Explanation: In economics, the relationship between the price of a good and the quantity demanded is described by the law of demand. This law states that, all else being equal, as the price of a good increases, the quantity demanded decreases, and vice versa. This inverse relationship is a fundamental principle in microeconomics and is often illustrated using demand curves.
The concept of price elasticity of demand quantifies this relationship. Price elasticity of demand measures the responsiveness of the quantity demanded to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. In this problem, we are given a specific scenario where the price of an article increases by 50%, and we need to determine the corresponding decrease in quantity demanded.
To solve this problem, we can use the concept of expenditure, which is the product of price and quantity. If the expenditure remains constant, then the increase in price must be offset by a decrease in quantity demanded. Mathematically, this can be expressed as:
\[ \text{Initial Expenditure} = \text{Final Expenditure} \]
Let the initial price be \( P \) and the initial quantity be \( Q \). The initial expenditure is \( P \times Q \).
After the price increase, the new price is \( 1.5P \) (a 50% increase). Let the new quantity be \( Q' \). The final expenditure is \( 1.5P \times Q' \).
Since the expenditure remains constant:
\[ P \times Q = 1.5P \times Q' \]
Solving for \( Q' \):
\[ Q' = \frac{P \times Q}{1.5P} = \frac{Q}{1.5} = \frac{2}{3}Q \]
The new quantity \( Q' \) is \(\frac{2}{3}\) of the initial quantity \( Q \). This means the quantity demanded has decreased by:
\[ Q - Q' = Q - \frac{2}{3}Q = \frac{1}{3}Q \]
The percentage decrease in quantity demanded is:
\[ \frac{\frac{1}{3}Q}{Q} \times 100\% = \frac{1}{3} \times 100\% = 33.33\% \]
Therefore, when the price of an article increases by 50%, the quantity demanded decreases by 33.33% to maintain the balance of expenditure. This is the correct answer, and it aligns with the principles of price elasticity and the inverse relationship between price and quantity demanded.