Price–demand function

Definition

A price–demand function models the relationship between the price of a good and the quantity demanded by consumers. It is typically represented as $p(x)$, where $p$ is the price and $x$ is the quantity demanded.

5 Must Know Facts For Your Next Test

1. The price–demand function can be integrated to find total revenue, which is given by $$R(x) = \int p(x) \, dx$$.
2. In calculus, finding the elasticity of demand involves differentiating the price–demand function.
3. A common form of a price–demand function is linear, such as $$p(x) = a - bx$$, where $a$ and $b$ are constants.
4. The inverse of a price–demand function gives the demand at any given price, often used in economic analyses.
5. Integration involving exponential or logarithmic forms of price–demand functions might require techniques like substitution or integration by parts.

Review Questions

• How do you integrate a linear price–demand function to find total revenue?
• What steps are involved in finding the elasticity of demand from a given price–demand function?
• Describe how you would handle integrating an exponential form of a price–demand function.

Related terms

Total Revenue: The total income received from selling a certain quantity of goods, calculated as $$R(x) = \int p(x) \, dx$$.

Elasticity of Demand: A measure of how much the quantity demanded responds to changes in price, often derived using differentiation.

Integration by Parts: A technique used to integrate products of functions, based on the formula $$\int u \, dv = uv - \int v \, du$$.