Question

Where along a straight-line demand curve does consumer spending reach a maximum? Explain why. What use is this information to the owner of a football club?

Short answer

Consumer spending is maximized where elasticity equals one along the demand curve. This information helps club owners set ticket prices for maximum revenue.

Step-by-step solution

Understanding the Concept

The demand curve is a graphical representation of the quantity of a good that consumers are willing to buy at different prices. Consumer spending (or expenditure) is the product of the price and quantity demanded: \( \text{Spending} = \text{Price} \times \text{Quantity} \).

Identifying Maximum Consumer Spending

Consumer spending is maximized where the demand curve's elasticity is unitary. At this point, the percentage change in quantity demanded is equal to the percentage change in price, meaning that a small change in price does not affect the total revenue.

Calculating Elasticity on a Linear Demand Curve

Elasticity can be calculated at any point on the curve using the formula: \( E = \frac{P}{Q} \times \frac{1}{\text{slope}} \), where \(P\) is price and \(Q\) is quantity. Maximum spending occurs where \(E = 1\).

Determining the use of this Information

For the owner of a football club, understanding where maximum consumer spending occurs can help in setting ticket prices. By pricing tickets where spending is maximized, the club can ensure the highest possible revenue from ticket sales.

Key concepts

Demand Curve

The demand curve is a fundamental concept in economics that illustrates the relationship between the price of a good and the quantity of that good consumers are willing to purchase. Picture it as a graph that slopes downward from left to right.

When prices are high, fewer people are willing to buy the product, resulting in a lower quantity demanded. Conversely, when prices drop, more consumers find the product affordable, leading to a higher quantity demanded. This inverse relationship between price and quantity demanded is the essence of the demand curve.

Understanding this relationship helps businesses determine the best pricing strategies. They can use it to predict how changes in price may affect consumer behavior.

Elasticity

Elasticity is an important economic concept that measures how sensitive the quantity demanded of a good is to a change in its price.

There are several terms related to elasticity you might hear about:

• Elastic Demand: A situation where a small change in price leads to a large change in the quantity demanded.
• Inelastic Demand: A situation where changes in price have little impact on the quantity demanded.

Elasticity is calculated using the formula:\[E = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}}\]
A higher elasticity means consumers are more responsive to price changes, whereas a lower elasticity indicates less sensitivity.

Unitary Elasticity

Unitary elasticity occurs at a specific point along the demand curve where a change in price results in a proportional change in quantity demanded. In other words, the percentage change in price is exactly equal to the percentage change in quantity demanded.

Mathematically, unitary elasticity is when \( E = 1 \). At this point, the demand curve has a unique property where total revenue, which is price multiplied by quantity, is maximized. This indicates that consumers' response to a change in price neither increases nor decreases total spending.

Understanding unitary elasticity is crucial for businesses because it helps in setting the price point at which revenue is maximized without altering demand significantly.

Total Revenue

Total revenue is the total amount of money a company receives from selling its goods or services. It's calculated simply by multiplying the price (P) of the good by the quantity (Q) sold:
\[\text{Total Revenue} = \text{Price} \times \text{Quantity}\]
The concept of total revenue ties closely to elasticity. When demand is elastic, a decrease in price leads to a rise in total revenue, while an increase in price causes total revenue to fall. Conversely, when demand is inelastic, raising prices leads to higher total revenue because the quantity demanded doesn't drop significantly.

For entities like football clubs, understanding total revenue is crucial. By setting ticket prices where the demand's elasticity is unitary, clubs can ensure that total revenue is maximized, capitalizing on consumer spending precisely.