Why Compare Demand and Supply Away From Equilibrium?
A market price does not have to make buyers’ desired purchases equal sellers’ desired sales. At a particular price, consumers may want more of a good than firms offer, or firms may offer more than consumers want to buy. Comparing the two quantities identifies the direction and size of that imbalance. This calculation is useful for describing a market at a given price; by itself, it does not explain how the price will change.
The key is to evaluate both sides of the market at the same price, for the same good, over the same time period, and in the same quantity units. A comparison that mixes, for example, weekly demand with monthly supply does not measure a meaningful shortage or surplus.
A useful signed measure is net excess demand, \(Q_d(P)-Q_s(P)\). A positive value indicates a shortage; a negative value indicates a surplus, whose size is the absolute value of that negative amount. Some questions ask directly for excess supply instead, in which case calculate \(Q_s(P)-Q_d(P)\). State which quantity is larger and give the imbalance as a nonnegative amount to avoid ambiguity.
These quantities describe what buyers and sellers would like to buy and sell at the stated price according to the market schedules. They do not necessarily equal the number of units that actually change hands. If buyers want 100 units and sellers offer 70, the schedules show a shortage of 30 units, but they do not specify which buyers obtain the units or how sales are allocated.
How to Calculate the Imbalance
With equations, substitute the stated price into each equation separately before subtracting. With a table, read demand and supply from the row for the stated price. Then compare the quantities, classify the imbalance, and report its size with the schedule’s unit and time period. The following process keeps the calculation organized.
Confirm that demand and supply refer to the same good and time interval, such as boxes per week.
Substitute the price into both equations, or read both quantities from the matching schedule row.
For net excess demand, calculate quantity demanded minus quantity supplied. For excess supply, calculate quantity supplied minus quantity demanded.
Name a shortage or surplus, give its size, and retain the correct units. Convert units only after finding the difference if the answer requires a different unit.
Worked Calculations
Worked Example: Shortage From Linear Market Equations
A market’s weekly demand and supply are \(Q_d(P)=210-6P\) and \(Q_s(P)=30+3P\), where \(P\) is the price in dollars per unit and quantities are units per week. At a price of $15 per unit, calculate and interpret the imbalance.
Method. Evaluate each equation at $15, then subtract supply from demand to obtain net excess demand.
Quantity demanded. Substitute \(P=15\):
Quantity supplied. Use the same price:
Imbalance. Demand exceeds supply by:
At $15 per unit, the market has excess demand, or a shortage, of 45 units per week. The common mistake to avoid is subtracting the price from one quantity or using different prices in the two equations. Both schedules must be evaluated at the same price. As a check, the larger computed quantity is demand, so the classification must be a shortage.
Worked Example: Finding a Surplus From a Market Schedule
A market schedule gives the following weekly quantities:
| Price per unit | Quantity demanded (units per week) | Quantity supplied (units per week) |
|---|---|---|
| $8 | 145 | 92 |
| $10 | 124 | 116 |
| $12 | 103 | 140 |
Calculate the imbalance at $10 and at $12. State which price has a shortage and which has a surplus.
Method. Read both quantities from the row for each price. Do not combine a quantity from one row with a quantity from another.
At $10, quantity demanded is 124 and quantity supplied is 116. Therefore:
Demand is larger, so there is a shortage of 8 units per week at $10.
At $12, quantity demanded is 103 and quantity supplied is 140. Therefore:
Supply is larger, so there is a surplus of 37 units per week at $12. The common mistake to avoid is reporting \(103-140=-37\) as a “negative surplus.” The negative result is net excess demand; in words, it signals a surplus, and the surplus itself has size 37 units per week. The signs and comparisons agree with the table: at $10 demand is higher, while at $12 supply is higher.
Worked Example: Converting the Imbalance From Hundreds to Units
A market’s weekly quantities are measured in hundreds of boxes. Its schedules are \(Q_d(P)=460-8P\) and \(Q_s(P)=40+4P\), where \(P\) is the dollar price per box. At a price of $30, calculate the imbalance in both hundreds of boxes and individual boxes. Also express the shortage as a percentage of the quantity demanded, rounded to two decimals.
