .. controls (2,1) and (3,1.2) .. (4,4) node[above] {MC}; \draw[dashed] (3.3, 2.5) -- (3.3, 0) node[below] {$q_e$}; \fill (3.3,2.5) circle (2.5pt) node[above]{e}; \end{tikzpicture} \end{array}\]

Step 3: Final Answer:
The calculated values are as follows: \begin{itemize} \item Average Propensity to Consume (APC): \begin{itemize} \item At an income of Rupees 50, APC is 1.20. \item At an income of Rupees 100, APC is 1.00. \item At an income of Rupees 150, APC is 0.80. \end{itemize} \item Marginal Propensity to Consume (MPC): \begin{itemize} \item When income increases from Rupees 50 to Rupees100, MPC is 0.80. \item When income increases from Rupees 100 to Rupees150, MPC is 0.40. \end{itemize} \end{itemize}