Income and Demand for a Normal Good
A household with more purchasing power may choose to buy more of some products, even if the product’s price has not changed. That response is central to understanding a normal good. The key comparison is not how much a consumer buys at two different prices; it is how the consumer’s purchase plans differ at the same price when income changes.
The earlier material on demand shifts distinguishes a change in demand from a change in quantity demanded. An income change, with the product’s price and other relevant conditions held constant, changes the demand schedule. If the good is normal, higher income shifts demand to the right, and lower income shifts it to the left.
What “Shifts Right” Means
A demand curve records the quantity buyers plan to purchase at each possible price, with other relevant conditions held constant. To test whether a good is normal, compare the quantities demanded at one or more identical prices before and after the income change. If income rises and the quantity demanded is greater at each price in the relevant range, the new demand curve lies to the right of the original curve.
“Right” refers to a greater quantity on the horizontal axis at a given price. It does not mean that the product’s price has risen, nor does it require the new curve to be parallel to the old one. A simple linear model may produce parallel curves, but the definition of a normal good requires only the positive demand response to income.
The comparison assumes the product’s price, preferences, expectations, number of buyers and other relevant conditions are unchanged. In particular, if income is reported in dollars, treat the income change as a change in purchasing power for this comparison. If the product price also changes, an observed quantity change alone does not identify the income effect: the price change may also alter quantity demanded.
Worked Example: Reading Two Demand Schedules
A hypothetical household plans monthly purchases of a meal-kit subscription at the prices shown. Its monthly income rises from $3,000 to $3,600. Preferences and all other relevant conditions are unchanged. Determine whether the subscription is normal over this income change and state the direction of the demand shift.
| Price per kit | Quantity at $3,000 income | Quantity at $3,600 income |
|---|---|---|
| $20 | 2 | 3 |
| $30 | 1 | 2 |
| $40 | 0 | 1 |
Method. Compare quantities at the same price, rather than comparing entries from different rows. At $20, quantity rises from 2 to 3 kits, an increase of \(3-2=1\). At $30, it rises from 1 to 2, also an increase of \(2-1=1\). At $40, it rises from 0 to 1, again an increase of \(1-0=1\).
The quantity demanded is higher at every listed price after income rises. Therefore, this subscription is a normal good for this household over the stated income change, and its demand curve shifts right. The comparison does not say that the household buys the same quantity at every price; it says that at each matched price, its purchase plan increases.
Common mistake avoided: Comparing the old quantity at $20 with the new quantity at $30 would mix an income change with a price change. The matched-price comparisons isolate the response to income.
Using a Demand Equation
A demand equation can make the fixed-price comparison explicit. Suppose quantity demanded depends on the product’s price and income, written as \(Q_d(P,Y)\), where \(P\) is the product’s price and \(Y\) is income. For a normal good, increasing \(Y\) while holding \(P\) and the other conditions constant gives a higher \(Q_d\) over the range being considered.
For a linear equation, an income term that increases quantity demanded makes that relationship visible. The coefficient and units must be interpreted according to the equation: if income is measured in thousands of dollars, a one-unit change in \(Y\) means a $1,000 income change, not a $1 change.
Worked Example: Calculating a Linear Demand Shift
A hypothetical household’s monthly demand for a particular service is represented, over the relevant range, by \(Q_d=120-4P+2Y\), where \(Q_d\) is subscriptions per month, \(P\) is the monthly price in dollars, and \(Y\) is monthly household income in thousands of dollars. Income rises from $20,000 to $25,000 per month. Assume the equation remains valid at both incomes and all other demand conditions are unchanged. Calculate the old and new quantities at prices of $10 and $15, then describe the shift.
Method. Convert the incomes to the equation’s units: the old income is \(Y=20\), and the new income is \(Y=25\). At \(P=10\) and the old income, \(Q_d=120-4(10)+2(20)=120-40+40=120\) subscriptions.
At \(P=10\) and the new income, \(Q_d=120-4(10)+2(25)=120-40+50=130\) subscriptions. Thus, at this fixed price, quantity demanded increases by \(130-120=10\).
