Question

A 5 percent increase in the price of sugar causes the quantity demanded to fall by 15 pereent. The demand for sugar is (101) a) perfectly clastic d) inclastic b) elastic e) perfectly inelastic c) unit elastic

Short answer

The demand for sugar is elastic, as the calculated price elasticity of demand (PED) is -3, and the absolute value of -3 is greater than 1 (\( |PED| > 1 \)). The correct answer is (b) elastic.

Step-by-step solution

Understand the Price Elasticity of Demand formula

The formula for price elasticity of demand (PED) is: \[ PED = \frac{\% \, change \, in \, quantity \, demanded}{\% \, change \, in \, price} \] A positive PED value indicates normal goods, while a negative value indicates inferior goods.

Plug in the given percentages

In the given problem, the price of sugar increases by 5% and the quantity demanded falls by 15%. Plug these values into the PED formula: \[ PED = \frac{-15\%}{5\%} \]

Calculate PED

Divide -15% by 5% to find the value of the price elasticity of demand: \[ PED = -3 \]

Determine the category of elasticity

Based on the PED value, we can now determine the category of elasticity for sugar: - If PED = 0, the demand is perfectly inelastic. - If 0 < |PED| < 1, the demand is inelastic. - If |PED| = 1, the demand is unit elastic. - If |PED| > 1, the demand is elastic. - If |PED| = ∞, the demand is perfectly elastic. Our calculated PED is -3, which has an absolute value greater than 1. Therefore, the demand for sugar is elastic. So, the correct answer is (b) elastic.

Key concepts

Price Elasticity of Demand

Price elasticity of demand, often abbreviated as PED, is an essential economic concept that helps to understand consumer behavior. It measures how the quantity demanded of a good changes when its price changes. If the price changes, PED helps to predict whether consumers will continue buying at the same rate, buy more, or buy less.

The idea is quite straightforward: it answers the question, "How sensitive is the demand for a product to a change in its price?"
Here are some of the main types of elasticity:

• Perfectly elastic: Demand changes infinitely with a tiny price change.
• Elastic: Larger change in demand for a small change in price.
• Unit elastic: Proportional change in price leads to a proportional change in quantity demanded.
• Inelastic: Small change in demand despite price change.
• Perfectly inelastic: Demand does not change regardless of price.

Understanding these types will help you determine how a price change will impact the sales volume of a product.

Quantity Demanded

The quantity demanded refers to the total amount of goods or services that consumers are willing and able to purchase at a given price over a specific period. It is a core part of demand analysis, helping businesses and economists forecast how certain factors affect demand.

Various factors can influence quantity demanded. While price is a major factor, changes in income levels, preferences, and the price of related goods also have a significant impact. An increase in price usually reduces the quantity demanded, while a decrease in price tends to increase it. This inverse relationship is central to the law of demand.

• Price increase: Generally leads to lower quantity demanded.
• Price decrease: Generally leads to higher quantity demanded.

It is important to note that some goods, like luxury items, might not follow the typical rules of demand, as other social or economic factors drive their demand.

PED Formula

The PED formula is used to calculate the price elasticity of demand for a particular good. It is expressed as:
\[ PED = \frac{\% \, \text{change in quantity demanded}}{\% \, \text{change in price}} \]

This formula allows economists and businesses to calculate the responsiveness of demand to a change in price. It is the foundational tool to determine if a product is elastic or inelastic.

To use the formula, you simply plug in the percentage changes in price and quantity demanded. A negative value is often expected since price and demand usually move in opposite directions. In the exercise, a 5% increase in price led to a 15% decrease in demand, giving a PED of -3. This tells us that the demand is elastic, meaning consumers significantly reduce their quantity demanded when the price rises a bit.

• PED > 1: Elastic demand.
• PED < 1: Inelastic demand.
• PED = 1: Unit elastic demand.

Calculating PED is crucial for strategic decisions in pricing, supply, and sales forecasting.