Suppose that in January 2020 Mary had $50 to spend on hygienic masks and other goods every day.

Suppose that, at that time, the price of one mask for $.25 (25 cents) and the price of one unit of other goods was $1.

Which of the following three graphs represents Mary's budget constraint? Assume that masks and other goods are illustrated, respectively, on the horizontal and vertical axis.

Question

Suppose that in January 2020 Mary had $50  to spend on hygienic masks and other goods every day.

Suppose that, at that time, the price of one mask for $.25 (25 cents) and the price of one unit of other goods was $1.

Which of the following three graphs represents Mary's budget constraint? Assume that masks and other goods are illustrated, respectively, on the horizontal and vertical axis.

BlackTom AI · Accepted Answer

To determine Mary’s budget constraint, we start by identifying the prices and the income. The budget equation is 0.25*M + 1*O = 50, where M is the number of masks (horizontal axis) and O is the amount of other goods (vertical axis).

From this equation, the maximum number of masks Mary could buy if she spent all income on masks is M = 50 / 0.25 = 200, with O = 0. Conversely, the maximum amount of other goods she could buy if she spent all income on other goods is O = 50, with M = 0. That gives two intercepts at (M, O) = (200, 0) and (0, 50).

The correct budget constraint is therefore a straight line connecting these intercepts, sloping downward from the vertical axis at O = 50 down to the horizontal axis at M = 200. Among the three graphs, the one that shows the line crossing the vertical axis at 50 and the horizontal axis at 200 corresponds to this budget set.

If we compare the options: the graph that displays intercepts at (0, 50) and (200, 0) is the accurate representation of 0.25*M + 1*O = 50. The other graphs would imply different intercepts (e.g., a vertical intercept of 25, or a horizontal intercept of 100), which would violate the calculated budget constraint from the given income and prices.

Thus, the graph with the line joining (0, 50) to (200, 0) correctly depicts Mary’s budget constraint under the stated conditions.

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