Understanding Price Elasticity and Total Revenue

The question asks about the relationship between a price increase, total revenue, and the price elasticity of demand. To answer this, we need to understand how changes in price affect the quantity demanded and, consequently, the total revenue earned by a seller.

Total Revenue (TR) is calculated as the price of a commodity multiplied by the quantity sold:

\( TR = Price \times Quantity \)

The Price Elasticity of Demand (PED) measures how sensitive the quantity demanded of a good is to a change in its price. It is calculated as:

\( PED = \frac{\% \Delta Quantity \, Demanded}{\% \Delta Price} \)

Depending on the value of the PED coefficient, demand can be classified as:

• Elastic Demand (PED > 1): The percentage change in quantity demanded is greater than the percentage change in price.
• Inelastic Demand (PED < 1): The percentage change in quantity demanded is less than the percentage change in price.
• Unitary Elastic Demand (PED = 1): The percentage change in quantity demanded is equal to the percentage change in price.
• Perfectly Inelastic Demand (PED = 0): Quantity demanded does not change at all when the price changes.
• Perfectly Elastic Demand (PED = \(\infty\)): Quantity demanded changes infinitely with any small change in price.

Analyzing the Relationship between Price Changes and Total Revenue

The key to solving this question lies in understanding how PED affects Total Revenue when price changes. Let's examine the different cases:

• If demand is Elastic (PED > 1): When the price increases, the quantity demanded falls by a proportionally larger amount. This larger drop in quantity outweighs the price increase, causing Total Revenue to decrease. Conversely, if the price decreases, quantity demanded rises by a proportionally larger amount, causing Total Revenue to increase.
• If demand is Inelastic (PED < 1): When the price increases, the quantity demanded falls, but only by a proportionally smaller amount. The increase in price outweighs the smaller drop in quantity, causing Total Revenue to increase. Conversely, if the price decreases, quantity demanded rises by a proportionally smaller amount, causing Total Revenue to decrease.
• If demand is Unitary Elastic (PED = 1): When the price changes, the quantity demanded changes by the exact same proportion. The effects on price and quantity cancel each other out, leaving Total Revenue unchanged.

Applying the Scenario to Determine Elasticity

The question states that "When the price increase of a commodity is followed by increased total revenue". We just analysed that this specific outcome (Price Increase \(\rightarrow\) Total Revenue Increase) happens when the demand for the commodity is inelastic.

Inelastic demand corresponds to a Price Elasticity of Demand coefficient that is less than one (PED < 1).

Evaluating the Given Options

Let's consider the options based on our analysis:

1. Zero: This represents perfectly inelastic demand (a specific case of less than one). If PED is zero, quantity demanded does not change at all when price changes. A price increase would indeed lead to an increase in total revenue (\(TR = Price \times Quantity\), Quantity is constant, Price increases). This fits the condition, but "less than one" is a broader category that includes zero.
2. Equal to one: This represents unitary elastic demand. A price increase would result in Total Revenue remaining unchanged, not increasing. This does not fit the condition.
3. More than one: This represents elastic demand. A price increase would result in Total Revenue decreasing, not increasing. This does not fit the condition.
4. Less than one: This represents inelastic demand. As we discussed, a price increase with inelastic demand leads to an increase in Total Revenue. This perfectly fits the condition described in the question.

Therefore, when a price increase leads to an increase in total revenue, the price elasticity coefficient is less than one.

Revision Table: Price Elasticity and Total Revenue Link

Additional Information on Price Elasticity

Understanding price elasticity is crucial for businesses when making pricing decisions. Factors that influence the price elasticity of demand for a good include:

• Availability of Substitutes: Goods with many close substitutes tend to have more elastic demand because consumers can easily switch if the price changes.
• Necessity vs. Luxury: Necessities typically have more inelastic demand than luxuries because consumers need them regardless of price.
• Proportion of Income: Goods that represent a large portion of a consumer's budget tend to have more elastic demand.
• Time Horizon: Demand tends to be more elastic over longer periods as consumers have more time to adjust to price changes and find substitutes.
• Definition of the Market: The more narrowly defined the market, the more elastic the demand (e.g., demand for specific brand vs. demand for the product category).

Businesses can use the concept of price elasticity to predict the impact of price changes on their sales and total revenue, helping them set optimal prices.