Suppose a consumer has an income of $24, the price of A is $4, and the price of B is $3. Which of the following combinations is on the consumer’s budget line?
The correct answer and explanation is:
To determine which combination is on the consumer’s budget line, we use the budget constraint formula: PA⋅QA+PB⋅QB=IncomeP_A \cdot Q_A + P_B \cdot Q_B = \text{Income}
Where:
- PA=4P_A = 4 (price of good A)
- PB=3P_B = 3 (price of good B)
- Income = 24
Let’s test which combinations satisfy this equation. Although no options were given, a general explanation with example calculations will help.
Suppose a consumer chooses 3 units of A and 4 units of B: (4×3)+(3×4)=12+12=24(4 \times 3) + (3 \times 4) = 12 + 12 = 24
This totals $24, which matches the consumer’s income, so this combination is on the budget line.
Explanation:
A budget line shows all the possible combinations of two goods a consumer can buy with a given income, assuming fixed prices. The budget line equation is derived from setting total expenditure equal to total income. In this example: 4A+3B=244A + 3B = 24
To find all combinations on the budget line, one can plug in values for AA or BB and solve for the other. For example:
- If A=0A = 0, then 3B=24⇒B=83B = 24 \Rightarrow B = 8
- If B=0B = 0, then 4A=24⇒A=64A = 24 \Rightarrow A = 6
This means the consumer can afford up to 6 units of A (if buying only A) or 8 units of B (if buying only B). Any combination in between that keeps total spending at $24 lies on the budget line.
If the combination costs less than $24, it is inside the budget line. If it costs more than $24, it is outside the budget line and unaffordable.
So, a combination like (3A, 4B) or (6A, 0B) or (0A, 8B) is on the budget line, because it uses the entire income exactly.