Why a Demand Shift Changes Equilibrium
A change in demand can alter both the market-clearing price and quantity, even when producers’ conditions have not changed. For a market analyst, the first task is to identify what has shifted: a change in buyers’ willingness to purchase at each price shifts the demand curve, while a price change alone produces a movement along that curve.
This tutorial considers a demand shift with supply held fixed. Assume a competitive market in which the supply curve slopes upward and the demand curve slopes downward. The curves are continuous and intersect at a unique equilibrium. Under these assumptions, an increase in demand raises both equilibrium price and quantity; a decrease in demand lowers both. The graph and the market imbalance at the original price explain why.
Let \(P\) denote price, \(Q_D\) quantity demanded, and \(Q_S\) quantity supplied. Market equilibrium occurs at a price and quantity for which \(Q_D=Q_S\). On a standard graph, price is on the vertical axis and quantity on the horizontal axis. The upward-sloping supply curve and downward-sloping demand curve cross at the initial equilibrium. A demand shift changes the demand curve’s position; if supply is unchanged, the supply curve stays where it is.
The Direction of the New Equilibrium
Suppose demand increases. At the old equilibrium price, buyers now want more than sellers offer, so there is a shortage. The price is therefore under upward pressure. As price rises, sellers move upward along the unchanged supply curve and offer more. Buyers move upward along the new demand curve and want less than they did at the old price. The adjustment continues until the quantities demanded and supplied match.
The new intersection is above and to the right of the old intersection: equilibrium price and quantity are both higher. For a demand decrease, the reasoning reverses. At the old price, sellers offer more than buyers want, creating a surplus. Downward pressure on price moves the market along the unchanged supply curve toward a new intersection that is lower and to the left.
The imbalance at the old price provides a concise justification for the result. At the original equilibrium, \(Q_D=Q_S\). If demand increases, then at that same price \(Q_D\) becomes greater than the unchanged \(Q_S\). Price rises to eliminate the shortage. Along an upward-sloping supply curve, that higher price corresponds to greater quantity supplied, so the new equilibrium quantity is higher. If demand decreases, quantity demanded at the old price falls below quantity supplied. Price falls, and movement down the supply curve means a lower quantity supplied at the new equilibrium.
This direction-of-change result depends on the slopes and the assumption that supply is fixed. With vertical supply, quantity is fixed, so a demand shift changes equilibrium price but not quantity. With horizontal supply, price is fixed, so a demand shift changes equilibrium quantity but not price. If a curve has a different shape or the market does not have a unique equilibrium, the simple prediction may need qualification.
Worked Examples
Worked Example: A Preference Change Raises Demand
Suppose a hypothetical market for reusable shipping containers has supply \(Q_S=10+2P\) and initial demand \(Q_D=70-2P\), where price is measured in dollars per container and quantities are measured in hundreds of containers per month. A new buyer preference increases demand to \(Q_D=82-2P\), with supply unchanged. Find the old and new equilibria, and explain the direction of the change.
Method. First find each intersection by setting quantity supplied equal to quantity demanded. Then check that both curves give the same quantity. The common mistake avoided here is to identify the demand increase but forget that the new equilibrium must be checked against the unchanged supply curve.
Old equilibrium. Set the initial quantities equal:
Adding \(2P\) to both sides and subtracting 10 gives \(4P=60\), so \(P=15\). Substituting into supply gives \(Q_S=10+2(15)=40\). Substituting into initial demand gives \(Q_D=70-2(15)=40\). The old equilibrium is \(P=\$15\), \(Q=40\) hundred containers per month.
New equilibrium. Set unchanged supply equal to shifted demand:
Adding \(2P\) to both sides and subtracting 10 gives \(4P=72\), so \(P=18\). Supply at this price is \(10+2(18)=46\); shifted demand is \(82-2(18)=46\). Thus the new equilibrium is \(P=\$18\), \(Q=46\) hundred containers per month. Both price and quantity have increased, as the graph predicts.
Worked Example: Lower Income Reduces Demand for a Normal Good
In a hypothetical market for home-delivery meal kits, supply is \(Q_S=4+P\). Initial demand is \(Q_D=40-2P\). After household income falls, demand decreases to \(Q_D=28-2P\). Price is in dollars per kit and quantity is in thousands of kits per week. Treat meal kits as a normal good in this scenario, and assume supply is unchanged. Find both equilibria and the imbalance at the old price after the shift.
Method. Solve the market-clearing condition before and after the demand change, then compare demand and supply at the old price. The common mistake avoided is to say that a demand decrease itself creates a surplus at every price; it creates a surplus at the old equilibrium price, while the new equilibrium is found at a different price.
