Nick consumes two goods, chips and lemonade. Located on the x-axis is the quantity of chips and on the y-axis is the quantity of lemonade. The magnitude of the slope of the budget line equals the
A) price of lemonade.
B) price of chips.
C) price of chips/price of lemonade.
D) price of lemonade/price of chips.
The correct answer and explanation is :
The correct answer is:
C) price of chips / price of lemonade
Explanation:
In microeconomics, the budget line (or budget constraint) represents all combinations of two goods that a consumer can afford, given their income and the prices of the goods. For Nick, these two goods are chips (on the x-axis) and lemonade (on the y-axis).
Let’s define:
- Pₓ = Price of chips
- Pᵧ = Price of lemonade
- I = Nick’s income
The general equation of the budget line is:
Pₓ × Qₓ + Pᵧ × Qᵧ = I,
where Qₓ is the quantity of chips and Qᵧ is the quantity of lemonade.
We can rearrange this to express Qᵧ (lemonade) in terms of Qₓ (chips), which gives a slope-intercept form of the budget line:
Qᵧ = (I / Pᵧ) – (Pₓ / Pᵧ) × Qₓ
From this equation, we can identify:
- The vertical intercept is I / Pᵧ, meaning how much lemonade Nick can buy if he buys zero chips.
- The slope is –(Pₓ / Pᵧ).
The magnitude of the slope (ignoring the negative sign) is:
Pₓ / Pᵧ,
which is the price of chips divided by the price of lemonade.
This slope represents the opportunity cost of consuming chips in terms of lemonade. That is, how many units of lemonade Nick must give up to consume one more unit of chips.
Why Not the Other Options?
- A) Price of lemonade — Incorrect. This is only part of the slope.
- B) Price of chips — Incorrect. This is also only part of the slope.
- D) Price of lemonade / price of chips — Incorrect. This is the inverse of the correct slope (it would be the slope if lemonade were on the x-axis and chips on the y-axis).
Thus, the correct interpretation of the magnitude of the slope of the budget line, when chips are on the x-axis and lemonade on the y-axis, is:
C) price of chips / price of lemonade.