Understanding Price Elasticity and Total Expenditure

This question asks about the relationship between price elasticity of demand and the total expenditure on a good when demand is price inelastic. Let's break down the concepts involved.

Total Expenditure (TE) on a good is calculated by multiplying the price of the good (P) by the quantity demanded (Q).

$$ \text{TE} = \text{P} \times \text{Q} $$

Price Elasticity of Demand ($\text{E}_d$) measures how much the quantity demanded of a good responds to a change in the price of that good. It is calculated as:

$$ \text{E}_d = \frac{\text{\% Change in Quantity Demanded}}{\text{\% Change in Price}} $$

We are told that the demand for the good is price inelastic. This means that the percentage change in quantity demanded is less than the percentage change in price (in magnitude). In other words, $|\text{E}_d| < 1$.

When demand is price inelastic, changes in price have a relatively small impact on the quantity demanded. Now let's consider how total expenditure changes when the price changes for an inelastic good.

Let's think about what happens when the price increases:

• Price (P) goes up.
• Quantity Demanded (Q) goes down, but by a smaller percentage than the price increase (because demand is inelastic).
• Total Expenditure (TE = P × Q). Since the percentage increase in P is greater than the percentage decrease in Q, the overall product P × Q will increase.

Example: Suppose Price increases by 10%, and Quantity Demanded decreases by only 5% (inelastic). The 10% price increase has a stronger effect on Total Expenditure than the 5% quantity decrease. Thus, Total Expenditure increases.

Now let's think about what happens when the price decreases:

• Price (P) goes down.
• Quantity Demanded (Q) goes up, but by a smaller percentage than the price decrease (because demand is inelastic).
• Total Expenditure (TE = P × Q). Since the percentage decrease in P is greater than the percentage increase in Q, the overall product P × Q will decrease.

Example: Suppose Price decreases by 10%, and Quantity Demanded increases by only 5% (inelastic). The 10% price decrease has a stronger effect on Total Expenditure than the 5% quantity increase. Thus, Total Expenditure decreases.

From these examples, we can see that when demand is price inelastic, Total Expenditure changes in the same direction as the price change. If price goes up, expenditure goes up. If price goes down, expenditure goes down.

Comparing Elasticity and Total Expenditure Changes

Analyzing the Options for Inelastic Demand

Based on our understanding, let's evaluate the given options:

1. Change in the opposite direction as the price change: This describes elastic demand ($|\text{E}_d| > 1$). This is incorrect for inelastic demand.
2. Change in the same direction as the price change: This describes inelastic demand ($|\text{E}_d| < 1$). This matches our conclusion.
3. Change in reverse direction to income: This relates to income elasticity, not price elasticity and total expenditure relationship. This is irrelevant.
4. Remain unchanged: This describes unit elastic demand ($|\text{E}_d| = 1$). This is incorrect for inelastic demand.

Therefore, for a price inelastic good, the expenditure on the good would change in the same direction as the price change.

Revision Table: Price Elasticity and Expenditure

Additional Information: Factors Affecting Price Elasticity

Several factors can influence whether the demand for a good is elastic or inelastic:

• Availability of Substitutes: Goods with many close substitutes tend to have more elastic demand because consumers can easily switch if the price changes. Goods with few substitutes (like essential medicines) tend to have inelastic demand.
• Necessity vs. Luxury: Necessities (like basic food or housing) often have more inelastic demand because people need them regardless of price. Luxuries tend to have more elastic demand.
• Proportion of Income Spent: Goods that represent a small portion of a consumer's budget tend to have more inelastic demand (e.g., salt). Goods that are a significant expense (e.g., a car) tend to have more elastic demand.
• Time Horizon: Demand tends to be more elastic over longer periods. Consumers have more time to find substitutes or adjust their behavior in response to price changes. In the short run, demand might be more inelastic.
• Definition of the Market: The more narrowly defined the market, the more elastic the demand tends to be. For example, the demand for specific brand of coffee might be elastic (many substitutes), but the demand for coffee in general might be more inelastic.

Understanding price elasticity is crucial for businesses deciding on pricing strategies and for governments considering taxation policies.