Book cover for Microeconomics

Microeconomics

Jeffrey M. Perloff

ISBN #9781292056531

7th Edition

753 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section explains how the quantity demanded is influenced by the price of a good and other external factors. It introduces the demand curve as a graphical tool to capture the Law of Demand, where lower prices lead to higher quantities demanded, and vice versa. The demand function and its inverse are derived to quantify how changes in price lead to specific changes in quantity demanded. Additionally, the section differentiates between movements along a demand curve (caused by price changes) and shifts in the curve (resulting from changes in other factors), and it explains how individual demands can be aggregated into a market demand curve.

Learning Objectives

1

Explain the concept of quantity demanded and how it differs from the quantity purchased.

2

Interpret graphical representations of the demand curve and understand the Law of Demand.

3

Distinguish between movements along a demand curve (price changes) and shifts in the demand curve (changes in other factors such as income or substitute prices).

4

Derive and use the demand function and its inverse to analyze how price changes affect quantity demanded.

5

Demonstrate how individual demand curves can be aggregated to form a market demand curve.

Key Concepts

CONCEPT

DEFINITION

Quantity Demanded

The amount of a good that consumers are willing to buy at a given price, holding constant other influencing factors.

Demand Curve

A graphical representation showing the quantity demanded for a good at each possible price, with all other factors held constant.

Law of Demand

A principle stating that, ceteris paribus, consumers demand more of a good when its price decreases and less when its price increases.

Inverse Demand Function

An expression derived from the demand function that shows the price consumers are willing to pay as a function of the quantity demanded.

Movement vs. Shift

A movement along the demand curve is caused by a change in the good’s own price, while a shift in the demand curve results from changes in other determinants (e.g., income, prices of substitutes, tastes).

Example Problems

Example 1

The estimated demand function (Moschini and Meilke, 1992 , for Canadian processed pork is $Q=161-20 p+20 p_{b}+3 p_{\mathrm{c}}+2 Y,$ where $Q$ is the quantity in million kilograms (kg) of pork per year, $p$ is the dollar price per kg (all prices cited are in Canadian dollars), $p_{b}$ is the price of beef per $\mathrm{kg}, p_{c}$ is the price of chicken in dollars per $\mathrm{kg},$ and $Y$ is average income in thousands of dollars. What is the demand function if we hold $p_{b}, p_{c},$ and $Y$ at their typical values during the period studied: $p_{b}=3.2, p_{c}=3 \frac{3}{10},$ and $Y=13 ? \mathbf{A}$

Example 2

The estimated demand function (Moschini and Meilke, 1992 ) for Canadian processed pork is $Q=161-20 p+20 p_{b}+3 p_{c}+2 Y,$ where $Q$ is the quantity in million kilograms (kg) of pork per year, $p$ is the dollar price per kg (all prices cited are in Canadian dollars), $p_{b}$ is the price of beef per $\mathrm{kg}, p_{c}$ is the price of chicken in dollars per $\mathrm{kg}$, and $Y$ is average income in thousands of dollars. What is the demand function if we hold $\rho_{b}, p_{c}$ and $Y$ at their typical values during the period studied: $p_{b}=3.2, p_{c}=3 \frac{3}{10},$ and $Y=13 ? A$.

Example 3

The estimated demand function (Moschini and Meilke, 1992 ) for Canadian processed pork is $Q=161-20 p+20 p_{b}+3 p_{c}+2 Y,$ where $Q$ is the quantity in million kilograms (kg) of pork per year, $p$ is the dollar price per kg (all prices cited are in Canadian dollars), $p_{b}$ is the price of beef per $\mathrm{kg}, p_{c}$ is the price of chicken in dollars per $\mathrm{kg},$ and $Y$ is average income in thousands of dollars. What is the demand function if we hold $p_{b}, p_{c},$ and $Y$ at their typical values during the period studied: $p_{b}=3.2, p_{c}=3 \frac{3}{10},$ and $Y=13 ? \mathbf{A}$

Example 4

Using the estimated demand function for processed pork from Question $1.1,$ show how the quantity demanded at a given price changes as per capita income, $Y$, increases by $\$ 90$ a year. $A$

Example 5

Using the estimated demand function for processed pork from Question $1.1,$ show how the quantity demanded at a given price changes as per capita income, $Y$, increases by $\$ 90$ a year. A
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Step-by-Step Explanations

QUESTION

How much must the price fall for consumers to be willing to buy 1 million more lbs of avocados per month, given the demand function Q = 160 - 40p?

STEP-BY-STEP ANSWER:

Step 1: Start with the demand function Q = 160 - 40p. This function tells us that at p dollars per lb, the expected quantity demanded is Q million lbs per month.
Step 2: Rearrange the equation to derive the inverse demand function, where price is expressed as a function of quantity. Add 40p to both sides and subtract Q: 40p = 160 - Q.
Step 3: Divide both sides by 40 to solve for p: p = 160/40 - (1/40) * Q, which simplifies to p = 4 - 0.025Q.
Step 4: Recognize that if the quantity demanded increases by 1 million lbs (∆Q = 1), the change in price (∆p) is given by the coefficient of Q in the inverse demand function. Thus, ∆p = -0.025 × ∆Q = -0.025.
Step 5: Interpret the result. The negative sign indicates that to sell an additional 1 million lbs of avocados per month, the price must fall by 2.5 cents per lb.
Final Answer: The price must fall by 2.5¢ per pound for consumers to buy 1 million more lbs of avocados per month.

Calculating the Change in Price for an Increase in Quantity Demanded

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Common Mistakes

  • Assuming that a change in the amount purchased always reflects a change in quantity demanded, without recognizing that inventory limitations can cause discrepancies.
  • Confusing a movement along the demand curve (due to a price change) with a shift of the entire curve (caused by changes in income, tastes, or substitute prices).
  • Incorrectly deriving the inverse demand function by mismanaging the algebraic manipulation of the demand function.
  • Overlooking the assumption that all other factors are held constant, which is crucial for isolating the effect of a price change.