Income and Demand for Inferior Goods
A household’s income can change the amount it plans to buy even when the good’s own price has not changed. For some goods, higher income leads consumers to buy less: as their budgets expand, they switch toward alternatives or allocate more spending elsewhere. These goods are called inferior goods. The term describes a pattern in consumer demand, not a judgment about the good’s quality.
The key comparison is between quantities demanded at different income levels while holding the good’s price and other relevant conditions constant. If income rises and the quantity demanded falls at each given price, demand shifts left. If income falls, the quantity demanded of an inferior good rises at each given price, shifting demand right. These are changes in demand, not movements along a fixed demand curve.
“Other things equal” matters. A comparison meant to identify the income effect must hold the good’s own price fixed, along with other influences on demand. If price changes at the same time as income, a change in purchases alone does not show which change caused it. Earlier material on demand shifts establishes the graphing convention used here: price is on the vertical axis, quantity on the horizontal axis, and a shift changes planned quantity at a given price.
Reading the Direction of the Shift
For an inferior good, higher income reduces the quantity consumers plan to buy at every fixed price. On a conventional demand graph, each price therefore corresponds to a smaller quantity, so the demand curve shifts left. When income falls, planned quantity is higher at each fixed price, so the curve shifts right. The curve is not becoming a different kind of curve merely because income changed; it represents a new set of purchase plans under the new income condition.
| Change in income | Quantity demanded for an inferior good, at a fixed price | Demand-curve shift |
|---|---|---|
| Income rises | Decreases | Left |
| Income falls | Increases | Right |
A linear demand equation makes the relationship especially visible. Consider the hypothetical model \(Q_d=a-bP-cY\), where \(Q_d\) is quantity demanded, \(P\) is the good’s own price, \(Y\) is income, and \(a\), \(b\), and \(c\) are positive constants. The model applies only over a range where it gives economically meaningful, nonnegative quantities. The negative coefficient on income means that, holding price fixed, an increase in income lowers quantity demanded.
To see the shift directly, compare two income levels, \(Y_1\) and \(Y_2\), at the same price. Subtract the quantity at the first income from the quantity at the second:
If income rises, then \(Y_2>Y_1\), so \(-c(Y_2-Y_1)<0\): quantity demanded is lower at that price. Because the result holds for every price in the model’s relevant range, the entire demand curve shifts left. If income falls, the difference is positive and the curve shifts right. This is a comparative-static argument: it compares demand at two income levels while keeping the other specified conditions unchanged.
Worked Example: Rising Income and a Leftward Shift
Suppose a hypothetical market for a basic packaged meal is represented, over the relevant range, by \(Q_d=100-5P-0.01Y\). Quantity is measured in meals per week, price \(P\) in dollars per meal, and annual household income \(Y\) in dollars. Find the demand equations at incomes of $2,000 and $4,000, compare quantities at two prices, and state the shift.
Method. Substitute each income into the demand equation, then compare quantities at identical prices. This avoids mistaking an income shift for a price-related movement along demand.
At \(Y=\$2{,}000\), the income term is \(0.01(2{,}000)=20\). Thus:
At \(Y=\$4{,}000\), the income term is \(0.01(4{,}000)=40\). Thus:
At \(P=\$4\), quantity at the lower income is \(80-5(4)=80-20=60\) meals per week. At the higher income it is \(60-5(4)=60-20=40\). At \(P=\$8\), the corresponding quantities are \(80-5(8)=80-40=40\) and \(60-5(8)=60-40=20\).
At both prices, higher income reduces quantity by 20 meals per week. The demand curve shifts left: \(Q_d=60-5P\) lies to the left of \(Q_d=80-5P\) at each fixed price. The check is consistent with the income coefficient: \(0.01(\$4{,}000-\$2{,}000)=20\), a reduction of 20 meals.
Falling Income and a Rightward Shift
The definition works in both directions. If a good is inferior over the range in question, falling income raises the quantity demanded at each fixed price. A rightward shift does not mean that consumers are moving down the same curve because the price fell; it means that their purchase plans have changed at unchanged prices. The next example reverses the income change while keeping the same kind of model.
Worked Example: Falling Income and Increased Demand
In a hypothetical market for a basic frozen dinner, monthly quantity demanded is \(Q_d=70-3P-0.005Y\), where \(Q_d\) is dinners per month, \(P\) is dollars per dinner, and \(Y\) is annual income in dollars. Income falls from $6,000 to $4,000. Find the demand equations and quantities at prices of $5 and $10, then determine the shift.
Method. Substitute each income first, and compare quantities at the same prices. The price is not changing between the comparisons.
At \(Y=\$6{,}000\), \(0.005(6{,}000)=30\), giving:
At \(Y=\$4{,}000\), \(0.005(4{,}000)=20\), giving:
At \(P=\$5\), quantities are \(40-3(5)=40-15=25\) dinners at the higher income and \(50-3(5)=50-15=35\) at the lower income. At \(P=\$10\), quantities are \(40-3(10)=10\) and \(50-3(10)=20\), respectively.
