Own-Price Changes as Movements Along Demand

Introduction

Suppose the price of a good falls while buyers’ circumstances remain unchanged. The standard demand model predicts that buyers choose a greater quantity of that good. The key is to describe this as a change in quantity demanded: the selected point moves along the existing demand curve. The curve itself does not move just because the good’s own price changed.

This distinction matters when reading schedules, equations, and graphs. A price change gives a new price and a new quantity demanded under the same demand relationship. By contrast, a change in the relationship would mean that the old curve no longer describes buyers’ purchase plans. This tutorial focuses on tracing the first case in either direction.

Definition: A movement along a demand curve is a change in quantity demanded caused by a change in the good’s own price, with other relevant conditions held fixed. A price decrease is associated with an increase in quantity demanded, called an extension of demand. A price increase is associated with a decrease in quantity demanded, called a contraction of demand. In both cases, the demand curve is unchanged.

The Fixed-Curve Model

A demand curve describes the quantities buyers are willing and able to purchase at different prices during a specified period, given the other conditions affecting their purchase plans. Write this relationship as $Q_d=D(P;Z)$, where $Q_d$ is quantity demanded, $P$ is the good’s own price, and $Z$ represents all other relevant conditions. For a movement along a fixed curve, $Z$ stays constant.

The standard law-of-demand model assumes that, over the range being considered, the demand curve slopes downward: a higher price corresponds to a lower quantity demanded, and a lower price corresponds to a higher quantity demanded. The curve need not be linear. If it is linear, its equation can make the quantities at two prices straightforward to calculate.

On the usual graph, price is on the vertical axis and quantity is on the horizontal axis. A point on the curve pairs one price with the quantity demanded at that price. A movement to a lower price and higher quantity goes down and to the right along the curve. A movement to a higher price and lower quantity goes up and to the left.

Z \text{ fixed},\quad P_1>P_0 \quad\Longrightarrow\quad D(P_1;Z)<D(P_0;Z)

The inequality states the standard downward-sloping relationship: at the higher price $P_1$, buyers choose less than at the lower price $P_0$. Reversing the price comparison reverses the quantity comparison. These are two directions of movement on the same curve, not two different changes in demand.

Why a Price Change Produces a Movement

A demand curve is a mapping from price to quantity demanded under fixed conditions. Holding $Z$ constant means that $D(P;Z)$ remains the same relationship while its price input changes. The new quantity is therefore found by evaluating that same relationship at the new price.

Hold the curve’s conditions fixed.
Keep the good, market, time period, and other relevant conditions the same.

Identify the own-price change.
Compare the initial price with the new price, taking care to note whether price rose or fell.

Find quantity demanded at each price.
Read both quantities from the schedule or substitute both prices into the same demand equation.

Describe the movement.
A price fall with a quantity increase is an extension; a price rise with a quantity decrease is a contraction. The curve remains fixed.

This method follows directly from the model: if the function $D$ and the conditions $Z$ have not changed, only the input $P$ has changed. The resulting difference in $Q_d$ is a change in quantity demanded along the given function. If the conditions do not remain fixed, the comparison cannot automatically be interpreted as a pure movement along one unchanged curve.

Worked Example: Tracing a Price Change in a Schedule

A hypothetical campus shop records the weekly demand for insulated lunch containers while other relevant conditions are held fixed.

Price per container	Quantity demanded per week
$15	10
$12	16
$9	22

Method. Read the quantity paired with each price in the same schedule, then compare the two price-quantity pairs.

Price falls from $12 to $9. At $12, quantity demanded is 16 containers per week. At $9, it is 22. The quantity change is $22-16=6$ containers per week. Thus, the price decrease produces an extension of demand: the point moves from $(Q_d,P)=(16,12)$ to $(22,9)$ on the same curve.

Reverse direction. If price rises from $9 to $12, quantity demanded falls from 22 to 16, a decrease of 6 containers per week. This is a contraction along the same curve.

Check. The two movements reverse one another: the price changes by $3 in opposite directions, and the schedule shows quantities of 16 and 22 at those prices. The common mistake to avoid is saying the price decrease shifts demand; here it changes the chosen quantity on the existing schedule.

Using a Demand Equation

An equation provides the same comparison in algebraic form. Suppose a linear demand equation is $Q_d=a-bP$, where $a>0$, $b>0$, and the prices considered give nonnegative quantities. The negative coefficient on price means that an increase in price reduces quantity demanded in this model. To trace a movement, calculate $Q_d$ at both prices using the same values of $a$ and $b$.

Q_{d,0}=a-bP_0,\qquad Q_{d,1}=a-bP_1

Subtracting the initial quantity from the new quantity gives $Q_{d,1}-Q_{d,0}=-b(P_1-P_0)$. Since $b>0$, a positive price change produces a negative quantity change; a negative price change produces a positive quantity change. This algebra explains the movement’s direction without changing the equation or the curve.

Worked Example: Calculating an Extension From a Linear Demand Equation

A hypothetical repair cooperative models weekly demand for a replacement filter by $Q_d=84-4P$, where $P$ is the price in dollars and $Q_d$ is the number of filters per week. Find the movement when price falls from $9 to $7.

Method. Substitute each price into the same linear demand equation. The coefficient on price is negative, so the model predicts an extension when price falls, provided the calculated quantities are in the feasible range.

