Introduction: Price Changes and the Supply Curve
A supply curve describes how much of a good producers are willing and able to sell at different prices, with other relevant conditions held fixed. If the good’s own price changes while those other conditions remain unchanged, the quantity supplied changes. On a graph, this is a movement along the same supply curve, not a change in the supply curve itself.
The distinction is about what changed. A different price is a change in one coordinate on the existing curve; a different supply relationship would mean that the curve itself had changed. This tutorial focuses on tracing the first case using schedules, functions, and graphs. It is aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus.
Reading a Movement from a Supply Schedule
A supply schedule lists the quantity producers will supply at each price under the conditions described by that schedule. Each row is one point on the supply curve. If price rises, the usual upward-sloping supply relationship implies that quantity supplied rises as well; the graph shows a movement up and to the right. If price falls, quantity supplied usually falls, and the movement is down and to the left.
For a standard supply graph, price is on the vertical axis and quantity is on the horizontal axis. A point with quantity \(Q\) and price \(P\) can therefore be written as \((Q,P)\). A change in price changes the vertical coordinate. The associated change in quantity supplied changes the horizontal coordinate. Both points remain on the same curve when the underlying supply relationship is unchanged.
| What changes? | What happens? | Graph interpretation |
|---|---|---|
| The good’s own price; other conditions are fixed | Quantity supplied changes | Movement along the same supply curve |
| The supply relationship itself | The quantity producers supply at a given price changes | The supply curve changes position |
The table summarizes the key diagnostic question: Did the good’s own price change, or did the supply relationship change? For this tutorial, assume the supply relationship stays fixed. The earlier material on ceteris paribus and supply shifters explains why holding other conditions fixed matters; here, the task is to trace the resulting movement when price varies.
Worked Example: Moving Between Rows in a Supply Schedule
A hypothetical producer’s weekly supply schedule is shown below. Assume the schedule’s underlying conditions do not change. If the market price rises from $10 to $15 per unit, find the change in quantity supplied and describe the movement on a standard supply graph.
| Price per unit | Quantity supplied per week |
|---|---|
| $5 | 20 |
| $10 | 32 |
| $15 | 44 |
Step 1: Read the initial quantity. At a price of $10, the schedule gives a quantity supplied of 32 units per week.
Step 2: Read the new quantity. At a price of $15, the schedule gives a quantity supplied of 44 units per week.
Step 3: Calculate the change. The change in quantity supplied is \(44-32=12\) units per week. Price rose by \(15-10=\$5\) per unit.
Step 4: Describe the graph movement. With quantity on the horizontal axis and price on the vertical axis, the initial point is \((32,10)\) and the new point is \((44,15)\). The movement is up and to the right along the same curve because the schedule is unchanged.
Check. Both points are entries in the same schedule, and the higher price is paired with the higher supplied quantity. The calculation avoids the common mistake of calling the increased quantity a shift in supply: only the own price changed.
Using a Supply Function to Trace the Change
A supply function expresses quantity supplied as a rule for a given price. For a simple linear example, write \(Q_s=a+bP\), where \(Q_s\) is quantity supplied, \(P\) is the good’s own price, \(a\) and \(b\) are fixed parameters, and \(b>0\). This model assumes that the linear relationship applies over the prices being considered and that the other conditions represented by the function do not change. The positive value of \(b\) means that a higher price is associated with a higher quantity supplied over that range.
To trace a price change, substitute each price into the same function. Do not change its parameters just because the price changes. If the function gives two different quantities, those quantities correspond to two points on one curve.
Worked Example: Evaluating a Supply Function at Two Prices
A hypothetical workshop’s weekly supply is described, over the relevant price range, by \(Q_s=3P-12\), where \(P\) is dollars per unit and \(Q_s\) is units per week. The price rises from $8 to $11. Find both quantities, the change in quantity supplied, and the graph coordinates.
Method and assumption. Use the same linear supply function at both prices. Its parameters are fixed, and the prices $8 and $11 are assumed to lie within the range where the function applies.
Step 1: Calculate the initial quantity. At \(P=8\), \(Q_s=3(8)-12=24-12=12\) units per week.
Step 2: Calculate the new quantity. At \(P=11\), \(Q_s=3(11)-12=33-12=21\) units per week.
Step 3: Find the change. Quantity supplied changes by \(21-12=9\) units per week as price changes by \(11-8=\$3\) per unit.
Step 4: Place the points on the graph. With quantity on the horizontal axis, the initial point is \((12,8)\), and the new point is \((21,11)\). The movement is up and to the right, and both points are generated by \(Q_s=3P-12\).
Check. Substituting either point’s price into the stated function returns its quantity. A common mistake is to treat the new quantity, 21, as evidence that the curve shifted. It is instead the quantity supplied at the new price on the original curve.
Why the Price Change Produces a Movement
The logic can be stated directly from the definition of a supply curve. A supply curve records the quantities associated with different prices while the supply relationship is held fixed. Therefore, when price changes, the producer moves to the quantity paired with that new price by the same relationship. The curve changes only if the relationship used to pair prices and quantities changes; that is not the situation considered here.