At each price, falling income increases demand by 10 dinners per month. The curve shifts right. As a check, the income decrease is $2,000, and the model’s income term changes by \(0.005(2{,}000)=10\). The calculated difference at both prices is therefore consistent with the equation.
From Individual Demand to Market Demand
Market demand is the sum of the quantities all consumers plan to buy at each price. If the relevant consumers experience an income change and demand for a good is inferior for them over the range considered, their individual demand curves shift left when income rises. Adding their quantities at each price then gives lower market quantity demanded at that price. The market demand curve shifts left as well.
The conclusion depends on the consumers and income changes being described. If only some consumers’ incomes change, or if consumers respond differently, the market effect depends on how those individual changes add up. The following hypothetical example calculates that sum explicitly.
Worked Example: Adding Two Consumers’ Income Shifts
Two hypothetical households have individual demand equations for a basic repair kit. For household A, \(Q_A=20-2P-0.001Y_A\); for household B, \(Q_B=30-P-0.002Y_B\). Quantities are kits per month, price is dollars per kit, and each household’s annual income is initially $4,000, then rises to $6,000. Find market demand at each income level and compare market quantity at \(P=\$4\).
Method. Substitute each household’s income into its own equation, then add the two quantities at the same price. Adding demands horizontally means adding quantities, not prices.
Initially, household A’s income term is \(0.001(4{,}000)=4\), so \(Q_A=16-2P\). Household B’s income term is \(0.002(4{,}000)=8\), so \(Q_B=22-P\). Adding these equations gives initial market demand:
After both incomes rise to $6,000, household A’s income term is \(0.001(6{,}000)=6\), so \(Q_A=14-2P\). Household B’s is \(0.002(6{,}000)=12\), so \(Q_B=18-P\). The new market demand equation is:
At \(P=\$4\), initial market quantity is \(38-3(4)=38-12=26\) kits per month. After the income rise, it is \(32-3(4)=32-12=20\). Market quantity has fallen by 6 kits at that price, so market demand shifts left. The individual check gives the same result: household A’s quantity falls by 2 and household B’s by 4, for a total reduction of \(2+4=6\).
Common Mistakes and Interpretation
The most important exam distinction is between a change in demand and a change in quantity demanded. A change in income changes the demand relationship, provided income is a relevant determinant for the good. A change in the good’s own price, with income and other demand conditions fixed, changes quantity demanded along the existing curve. When both income and own price change, a simple before-and-after purchase comparison does not by itself isolate the income effect.
“Inferior” does not mean defective, unpopular, or necessarily inexpensive. A basic meal, a shared form of transport, or a second-hand item could be inferior in a particular hypothetical market if consumers buy less of it as their incomes rise, holding other conditions fixed. Those examples are not classifications that apply automatically: the relevant income-demand relationship must support the classification. A product can also be inferior for one group or income range and not for another.
A related diagnostic is to compare purchase plans at the same price. If the good’s own price also changed, a decrease in purchases cannot establish that the good is inferior. Likewise, an increase in nominal income does not necessarily mean an increase in purchasing power if the general price level also changes. For this demand comparison, interpret the income change as a change in the consumer’s relevant purchasing power, with other demand conditions held constant.
Check Your Understanding
For each problem, hold the stated conditions fixed and determine what the income change implies for quantity demanded or demand.
- A hypothetical product has demand \(Q_d=48-2P-0.004Y\), where \(Y\) is annual income in dollars. Income rises from $3,000 to $5,000. Calculate quantity demanded at \(P=\$6\) at each income and state the shift. (Answer: At $3,000, \(48-12-12=24\); at $5,000, \(48-12-20=16\). Quantity falls by 8, so demand shifts left.)
- For a hypothetical good, \(Q_d=90-4P-0.002Y\). Income falls from $8,000 to $5,000. Calculate quantity demanded at \(P=\$7\) before and after the income change, and state the shift. (Answer: At $8,000, \(90-28-16=46\); at $5,000, \(90-28-10=52\). Quantity rises by 6, so demand shifts right.)
- At the same price and with other conditions unchanged, consumers plan to buy 18 units of product A at one income and 14 units at a higher income. They plan to buy 7 units of product B at the lower income and 10 units at the higher income. Which product is inferior over this range, and why? (Answer: Product A; its quantity demanded falls as income rises. Product B has the opposite relationship.)
- Two households have demand equations \(Q_A=12-P-0.001Y_A\) and \(Q_B=18-2P-0.001Y_B\). Each household’s income rises from $3,000 to $5,000. Find total market quantity at \(P=\$3\) before and after the change, and state the market shift. (Answer: Initially, \(Q_A=12-3-3=6\) and \(Q_B=18-6-3=9\), for 15. Afterward, \(Q_A=12-3-5=4\) and \(Q_B=18-6-5=7\), for 11. Market demand shifts left.)
- A report says a household bought fewer units of a product after its income rose, but the product’s price also rose over the same period. Can this observation alone establish that the good is inferior? (Answer: No. The own-price change also affects quantity demanded, so the income relationship cannot be isolated without comparing at a fixed price and holding other conditions constant.)