At \(P=15\) and the old income, \(Q_d=120-4(15)+2(20)=120-60+40=100\) subscriptions. At the same price and new income, \(Q_d=120-4(15)+2(25)=120-60+50=110\) subscriptions. The increase at this price is \(110-100=10\).
At both tested prices the higher income adds 10 subscriptions to quantity demanded. The good is normal under this model over the stated income change, and the demand curve shifts right. The equation gives parallel shifts because the income term adds the same amount at each price; that parallel shape follows from this particular equation, not from the definition of a normal good.
Common mistake avoided: Substituting $25,000 directly for \(Y\) would use the wrong units. Here \(Y\) is measured in thousands of dollars, so the correct substitution is \(Y=25\).
Why a Positive Income Response Shifts Demand
The logic can be stated directly from the definition. Let the original income be \(Y_1\), the higher income be \(Y_2\), and consider any fixed price \(P\). For a normal good over this range, the defining condition is \(Y_2>Y_1\) and \(Q_d(P,Y_2)>Q_d(P,Y_1)\). Since this comparison holds at each price in the relevant range, the new demand schedule specifies greater quantities at those prices. On a graph with price vertical and quantity horizontal, greater quantities at the same prices place the new curve to the right.
For the linear equation in the previous example, the same conclusion can be verified by subtraction. If \(Q_d=120-4P+2Y\), then at any fixed \(P\), the change in quantity when income moves from \(Y_1\) to \(Y_2\) is
The price terms and the constant cancel because price is held fixed. If \(Y_2>Y_1\), then \(2(Y_2-Y_1)>0\), so quantity demanded rises at every fixed price for which the model applies. This is why the curve shifts right. Reversing the comparison, \(Y_2<Y_1\) gives \(2(Y_2-Y_1)<0\), so quantity demanded falls at each fixed price and the curve shifts left. The direction for falling income is the reverse of the normal good’s rising-income response.
From Individual Responses to Market Demand
Market demand is the sum of the quantities demanded by all buyers at each price. If the buyers’ numbers and composition stay fixed, and each group’s demand rises at a given price when its income rises, adding those quantities gives a higher market quantity at that price. The market demand curve therefore shifts right. If income falls and those groups reduce their quantities at fixed prices, market demand shifts left.
This conclusion depends on the assumptions. A change in the number of buyers, the mix of buyers, or another demand condition may also affect market demand. To attribute a shift to income alone, keep those factors fixed or account for them separately.
Worked Example: Combining Two Buyer Groups
A hypothetical market has 40 households in Group A and 60 households in Group B. Every household’s income rises, and the following quantities are average monthly purchases per household. Assume group sizes, product prices, preferences and all other relevant conditions remain unchanged. Determine the market quantity at each listed price before and after the income rise.
| Price | Group A before | Group A after | Group B before | Group B after |
|---|---|---|---|---|
| $8 | 1 | 2 | 2 | 3 |
| $12 | 0 | 1 | 1 | 2 |
Method. Multiply each group’s average purchase by the number of households in that group, then add the group totals at the same price. At $8 before the income rise, market quantity is \(40(1)+60(2)=40+120=160\) units per month. After the rise it is \(40(2)+60(3)=80+180=260\) units per month. The increase is \(260-160=100\) units.
At $12 before the rise, market quantity is \(40(0)+60(1)=0+60=60\) units per month. After the rise it is \(40(1)+60(2)=40+120=160\) units per month. The increase is \(160-60=100\) units.
Both groups demand more at each fixed price, and the market total is higher at both prices. Market demand shifts right. Because the group sizes are fixed, these calculations isolate the change in purchase plans rather than a change in the number of buyers.
Common mistake avoided: Adding the two groups’ per-household quantities without weighting by group size would not give market demand. For example, at $8 after the rise, \(2+3=5\) is not the market total; the correct total is \(40(2)+60(3)=260\).
Separating an Income Shift from a Price Change
A change in observed purchases does not, by itself, show that income caused a demand shift. If price changes as well, part of the quantity change may be a movement along a demand curve. To identify the income-related shift, compare quantities at the same price, using a schedule or equation. Then consider a price change separately at a fixed income.
