Question

Draw a demand curve whose price elasticity of demand \( e = 1 \).

Hint:

In unitary elasticity (\( e = 1 \)), the total revenue remains constant when the price changes, as the percentage change in price is exactly offset by the percentage change in quantity demanded.

Answer 1

The price elasticity of demand (\( e \)) measures the responsiveness of quantity demanded to a change in the price of a good. When the price elasticity of demand is equal to 1, it is known as unitary elastic demand. In this case, a change in price leads to an equal proportional change in quantity demanded.

Step 1: Characteristics of Unit Elastic Demand.
For unitary elasticity (\( e = 1 \)), the percentage change in quantity demanded is exactly equal to the percentage change in price. The demand curve for unitary elasticity is a rectangular hyperbola.

Step 2: Graph of Unit Elastic Demand.
The graph of the demand curve with unitary elasticity is shown below.
\begin{center} \begin{tikzpicture} \begin{axis}[ axis lines = middle, xlabel = {Price (P)}, ylabel = {Quantity Demanded (Q)}, domain=0.1:10, samples=100, width=10cm, height=8cm, enlargelimits=true, xtick=\empty, ytick=\empty, grid=major ] \addplot [ thick, blue ] {1/x}; % This is the equation for the rectangular hyperbola for unitary elasticity. \end{axis} \end{tikzpicture} \end{center} This curve represents the situation where any percentage change in price results in an equal percentage change in quantity demanded, leading to a constant total revenue across different price levels.