A study of the demand for air travel in Australia found that...

A study of the demand for air travel in Australia found that the demand for discount air travel from Sydney to Melbourne (in revenue passenger kilometre per capita, the product of the number of passengers travelling on a route and the distance of the route, divided by the populations of the host cities) depends on the airfare according to the equation $$q=55.2-0.022 p$$ Source: International Journal of Transport Economics. a. Find the elasticity when the price is $\$ 166.10$ , the average dis- count airfare deflated by the consumer price index to $1989-1990$ prices, according to the authors of the study. b. Is the demand for airfare elastic or inelastic at this price? c. Find the price that maximizes revenue.

A study of the demand for air travel in Australia found that the demand for discount air travel from Sydney to Melbourne (in revenue passenger kilometre per capita, the product of the number of passengers travelling on a route and the distance of the route, divided by the populations of the host cities) depends on the airfare according to the equation
$$q=55.2-0.022 p$$
Source: International Journal of Transport Economics.
a. Find the elasticity when the price is $\$ 166.10$ , the average dis- count airfare deflated by the consumer price index to $1989-1990$ prices, according to the authors of the study.
b. Is the demand for airfare elastic or inelastic at this price?
c. Find the price that maximizes revenue.

Key Concepts

Revenue Maximization

Revenue maximization involves determining the price at which total revenue—calculated as price times quantity demanded—is highest. This is achieved by using the demand function to form a revenue function and then finding the price that maximizes this function, usually through differentiation. The concept is fundamental for businesses seeking to optimize pricing strategies to maximize income.

Linear Demand Function

A linear demand function represents the relationship between price and quantity demanded with a straight-line equation. Its simplicity allows for straightforward calculations of changes in quantity when the price changes. This serves as a basic tool to model consumer behavior in response to price variations.

Elastic vs. Inelastic Demand

This concept distinguishes between products whose quantity demanded reacts strongly to price changes (elastic) and those whose quantity demanded is relatively impervious to price changes (inelastic). When the absolute value of the price elasticity is greater than one, demand is elastic; when it is less than one, demand is inelastic; and when it equals one, demand is unit elastic.

Price Elasticity of Demand

Price elasticity of demand measures the responsiveness of the quantity demanded to a change in the price of a good. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. This concept helps determine how sensitive consumers are to price changes, which is critical for pricing and revenue strategies.

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