Question

In \(2003,\) when music downloading first took off, Universal Music slashed the average price of a CD from \(\$ 21\) to \(\$ 15 .\) The company expected the price cut to boost the quantity of CDs sold by 30 percent, other things remaining the same. a. What was Universal Music's estimate of the price elasticity of demand for CDs? b. If you were making the pricing decision at Universal Music, what would be your pricing decision? Explain your decision.

Short answer

Elasticity is \( -1.05 \). Lowering the price is advisable since demand is elastic.

Step-by-step solution

- Understand Price Elasticity of Demand Formula

The price elasticity of demand is calculated using the formula: \[ E_d = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}} \]

- Calculate Percentage Change in Quantity Demanded

From the information given, the expected increase in quantity sold is \(30\%\). Hence, the percentage change in quantity demanded: \( \% \Delta Q = 30\% \).

- Calculate Percentage Change in Price

First, find the initial and new prices, and then calculate the percentage change: Initial Price: \( \$21 \)New Price: \( \$15 \)Percentage change in price is given by: \[ \% \Delta P = \frac{\text{New Price} - \text{Initial Price}}{\text{Initial Price}} \times 100 \] So, \[ \% \Delta P = \frac{15 - 21}{21} \times 100 = \frac{-6}{21} \times 100 \approx -28.57\%\]

- Calculate Price Elasticity of Demand

Substitute the calculated values into the elasticity formula: \[ E_d = \frac{\% \Delta Q}{\% \Delta P} = \frac{30\%}{-28.57\%} \approx -1.05 \]

- Interpret Elasticity

The elasticity value of \( -1.05 \) suggests that the demand for CDs is elastic, meaning that the percentage change in the quantity demanded is larger than the percentage change in price.

- Pricing Decision

If making the pricing decision, one would consider the elasticity. Since the demand is elastic, lowering the price leads to a proportionally larger increase in quantity demanded, which could increase total revenue. Therefore, it would be advisable to reduce the price as originally planned.

Key concepts

quantity demanded

Quantity demanded refers to the number of units of a good or service that consumers are willing to buy at a given price. When Universal Music lowered the price of CDs from \(21 to \)15, they expected the quantity demanded to increase by 30%. This anticipated increase shows how price changes can affect consumer behavior. By understanding quantity demanded, companies can tailor their pricing strategies to meet market demand and maximize sales.

percentage change

Percentage change is a crucial concept in economics that measures how a variable has changed over time, expressed as a percentage. In the case of Universal Music, the percentage change in price was calculated as:
\[ \% \Delta P = \frac{\text{New Price} - \text{Initial Price}}{\text{Initial Price}} \times 100 = \frac{15 - 21}{21} \times 100 \approx -28.57\% \]
Similarly, the percentage change in quantity demanded was given as 30%. These percentage changes help in calculating the price elasticity of demand, which in turn helps businesses understand the impact of price changes on sales.

elastic demand

Elastic demand means that the quantity demanded of a good or service is highly responsive to price changes. In the exercise, the price elasticity of demand for CDs was calculated to be approximately -1.05, indicating elastic demand (because the absolute value is greater than 1). This means a small decrease in the price of CDs led to a proportionally larger increase in the quantity demanded. Understanding if demand is elastic or inelastic helps businesses make more informed pricing decisions.
Key characteristics:

• Sensitive to price changes
• Proportional larger change in quantity demanded
• Elasticity value (absolute) > 1

pricing strategy

A good pricing strategy considers the price elasticity of demand. Since Universal Music found that the demand for CDs was elastic (\( E_d \text{approx} -1.05 \text \)), they decided to lower the price. When demand is elastic, lowering prices can lead to higher total revenue because the increase in quantity demanded more than compensates for the lower price.
Key factors in pricing strategy:

• Understanding market demand
• Analyzing competition
• Evaluating cost structures
• Considering elasticity of demand

total revenue

Total revenue is the total income a company earns from selling its goods or services. It is calculated by multiplying the price per unit by the quantity sold. In the exercise, Universal Music's pricing decision aimed to increase total revenue by lowering the price. For elastic demand, like that of the CDs, a price decrease leads to a larger percentage increase in quantity demanded, thus boosting total revenue.
Equation: \[ \text{Total Revenue} = \text{Price} \times \text{Quantity Demanded} \] Understanding how variances in price and demand affect total revenue is crucial for developing effective pricing strategies.