Old equilibrium. Equate the initial schedules:
Adding \(2P\) and subtracting 4 gives \(3P=36\), so \(P=12\). Supply is \(4+12=16\), and initial demand is \(40-2(12)=16\). The old equilibrium is \(P=\$12\), \(Q=16\) thousand kits per week.
Imbalance at the old price. At \(P=12\), unchanged supply remains \(4+12=16\). New demand is \(28-2(12)=4\). Therefore, at the old price, supply exceeds demand by \(16-4=12\) thousand kits per week: there is a surplus.
New equilibrium. Set supply equal to the decreased demand:
Adding \(2P\) and subtracting 4 gives \(3P=24\), so \(P=8\). Supply is \(4+8=12\), and new demand is \(28-2(8)=12\). The new equilibrium is \(P=\$8\), \(Q=12\) thousand kits per week. Both equilibrium price and quantity are lower than before.
Worked Example: Read the New Intersection From a Schedule
A hypothetical market has supply and initial demand recorded at selected prices. Between listed prices, each schedule is linear. At prices of $2, $4, and $6, supply quantities are 8, 14, and 20 units, while initial demand quantities are 20, 14, and 8 units. A shift in buyer preferences raises demand by 6 units at each listed price, and supply is unchanged. Find the initial and new equilibrium, using interpolation where needed.
Method. Identify the initial intersection from the table, shift demand at each price, and find where the shifted demand intersects supply. The common mistake avoided is choosing a plausible price without checking both quantities at that price.
At \(P=4\), initial demand and supply are both 14, so the old equilibrium is \(P=\$4\), \(Q=14\). After the increase, demand at prices $2, $4, and $6 is respectively \(20+6=26\), \(14+6=20\), and \(8+6=14\).
The new equilibrium lies between $4 and $6: at $4, supply is 14 and shifted demand is 20; at $6, supply is 20 and shifted demand is 14. Linear interpolation halfway between those prices gives supply halfway between 14 and 20:
Shifted demand falls linearly from 20 at \(P=4\) to 14 at \(P=6\). At \(P=5\), it is:
Both quantities equal 17, so the new equilibrium is \(P=\$5\), \(Q=17\) units. The price and quantity rise, and the equality check confirms the intersection.
Common Mistakes and Their Corrections
A demand shift changes the demand curve at each price; it is not a change in the good’s own price. That distinction matters because a price change leads to movement along the current demand curve, while a demand shifter creates a new curve. For example, a change in buyers’ preferences can shift demand. A resulting price increase is then movement along the new demand curve as the market adjusts.
Another frequent error is to report the direction of the demand shift as the direction of equilibrium quantity without considering supply and the new intersection. The familiar result that both price and quantity rise after a demand increase assumes an upward-sloping supply curve. In the vertical-supply case, quantity cannot rise; the price absorbs the demand change instead.
For numerical work, always check the proposed equilibrium by evaluating both schedules at the proposed price. A price can lie between the old and new prices and still fail to clear the market. In the schedule example, at \(P=4\), unchanged supply is 14 while shifted demand is 20, so the old price is not the new equilibrium. At \(P=5\), both quantities are 17, which verifies the answer.
Check Your Understanding
For each problem, identify the demand change, predict the direction first, and then check the result using the supplied information.
- A market has \(Q_S=6+2P\) and initial demand \(Q_D=54-2P\). Demand increases to \(Q_D=66-2P\), with supply fixed. Find the old and new equilibrium price and quantity. (Answer: Old \(P=12,\ Q=30\); new \(P=15,\ Q=36\).)
- Supply and initial demand are linear between the listed prices. At \(P=3\), supply is 12 and demand is 28; at \(P=7\), supply is 28 and demand is 12. Demand then decreases by 8 units at every price. Find the new equilibrium using interpolation. (Answer: \(P=4,\ Q=16\).)
- Suppose a fixed vertical supply curve provides exactly 50 units. Demand increases, and the downward-sloping demand curve crosses that supply curve at a higher price than before. What happens to equilibrium price and quantity? (Answer: Price rises and quantity remains 50 units.)
- A hypothetical market has \(Q_S=10+P\) and initial demand \(Q_D=50-P\). Demand decreases to \(Q_D=42-P\). Find the initial and new equilibrium, then state the surplus at the old price after demand shifts. (Answer: Old \(P=20,\ Q=30\); new \(P=16,\ Q=26\); surplus at the old price is 8 units.)