Demand for Smartphones The following table shows worldwide...

Demand for Smartphones The following table shows worldwide sales of smartphones and their average selling prices in 2013 and $2017:^{45}$ \begin{tabular}{|r|c|c|} \hline Year & 2013 & 2017 \\ \hline Selling Price $(\$)$ & 335 & 265 \\ \hline Sales (millions) & 1,010 & 1,710 \\ \hline \end{tabular} a. Use the data to obtain a linear demand function for smartphones, and use your demand equation to predict sales if the price is raised to $\$ 385 .$ b. Fill in the blanks: For every $\quad$ increase in price, sales of smartphones decrease by

Demand for Smartphones The following table shows worldwide sales of smartphones and their average selling prices in 2013 and $2017:^{45}$
\begin{tabular}{|r|c|c|}
\hline Year & 2013 & 2017 \\
\hline Selling Price $(\$)$ & 335 & 265 \\
\hline Sales (millions) & 1,010 & 1,710 \\
\hline
\end{tabular}
a. Use the data to obtain a linear demand function for smartphones, and use your demand equation to predict sales if the price is raised to $\$ 385 .$
b. Fill in the blanks: For every $\quad$ increase in price, sales of smartphones decrease by

Key Concepts

Marginal Change

Marginal change in the context of a demand function refers to the immediate change in the quantity demanded as a result of a small increase or decrease in price. This concept is directly tied to the slope of the demand function and quantifies the sensitivity of demand to price changes.

Intercept

The intercept in a linear demand function is the quantity demanded when the price is set to zero. It provides a baseline level of demand in the absence of pricing constraints and is critical for defining the entire demand equation.

Prediction Using a Linear Model

By substituting a specific price value into a linear demand function, one can predict the corresponding quantity demanded. This approach allows for forecasting market behavior based on changes in price.

Linear Demand Function

A linear demand function is a straight-line relationship that expresses the quantity demanded as a function of price. It typically has the form Q = a + bP, where Q is quantity demanded, P is price, a is the intercept, and b is the slope. This model assumes constant changes in demand for each unit change in price.

Slope

In a linear demand function, the slope represents the rate at which demand changes as price changes. A negative slope indicates an inverse relationship between price and demand, meaning that as price increases, demand decreases by a constant amount per unit of price change.

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