At $P=9$:

$$ Q_d=84-4(9)=84-36=48 $$

At $P=7$:

$$ Q_d=84-4(7)=84-28=56 $$

Quantity demanded rises by $56-48=8$ filters per week as price falls by $2. The movement is from $(48,9)$ to $(56,7)$ when points are written as $(Q_d,P)$. Both calculated quantities are nonnegative, so they are consistent with the stated range of this simple model.

Check. The equation implies that each $1 increase in price reduces quantity by 4 filters; a $2 decrease therefore increases quantity by $4(2)=8$, matching the direct calculation. Do not change the sign of the price coefficient when price falls: substituting the new price into the original equation gives the correct result.

Tracing a Market Movement

A market schedule or market demand equation can be used in the same way: compare market quantity demanded at two prices while treating the market’s other relevant conditions as fixed. If the market quantity is formed from several buyers’ quantities, each buyer’s quantity at a given price contributes to the market total. The calculations below use that total only to trace a change in the common price.

Worked Example: A Price Change Affecting Two Buyers

Two hypothetical buyers have weekly demand equations for a refillable water cartridge. Buyer A’s demand is $Q_A=24-2P$, and Buyer B’s is $Q_B=18-P$, where price $P$ is in dollars. Find total quantity demanded when price falls from $8 to $5, assuming both buyers and their other conditions are unchanged.

Method. Calculate each buyer’s quantity at each price, then add the quantities at that price. This identifies market quantity at both points without changing either individual equation.

At $P=8$, Buyer A demands $24-2(8)=24-16=8$ cartridges per week. Buyer B demands $18-8=10$. Total quantity is $8+10=18$.

At $P=5$, Buyer A demands $24-2(5)=24-10=14$ cartridges per week. Buyer B demands $18-5=13$. Total quantity is $14+13=27$.

As price falls by $3, market quantity demanded increases by $27-18=9$ cartridges per week. The market moves from $(18,8)$ to $(27,5)$, with coordinates shown as $(Q_d,P)$. The common mistake is to compare only one buyer’s quantities and report that as the market change; adding both buyers at each price gives the correct market totals.

Check. Buyer A’s quantity rises by $14-8=6$, and Buyer B’s rises by $13-10=3$. Their increases sum to $6+3=9$, which agrees with the increase in total quantity.

Common Mistakes and Exam Traps

The most important discipline is to separate the cause of the change from the result. An own-price change is the cause in this tutorial; the associated change in quantity demanded is the result. The curve stays fixed when the comparison holds other relevant conditions constant.

Reversing the direction: Saying that a price decrease reduces quantity demanded conflicts with the standard downward-sloping demand model. For example, $Q_d=84-4P$ gives 48 at $P=9$ and 56 at $P=7$, so the decrease in price raises quantity by 8.
Calling a movement a shift: A new point at a different own price does not mean the whole demand curve has changed. Keep the original schedule or equation when only price changes.
Mixing up graph coordinates: A graph point is often written $(Q_d,P)$ when quantity is on the horizontal axis and price is on the vertical axis. State the axis order before giving coordinates; otherwise $(16,12)$ could be misread.
Comparing different conditions: If the initial and final observations do not share the same relevant conditions, they may not lie on one fixed demand curve. Do not attribute the entire quantity difference to price without that condition.
Using a formula outside its range: A simple linear equation may predict negative quantity at sufficiently high prices. Check that calculated quantities are feasible and within the model’s stated range before interpreting them.

Key takeaway: For a fixed demand curve in the standard downward-sloping model, a fall in the good’s own price increases quantity demanded, and a rise in its own price decreases quantity demanded. Both are movements along the same curve, not changes in the curve itself.

Check Your Understanding

For each problem, identify the price direction, calculate the relevant quantities, and describe the movement along the fixed demand curve.

A schedule shows weekly demand of 48 units at a price of $4, 36 units at $6, and 24 units at $8. Price rises from $6 to $8. How does quantity demanded change, and what is the movement called? (Answer: Quantity falls from 36 to 24, a decrease of 12 units; this is a contraction along the curve.)
A hypothetical demand equation is $Q_d=70-5P$, with quantity per week and price in dollars. Calculate quantity demanded at prices of $6 and $8, then describe the change when price falls from $8 to $6. (Answer: At $6, $Q_d=40$; at $8, $Q_d=30$. The price decrease raises quantity by 10 units per week, an extension along the curve.)
Two buyers have weekly demands $Q_A=20-P$ and $Q_B=14-0.5P$, with $P$ in dollars. Find total quantity demanded at $10 and at $4, then describe the market movement when price falls from $10 to $4. (Answer: At $10, quantities are 10 and 9, for a total of 19. At $4, quantities are 16 and 12, for a total of 28. Market quantity rises by 9 units per week, an extension along the fixed market demand curve.)
A linear demand curve is $Q_d=100-10P$. Find the graph points at prices $3 and $5, written in $(Q_d,P)$ order, and state the movement when price rises from $3 to $5. (Answer: At $3, $Q_d=70$, giving $(70,3)$; at $5, $Q_d=50$, giving $(50,5)$. Quantity falls by 20, so the movement is a contraction up and to the left.)
A schedule gives 24 units at $14, 32 units at $12, and 40 units at $10, with other conditions fixed. A buyer reports a price fall from $14 to $10 and claims quantity demanded decreases. Use the schedule to evaluate the claim and quantify the change. (Answer: The claim is incorrect: quantity rises from 24 to 40, an increase of 16 units. This is an extension along the same curve.)

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