In 2005, the Las Vegas monorail charged 3 per ride and had...

In 2005, the Las Vegas monorail charged $\$ 3$ per ride and had an average ridership of about 28,000 per day. In December, 2005 the Las Vegas Monorail Company raised the fare to $\$ 5$ per ride, and average ridership in 2006 plunged to around 19,000 per day. 29 a. Use the given information to find a linear demand equation. b. Give the units of measurement and interpretation of the slope. c. What would be the effect on ridership of raising the fare to $\$ 6$ per ride?

In 2005, the Las Vegas monorail charged $\$ 3$ per ride and had an average ridership of about 28,000 per day. In December, 2005 the Las Vegas Monorail Company raised the fare to $\$ 5$ per ride, and average ridership in 2006 plunged to around 19,000 per day. 29
a. Use the given information to find a linear demand equation.
b. Give the units of measurement and interpretation of the slope.
c. What would be the effect on ridership of raising the fare to $\$ 6$ per ride?

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Key Concepts

Intercept

The intercept is the value of the quantity demanded when the price is zero. It indicates the maximum potential demand if the goods or services were provided for free, serving as a baseline from which the effects of pricing are measured.

Using the Model for Prediction

Once the linear demand function is established, it can be used to predict future demand at any price by substituting the price into the equation. This predictive capability is crucial for forecasting changes in consumer behavior as a response to fare increases or decreases.

Linear Demand Function

A linear demand function models the relationship between price and quantity demanded as a straight line, typically in the form Q = mP + b. Here, Q stands for the quantity demanded and P represents the price per unit. This model helps in understanding how changes in price impact the quantity demanded in a predictable, constant manner.

Slope Interpretation

The slope in a linear demand equation represents the rate at which the quantity demanded changes with respect to changes in price. Its units are typically in terms of quantity per unit of currency (for example, rides per dollar), meaning it quantifies the reduction in the number of rides for a one-dollar increase in fare.

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