Explanations:In economics, the relationship between the price of a good and the quantity demanded is often inverse. This means that as the price of a good increases, the quantity demanded decreases, and vice versa. This relationship is a fundamental principle in demand theory and is often represented by a demand curve, which typically slopes downward from left to right.
To understand the specific scenario presented in the question, let's consider the concept of price elasticity of demand. 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 case, we are given a 25% increase in the price of chips and need to determine the corresponding decrease in the quantity demanded to maintain the same expenditure.
Let's denote the initial price of chips as \( P \) and the initial quantity demanded as \( Q \). The initial expenditure is \( P \times Q \). After the price increase, the new price is \( 1.25P \). Let the new quantity demanded be \( Q' \). The new expenditure is \( 1.25P \times Q' \). To maintain the same expenditure, we set the initial expenditure equal to the new expenditure:
\[
P \times Q = 1.25P \times Q'
\]
Dividing both sides by \( P \) and simplifying, we get:
\[
Q = 1.25Q'
\]
Solving for \( Q' \), we find:
\[
Q' = \frac{Q}{1.25} = \frac{Q}{\frac{5}{4}} = \frac{4Q}{5} = 0.8Q
\]
This means the new quantity demanded is 80% of the initial quantity demanded. Therefore, the quantity demanded decreases by 20% (since \( 100\% - 80\% = 20\% \)).
The inverse relationship between price and quantity demanded is a key concept in microeconomics and is essential for understanding how changes in price affect consumer behavior. This relationship is often used in various economic models and analyses, particularly in the context of supply and demand.