Understanding Demand Change with Price Elasticity

This question asks how the demand for a good changes when its price increases, given the initial price, initial quantity demanded, and the price elasticity of demand. To solve this, we need to use the concept of price elasticity of demand, which measures the responsiveness of the quantity demanded to a change in price.

Calculating the Change in Demand

The formula for price elasticity of demand ($E_d$) is:

\( E_d = \left| \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}} \right| \)

First, let's calculate the percentage change in price:

• Initial Price ($P_1$) = ₹5
• New Price ($P_2$) = ₹7
• Change in Price ($\Delta P$) = $P_2 - P_1 = ₹7 - ₹5 = ₹2$
• Percentage Change in Price = \( \left( \frac{\Delta P}{P_1} \right) \times 100 = \left( \frac{₹2}{₹5} \right) \times 100 = 0.4 \times 100 = 40\% \)

Now, we use the given elasticity of demand ($E_d = 0.5$) and the percentage change in price to find the percentage change in quantity demanded:

\( 0.5 = \left| \frac{\text{Percentage Change in Quantity Demanded}}{40\%} \right| \)

\( \text{Percentage Change in Quantity Demanded} = 0.5 \times 40\% = 20\% \)

Since the price has increased, and the relationship between price and quantity demanded is typically inverse (Law of Demand), the quantity demanded will decrease. So, the percentage change in quantity demanded is actually -20%.

Next, we calculate the absolute change in quantity demanded:

• Initial Quantity Demanded ($Q_1$) = 15 units
• Percentage Change in Quantity Demanded = -20%
• Absolute Change in Quantity Demanded ($\Delta Q$) = \( \left( \frac{\text{Percentage Change in Quantity Demanded}}{100} \right) \times Q_1 = \left( \frac{-20}{100} \right) \times 15 \)
• \( \Delta Q = -0.20 \times 15 = -3 \) units

The new quantity demanded ($Q_2$) will be:

\( Q_2 = Q_1 + \Delta Q = 15 \text{ units} - 3 \text{ units} = 12 \text{ units} \)

The initial demand was 15 units, and the new demand is 12 units. Since 12 is less than 15, the individual will reduce his demand.

Analyzing the Options

• Increase his demand: This is incorrect. When the price of a normal good increases, the quantity demanded typically decreases according to the Law of Demand.
• No change in his demand: This would imply that the quantity demanded remains 15 units despite the price increase. This is incorrect, as our calculation shows a change.
• Reduce his demand: This is consistent with our calculation and the Law of Demand. The quantity demanded decreases from 15 units to 12 units.
• Shift to another Good: While a price increase might lead consumers to switch to substitute goods, the question asks what happens to the demand for this good. A reduction in demand for this good is the direct consequence calculated using elasticity. Shifting to another good is the underlying behavior that causes the reduction in demand for the original good, but "Reduce his demand" is the specific outcome for the good in question based on the elasticity value provided.

Therefore, when the price increases from ₹5 to ₹7 and the elasticity of demand is 0.5, the individual will reduce his demand for the good.

Revision Table: Key Concepts in Demand and Elasticity

Additional Information: Price Elasticity of Demand

Price elasticity of demand is a crucial concept in economics for understanding consumer behavior and market dynamics. It helps businesses and policymakers predict how changes in price will affect the quantity of goods sold.

• Factors Influencing Elasticity: several factors affect the elasticity of demand, including the availability of substitutes (more substitutes mean more elastic demand), the proportion of income spent on the good (larger proportion means more elastic), whether the good is a necessity or a luxury (necessities are less elastic), and the time period considered (demand becomes more elastic over longer periods).
• Types of Elasticity:
  • Perfectly Inelastic Demand ($E_d = 0$): Quantity demanded does not change at all when price changes (e.g., life-saving medicine).
  • Inelastic Demand ($0 < E_d < 1$): Percentage change in quantity demanded is less than the percentage change in price.
  • Unitary Elastic Demand ($E_d = 1$): Percentage change in quantity demanded is exactly equal to the percentage change in price.
  • Elastic Demand ($E_d > 1$): Percentage change in quantity demanded is greater than the percentage change in price.
  • Perfectly Elastic Demand ($E_d = \infty$): Quantity demanded changes infinitely with any price change (a theoretical concept often seen in perfect competition).
• In this question, the elasticity of 0.5 means the demand is inelastic. This indicates that while the quantity demanded does respond to a price change, it does so by a smaller percentage than the price change itself.