For the linear case \(Q_s=a+bP\), compare quantities at two prices:
The fixed intercept \(a\) cancels because it is the same at both prices. With \(b>0\), if \(P_2>P_1\), then \(b(P_2-P_1)>0\), so \(Q_{s2}>Q_{s1}\). If \(P_2<P_1\), then \(b(P_2-P_1)<0\), so \(Q_{s2}<Q_{s1}\). This shows why the price change traces a movement along the same upward-sloping linear curve: the rule and its parameters stay fixed while the input price changes.
This derivation depends on the stated linear model and \(b>0\). It does not establish that every real supply relationship is linear, nor does it determine how much quantity changes in a different model. For a schedule, the same reasoning is applied by comparing its entries rather than using the linear equation.
Worked Example: A Price Fall on the Same Supply Curve
A hypothetical supplier has the weekly supply function \(Q_s=4P+2\), with \(P\) measured in dollars per unit. Assume the function applies at prices of $9 and $6 and that its parameters remain fixed. Price falls from $9 to $6. Calculate the two quantities, describe the graph movement, and check the change using the function’s slope.
Step 1: Evaluate the function at the initial price. At \(P=9\), \(Q_s=4(9)+2=36+2=38\) units per week.
Step 2: Evaluate it at the new price. At \(P=6\), \(Q_s=4(6)+2=24+2=26\) units per week.
Step 3: Calculate the changes. Price changes by \(6-9=-\$3\) per unit. Quantity supplied changes by \(26-38=-12\) units per week.
Step 4: Describe the movement. The initial point is \((38,9)\), and the new point is \((26,6)\). The movement is down and to the left along the same curve.
Step 5: Check with the slope. Here \(b=4\), so the change in quantity must be \(b(P_2-P_1)=4(6-9)=4(-3)=-12\) units. This matches the direct calculation.
Check. The lower price produces the lower quantity in this upward-sloping supply function. The common mistake is to call the lower quantity a decrease in supply; with no change in the function’s parameters, it is a decrease in quantity supplied along the same curve.
Reading Tables and Graphs Carefully
A reliable way to answer a movement question is to identify the two prices first, then read or calculate the corresponding quantities. State the initial and new price-quantity pairs explicitly. This helps prevent swapping axes: on the usual supply graph, price is vertical and quantity is horizontal, even though a function may be written with quantity on its left-hand side.
Identify the good’s own initial and new prices. The question is about movement along supply only when the supply relationship is held fixed.
Use the same schedule or function for both prices. Do not alter the function’s parameters between calculations.
Report the change in quantity supplied and plot each pair as \((Q,P)\). For an upward-sloping relationship, a price rise moves up and right; a price fall moves down and left.
A graph question may ask only for the direction of movement, but a precise answer should still name both the price change and its quantity-supplied counterpart. For example, “price falls, so quantity supplied falls along the same curve” is clearer than “supply falls,” which can incorrectly imply a change in the curve itself.
Common Exam Trap: Calling a Movement a Shift
The terms quantity supplied and supply are not interchangeable. A change in the good’s own price changes quantity supplied on the given curve. A change in the curve itself means that the supply relationship has changed. When the prompt says that price changed and all other conditions stayed fixed, use the first interpretation.
For example, suppose a schedule gives 30 units at a price of $6 and 42 units at a price of $9. The incorrect description is “supply increased by 12 units, so the supply curve shifted right.” That wording treats the change in quantity at different prices as a curve shift. The corrected calculation is \(42-30=12\) additional units supplied when price rises by $3, represented by a movement from \((30,6)\) to \((42,9)\) along the same schedule.
The schedule supports that conclusion because both points belong to the same stated relationship. If a question does not say whether other conditions changed, do not assume that observed price and quantity data alone establish why the relationship changed. For a straightforward movement problem, follow the stated assumption that other conditions are fixed.
Check Your Understanding
For each problem, use the stated unchanged supply schedule or function and distinguish the change in quantity supplied from a change in the supply curve.
- A schedule lists 18 units at $4 per unit and 30 units at $7 per unit. Price rises from $4 to $7. Find the change in quantity supplied and give the initial and new graph coordinates in \((Q,P)\) order. (Answer: Quantity supplied rises by 12 units; the movement is from \((18,4)\) to \((30,7)\) along the same curve.)
- A hypothetical producer has \(Q_s=2P+6\). Price falls from $8 to $5, and the function remains applicable. Calculate both quantities and describe the movement. (Answer: \(Q_s\) falls from 22 to 16 units, a decrease of 6; movement down and left along the same curve.)
- A supply schedule gives 14 units at $3, 22 units at $5, and 30 units at $7. Price changes from $7 to $3. State the quantity change and graph movement. (Answer: Quantity supplied falls from 30 to 14 units, a decrease of 16; movement from \((30,7)\) to \((14,3)\), down and left along the same curve.)
- A hypothetical supply function is \(Q_s=5P-10\), applicable at prices of $6 and $9. Find the two quantities and verify the quantity change using the coefficient on price. (Answer: Quantities are 20 and 35 units; quantity supplied rises by 15 because \(5(9-6)=15\); movement up and right along the same curve.)
- A schedule has a quantity supplied of 40 units at $10 and 32 units at $8, with all other conditions fixed. A student says, “Supply decreased by 8 units, so the curve shifted left.” Correct the student’s interpretation and identify the graph movement. (Answer: Quantity supplied decreased by 8 units as price fell; this is a movement from \((40,10)\) to \((32,8)\) down and left along the same curve, not a shift.)