Worked Example: Avoiding a Mixed-Change Comparison
A hypothetical demand equation is \(Q_d=150-5P+Y\), where \(Q_d\) is units per month, \(P\) is the price in dollars, and \(Y\) is income in thousands of dollars per month. Initially, \(P=10\) and \(Y=20\). Later, the price is $8 and income is $25. Assume the model applies at both points and other demand conditions are unchanged. Find the observed quantity at each point, then isolate the income-driven shift by comparing quantities at a common price.
Method. Initially, \(Q_d=150-5(10)+20=150-50+20=120\) units. Later, \(Q_d=150-5(8)+25=150-40+25=135\) units. The observed increase is \(135-120=15\) units, but both price and income changed, so this comparison alone does not isolate the income effect.
Hold price at its initial value of $10 and change only income to \(Y=25\): \(Q_d=150-5(10)+25=150-50+25=125\) units. The income change therefore raises quantity at $10 by \(125-120=5\) units. At that higher income, reducing price from $10 to $8 raises quantity from 125 to 135, a further 10 units.
The calculations reconcile: the total observed increase is \(5+10=15\) units. Because the income increase raises quantity at the same price, this good is normal under the model over the stated range. The income-related demand shift is to the right; the additional change from the lower price is not itself a shift.
Common mistake avoided: Calling all 15 additional units an income effect confuses two changes. The fixed-price comparison shows that 5 units are associated with higher income; the other 10 arise from the lower price in this model.
Common Mistakes and Practical Checks
- Confusing a shift with movement along demand. A price change changes quantity demanded along a given curve; an income change, with price fixed, shifts the curve for a normal good.
- Comparing quantities at different prices. Use matched prices to identify the income response. Otherwise, price may be contributing to the difference.
- Assuming every good is normal. The classification must be established from the good’s response to income for the consumer or group and range in question.
- Assuming every normal-good shift is parallel. A rightward shift means more quantity at each fixed price; the shift’s shape or size can vary.
- Ignoring units in an equation. Check whether income is measured in dollars, thousands of dollars, or another unit before substituting values.
Check Your Understanding
For each problem, compare quantities at a fixed price before deciding whether income shifts demand.
- A household’s monthly demand for a hypothetical pantry box is 4 boxes at $15 and 2 boxes at $25 when income is $2,400. After income rises to $2,800, its quantities are 5 boxes at $15 and 3 boxes at $25. Is the good normal over this income change, and which way does demand shift? (Answer: Yes; quantity rises by 1 box at each listed fixed price, so demand shifts right.)
- A model for monthly demand is \(Q_d=90-3P+Y\), where \(P\) is dollars and \(Y\) is income in thousands of dollars. Income rises from $18,000 to $22,000. Calculate quantity at \(P=12\) for both incomes and state the shift. (Answer: At \(Y=18\), \(Q_d=90-36+18=72\); at \(Y=22\), \(Q_d=90-36+22=76\). Quantity rises by 4, so demand shifts right.)
- In a hypothetical market, 25 buyers each demand 2 units at $6 before an income rise and 3 units afterward. Another 15 buyers each demand 4 units before and 5 afterward. Calculate market quantity at $6 before and after, and give the shift direction. (Answer: Before, \(25(2)+15(4)=50+60=110\) units; after, \(25(3)+15(5)=75+75=150\) units. Market demand shifts right.)
- A model is \(Q_d=100-2P+2Y\), with \(Y\) measured in thousands of dollars. Initially \(P=10\), \(Y=15\); later \(P=8\), \(Y=17\). Find the initial and later quantities, then calculate the income-only change by holding price at $10. (Answer: Initially \(100-20+30=110\); later \(100-16+34=118\). At \(P=10\) and \(Y=17\), quantity is \(100-20+34=114\), so the income-only increase is 4 units.)
- At a fixed price of $30, a buyer’s planned quantity rises from 1 to 2 after income increases. At a different price of $20, the quantity falls from 3 to 2 over the same income change. Based on these data, is the good normal over the stated range at both prices, and can one conclude that its demand curve shifts right throughout the listed price range? (Answer: No. The income response is positive at $30 but negative at $20, so the data do not support classifying it as normal throughout the listed price range or concluding that demand shifts right at both prices.)