Question

A 5 percent increase in the price of sugar causes the quantity demanded to fall by 15 percent. The demand for sugar is (LO1) a) perfectly elastic d) inelastic b) elastic e) perfectly inelastic c) unit elastic

Short answer

The demand for sugar is elastic (option b). This is because the price elasticity of demand for sugar is -3, which falls into the category of elastic demand (E_d > 1).

Step-by-step solution

The price elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in its price. It is calculated using the formula: Price Elasticity of Demand (E_d) = \(\frac{% Change in Quantity Demanded}{% Change in Price}\) #Step 2: Identify the given changes in price and quantity demanded#

From the exercise, we are given: 1. A 5% increase in the price of sugar (which means a positive 5% change in price) 2. A 15% fall in the quantity demanded (which means a negative 15% change in quantity demanded) #Step 3: Calculate the price elasticity of demand#

Plug the given values into the price elasticity of demand formula: E_d = \(\frac{-15\%}{5\%}\) E_d = -3 The calculated price elasticity of demand for sugar is -3. #Step 4: Interpret the result and select the correct category of elasticity#

Based on the calculated price elasticity of demand, we can interpret the result as follows: 1. If E_d = 0, demand is perfectly inelastic. 2. If 0 < E_d < 1, demand is inelastic. 3. If E_d = 1, demand is unit elastic. 4. If E_d > 1, demand is elastic. 5. If E_d = -∞, demand is perfectly elastic. In our case, the price elasticity of demand for sugar is -3, which means the demand for sugar is elastic (option b).

Key concepts

Elasticity

Price elasticity of demand is a crucial concept in understanding how consumers respond to changes in prices. It captures the sensitivity or responsiveness of the quantity demanded of a product when its price changes. This concept helps companies and governments make informed decisions about pricing, subsidies, and taxes.
For instance, if consumers significantly decrease their quantity demanded due to a small increase in price, the demand is considered elastic. This means people are sensitive to price changes and may switch to substitutes if prices rise. Conversely, if quantity demanded hardly changes with price variations, demand is inelastic.

• Elastic: Large change in demand for a small price increase.
• Inelastic: Little change in demand despite large price hikes.

The formula for calculating elasticity is: \(E_d = \frac{\% \text{ Change in Quantity Demanded}}{\% \text{ Change in Price}}\).
Elasticity values help classify goods into these categories, influencing business strategies and economic policies.

Quantity Demanded

Quantity demanded refers to the specific amount of a product that consumers are willing and able to purchase at a given price point. It is an essential element of demand, forming the basis for analyzing how price changes influence consumer behavior.
When studying quantity demanded, consider factors such as consumer preferences, income levels, and availability of substitutes. These elements impact how much of a product people buy. For example, if sugar's price increases, fewer people might buy it, reducing the quantity demanded.
Economists often analyze scenarios like a rise in sugar prices to see how much the quantity demanded decreases. A significant drop indicates high elasticity, meaning consumers are sensitive to the price change. In the calculation, we observed a 15% decrease in quantity demanded due to a 5% price increase, highlighting elasticity.

Price Change

Price changes can significantly impact both consumers and producers. As seen in the exercise on sugar, even a small price increase can lead to noticeable shifts in buying habits.
Changes in price are not arbitrary; they result from a complex interplay of factors like supply, demand, costs, and competition. Understanding how these changes affect the market is crucial for businesses when setting prices to maintain profitability.
For consumers, price changes can alter purchasing power and force decisions about spending or saving. If a price hike leads to a substantial decrease in quantity demanded, as demonstrated by sugar's 5% price rise causing a 15% demand drop, it showcases the elasticity of demand.

• Price Increase: Can lead to less quantity demanded if demand is elastic.
• Price Decrease: Might boost quantity demanded if the product is elastic.

This helps explain consumer behavior and market dynamics more thoroughly.