Method. First evaluate both equations in the units stated in the problem. Find the difference before converting the result to individual boxes.
Quantity demanded.
Quantity supplied.
Shortage in the schedule’s units.
Since one hundred boxes is 100 boxes, this difference is \(60\times100=6{,}000\) boxes per week. The percentage of quantity demanded represented by the shortage is:
Thus, at $30 per box, excess demand is 60 hundreds, or 6,000 boxes per week. The shortage equals 27.27% of the quantity demanded. The common mistake to avoid is treating 60 hundreds as 60 boxes. The check is dimensional: \(60\) hundreds multiplied by \(100\) boxes per hundred gives \(6{,}000\) boxes.
Why the Difference Measures the Imbalance
The subtraction follows directly from what the two schedule quantities represent. At a given price, \(Q_d(P)\) counts the units buyers would choose to purchase, while \(Q_s(P)\) counts the units sellers would choose to offer. If the former is larger, the amount buyers want beyond the amount sellers offer is the difference between them. For example, if buyers want 120 units and sellers offer 75, the portion of desired purchases not matched by desired sales is \(120-75=45\) units. This is why the shortage is measured as demand minus supply, not as their sum or their ratio.
The same reasoning works in the other direction. If sellers offer 140 units and buyers want 103, the amount offered beyond desired purchases is \(140-103=37\) units. In general:
These statements describe the relationship between planned purchases and planned sales at the specified price. They do not require that the full quantity demanded or supplied is actually traded. At a shortage, the quantity actually exchanged may be limited by the amount available; at a surplus, it may be limited by the amount buyers choose to purchase. A demand and supply schedule alone does not specify the allocation of actual trades.
Interpretation and Common Traps
A shortage or surplus is always relative to a stated price. The same market can have excess demand at one price and excess supply at another, as the schedule example illustrates. Therefore, “the market has a shortage” is incomplete unless the price and relevant period are clear. The number also needs a unit: a shortage of 45 units per week is not interchangeable with a shortage of 45 units per month.
Keep the following checks in mind when working a problem:
- Use one price. Evaluate both quantities at the price asked about, not at different schedule rows or different price values.
- Classify from the comparison. If \(Q_d>Q_s\), demand exceeds supply and there is a shortage. If \(Q_s>Q_d\), there is a surplus.
- Distinguish sign from size. A negative value of \(Q_d-Q_s\) indicates a surplus; it is not a negative number of surplus units.
- Preserve units and periods. Check whether quantities are units, hundreds of units, or another scale, and whether they are measured daily, weekly, or over a different period.
- Do not equate imbalance with completed trades. The difference between desired demand and supply is not automatically the number of units actually bought and sold.
A final consistency check is often enough to catch a reversed subtraction: look first at which quantity is greater. If demand is greater, the answer must describe a shortage; if supply is greater, it must describe a surplus. Then verify that the reported size is the positive difference between the two quantities.
Check Your Understanding
For each problem, compare quantities at the stated price and include the direction of the imbalance. Keep the units in the answer.
- A market has \(Q_d(P)=150-5P\) and \(Q_s(P)=30+P\), with quantities in units per week and price in dollars per unit. At \(P=15\), calculate the imbalance. (Answer: Shortage of 30 units per week.)
- A schedule reports demand of 84 crates per day and supply of 102 crates per day at a price of $9 per crate. What is the imbalance? (Answer: Surplus of 18 crates per day.)
- In a market measured in units per month, \(Q_d(P)=500-10P\) and \(Q_s(P)=100+5P\). At a price of $20, calculate the excess demand or excess supply. (Answer: Shortage of 100 units per month.)
- A market’s schedules are \(Q_d(P)=720-12P\) and \(Q_s(P)=120+8P\), with quantities in dozens of items per week. At a price of $25, find the shortage in dozens and then convert it to individual items. (Answer: Shortage of 100 dozen, or 1,200 items, per week.)
- At a price of $15 per case, weekly demand is 110 cases. Two supplier groups offer \(10+2P\) and \(20+P\) cases per week, respectively, where \(P\) is the price in dollars per case. Find total supply and the market imbalance. (Answer: Total supply is 75 cases per week; shortage is 35 cases per week.)