Learn Before
Concavity of the Integrated Demand Function
As the inverse demand function, , is a decreasing function in accordance with the Law of Demand, it follows from the fundamental theorem of calculus that its integral, , represents a concave function. The function corresponds to the area beneath the demand curve.
0
1
Tags
Sociology
Social Science
Empirical Science
Science
Economics
Economy
CORE Econ
Introduction to Microeconomics Course
Ch.8 Supply and demand: Markets with many buyers and sellers - The Economy 2.0 Microeconomics @ CORE Econ
The Economy 2.0 Macroeconomics @ CORE Econ
The Economy 2.0 Microeconomics @ CORE Econ
Related
Calculating an Individual's Consumer Surplus
Concavity of the Integrated Demand Function
Inverse Demand Function: Price as a Function of Quantity
A fundamental principle of market behavior states that the price consumers are willing to pay for a good decreases as the quantity available in the market increases. Given this principle, which of the following mathematical expressions, where P is price and Q is quantity (and Q > 0), could NOT represent a valid relationship between price and the quantity demanded?
Validating a Demand Function
Consider an inverse demand function given by P = 100 / (Q + 5), where P is the price and Q is the quantity demanded (Q > 0). This function is consistent with the economic principle that the price consumers are willing to pay for a good decreases as the quantity available increases.
Evaluating a Pricing Strategy
Match each mathematical function, which expresses price (P) in terms of quantity (Q > 0), to the description that best characterizes its adherence to the economic principle that the price consumers are willing to pay for a good decreases as the quantity available increases.
Constructing a Valid Demand Function
For an inverse demand function, expressed as P = f(Q), to be consistent with the general economic principle that an increase in quantity leads to a decrease in the price consumers are willing to pay, the derivative of the function, f'(Q), must be __________.
An economist is presented with a mathematical model for the price (P) consumers are willing to pay for a certain quantity (Q) of a product, expressed as P = f(Q). To determine if this model is consistent with the principle that price falls as quantity rises, they must follow a specific analytical procedure. Arrange the following steps into the correct logical order.
Selecting an Appropriate Market Demand Model
Evaluating Competing Market Models
Learn After
An economist observes a market where, for a particular good, the price consumers are willing to pay consistently decreases as more units of the good are made available. Consider a function, F(Q), that calculates the total area under the inverse demand curve from a quantity of zero up to any quantity Q. Based on the market observation, what is the essential shape of this area function, F(Q)?
Evaluating a Model of Consumer Willingness to Pay
Evaluating Models of Consumer Willingness to Pay
An economist models the total area under an inverse demand curve up to quantity Q using the function F(Q) = 100Q - 0.5Q². This model implies that the price consumers are willing to pay for each additional unit increases as the quantity available in the market grows.
Interpreting the Shape of the Total Willingness-to-Pay Function
An economist is analyzing different mathematical models for the total area under an inverse demand curve up to a quantity Q. This total area is represented by the function F(Q). For each model of F(Q) provided, match it to the correct description of the behavior of the price consumers are willing to pay for each additional unit (the inverse demand function).
An economist proposes a model where the function representing the total area under an inverse demand curve up to quantity Q is given by F(Q). The second derivative of this function, F''(Q), is found to be consistently negative for all positive quantities Q. This mathematical property implies that the price consumers are willing to pay for each successive unit is constantly ________.
Arrange the following statements into a logical sequence that demonstrates why the function representing the total area under an inverse demand curve, up to a quantity Q, is concave.
Validating a Proposed Market Model
A market analyst determines that the price consumers are willing to pay for a product is described by the function P(Q) = 50 - 2Q, where Q is the quantity. Let A(Q) be the function representing the total area under this price-quantity curve from a quantity of 0 up to Q. Which of the following statements correctly describes the function A(Q)?