Demand: E-Readers The demand for Amazon's Kindle e-reader...

Demand: E-Readers The demand for Amazon's Kindle e-reader can be approximated by $q(p)=\frac{760}{p}-1$ million units per year $\quad(60 \leq p \leq 400)$ where $p$ is the price charged by Amazon. $^{25}$ a. Graph the demand function. b. What is the result on demand if the unit price is increased from $$\$ 100$$ to $$\$ 200 ?$$ [HINT: See Example $3 .]$ c. According to the graph in part (a), if the price is $$\$ 200$$ and successively increases in $$\$ 10$$ increments, then the demand (A) increases at a greater and greater rate. (B) decreases at a greater and greater rate. (C) increases at a smaller and smaller rate. (D) decreases at a smaller and smaller rate. (E) increases at the same rate. (F) decreases at the same rate.

Demand: E-Readers The demand for Amazon's Kindle e-reader can be approximated by
$q(p)=\frac{760}{p}-1$ million units per year $\quad(60 \leq p \leq 400)$
where $p$ is the price charged by Amazon. $^{25}$
a. Graph the demand function.
b. What is the result on demand if the unit price is increased from $$\$ 100$$ to $$\$ 200 ?$$ [HINT: See Example $3 .]$
c. According to the graph in part (a), if the price is $$\$ 200$$ and successively increases in $$\$ 10$$ increments, then the demand
(A) increases at a greater and greater rate.
(B) decreases at a greater and greater rate.
(C) increases at a smaller and smaller rate.
(D) decreases at a smaller and smaller rate.
(E) increases at the same rate.
(F) decreases at the same rate.

Key Concepts

Price Increments and Elasticity

Price increments involve analyzing the impact of specific, small increases or decreases in price on the quantity demanded. Although not explicitly termed in the problem, such analysis is related to the concept of price elasticity of demand, which measures the responsiveness or sensitivity of the quantity demanded to a change in price. Understanding this concept is crucial for making pricing decisions and predicting consumer behavior in response to price adjustments.

Marginal Change and Rate of Change

Marginal change and the concept of rate of change refer to how a small change in one variable, such as price, leads to a change in another variable, such as demand. By examining incremental changes (for instance, a price increase of a certain amount), one can understand how demand is sensitive to changes in price. This concept is closely related to the derivative of the demand function in calculus, which gives the instantaneous rate of change.

Demand Function

A demand function represents the relationship between the price of a good and the quantity that consumers are willing to purchase. It typically shows an inverse relationship, meaning that as the price increases, the quantity demanded decreases. This mathematical representation allows economists to analyze consumer behavior and forecast demand levels based on different pricing strategies.

Graphing Functions

Graphing functions involves plotting the relationship between two variables, typically on a coordinate system. In economic contexts, graphing the demand function helps visualize how changes in price affect the quantity demanded. It provides insight into the behavior of the demand curve, including its slope, intercepts, and any non-linear characteristics that might emerge as prices vary.

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