Question

What can you conclude about the price elasticity of demand in each of the following statements? a. "The pizza delivery business in this town is very competitive. I'd lose half my customers if I raised the price by as little as \(10 \%\)." b. "I owned both of the two Jerry Garcia autographed lithographs in existence. I sold one on eBay for a high price. But when I sold the second one, the price dropped by \(80 \%\)." c. "My economics professor has chosen to use the Krugman/Wells textbook for this class. I have no choice but to buy this book." d. "I always spend a total of exactly \(\$ 10\) per week on coffee."

Short answer

Question: Determine the price elasticity of demand for the following situations or products: a. Pizza delivery business b. Jerry Garcia autographed lithographs c. Krugman/Wells textbook d. Spending $10 on coffee Answer: a. Highly elastic demand (PED = -5) b. Very elastic demand (unable to calculate PED directly) c. Perfectly inelastic demand (PED = 0) d. Unitary elastic demand (PED = 1)

Step-by-step solution

a. Pizza delivery business

Based on the statement, if the price of pizza delivery increases by \(10 \%\), the business would lose \(50 \%\) of its customers. Therefore, the PED can be calculated using the formula: PED \(= \frac{-50 \%}{10 \%} = -5\) Since PED \(= -5\), the demand for pizza delivery is highly elastic. An increase in price leads to a significant decrease in the quantity demanded, resulting in a decrease in total revenue.

b. Jerry Garcia autographed lithographs

In this case, selling the second lithograph led to a price drop of \(80 \%\). There's no mention of percentage change in quantity demanded since both lithographs were unique and irreplaceable. It's not possible to calculate the PED directly, but we can make an educated inference. Considering the extreme decrease in price for the second lithograph, the demand for the product appears to be very elastic. Small changes in the supply (one less lithograph) lead to significant changes in price.

c. Krugman/Wells textbook

In this situation, students have no choice but to buy the Krugman/Wells textbook. This implies that the demand for this textbook is perfectly inelastic because the quantity demanded would remain unchanged regardless of the price. PED \(= 0\) (perfectly inelastic) A change in price for the textbook will not affect the quantity demanded, and if the price increases, the revenue will increase as well.

d. Spending \(10 on coffee

The given statement implies that the individual spends a fixed amount of money on coffee irrespective of the price of coffee. This implies that as the price of coffee increases, the individual would buy a smaller quantity in order to keep the total spending on coffee at \)10. Therefore, the demand for coffee in this case is unitary elastic because the total revenue remains constant as the price changes. If we let \(P\) represent the current price and \(Q\) represent the current quantity of coffee purchased, then Total revenue \(= PQ = \$10\) If the price changes to \(P(1 + %\Delta P)\), then the quantity demanded will change by a factor of \((1 + %\Delta Q)\), and the new total revenue would be New total revenue = \(P(1 + %\Delta P)Q(1 + %\Delta Q)\) Since the total revenue remains constant, this implies that \(1 + %\Delta Q = \frac{1}{1 + %\Delta P}\) From this equation, it's clear that the percentage change in quantity demanded is directly related to the percentage change in price, and the demand is unitary elastic (PED \(= 1\)).

Key concepts

Elastic Demand

Elastic demand occurs when a small change in price leads to a large change in the quantity demanded. In other words, consumers are quite responsive to price changes. This characteristic of demand is usually associated with products or services where many substitutes are available, or where consumers can delay purchases until prices become more favorable.

• Example: In the highly competitive pizza delivery market mentioned in the exercise, raising prices by just 10% resulted in losing half the customers. This indicates elastic demand where the percentage change in quantity demanded is greater than the percentage change in price.
• Effect on revenue: When demand is elastic, an increase in price will decrease total revenue, as the quantity demanded drops significantly.

Understanding elasticity is crucial for businesses to ensure they do not set prices that negatively impact their sales volumes and overall revenues.

Inelastic Demand

Inelastic demand is when a change in price results in a relatively smaller change in quantity demanded. Here, consumers are not very sensitive to price changes, often because there are few or no close substitutes available, or the good is considered a necessity.

• Example: As illustrated by the case of the Krugman/Wells textbook, students must buy the book regardless of its price, defining perfectly inelastic demand. Even with a price change, the quantity demanded stays the same.
• Effect on revenue: With inelastic demand, businesses can increase prices without fearing a substantial decrease in sales volume; indeed, higher prices can increase total revenue.

Grasping inelastic demand is vital for pricing strategies, especially for unique or essential products.

Unitary Elasticity

Unitary elasticity refers to a situation where a percentage change in price results in an equivalent percentage change in quantity demanded, keeping total revenue unchanged. When demand is unitary elastic, the value of price elasticity is one.

• Example: The exercise about spending $10 weekly on coffee shows how consumers adjust the quantity they purchase so that their total spending stays constant. Despite price increases or decreases, total expenditure on coffee remains the same, demonstrating unitary elasticity.
• Effect on revenue: For unitary elastic demand, changes in price do not affect total revenue because the loss in revenue from price increase (via lower quantity demanded) is exactly offset by the gain, and vice versa.

Understanding unitary elasticity helps in situations where maintaining a constant revenue stream is the business goal.

Total Revenue

Total revenue (TR) is calculated by multiplying the price of goods sold by the quantity sold. It's an important metric that businesses monitor closely, as it directly impacts profitability. Elasticity of demand plays a significant role in how changes in price affect total revenue.

• Elastic Demand: Total revenue decreases when prices rise because the fall in quantity demanded outweighs the rise in price.
• Inelastic Demand: Total revenue increases when prices rise because the fall in quantity demanded is less than the rise in price.
• Unitary Elastic Demand: Total revenue remains constant as any change in price leads to a proportional opposite change in quantity demanded.

By understanding how total revenue is affected by elasticity, businesses can make informed pricing decisions to maximize profit.

Demand and Supply Analysis

Demand and supply analysis is a fundamental concept in economics that examines the interaction between buyers and sellers in a market. It helps understand how equilibrium prices and quantities are determined and how various factors influence these.

• Elasticity plays a key role in these dynamics, illustrating how shifts in supply or demand impact price and quantity.
• Elastic products, like the pizza delivery, show significant quantity changes even with small price changes due to their competitive nature.
• Inelastic products, as in the textbook example, depict minimal response in quantity even with price shifts, crucial for goods with few alternatives or necessities.

Comprehending demand and supply analysis equips individuals and businesses with essential insights into market behavior and decision-making.