Suppose that, under these circumstances, Mary chose to consume 1 mask per day and 49.75 units of other goods. What was Mary's numerical value of her MRSmasks,other at that basket? Assume that Mary's indifference curves are smooth curves.

Question

Suppose that, under these circumstances, Mary chose to consume 1 mask per day and 49.75 units of other goods. What was Mary's numerical value of her MRSmasks,other  at that basket? Assume that Mary's indifference curves are smooth curves.

BlackTom AI · Accepted Answer

The question asks for the numerical value of Mary’s marginal rate of substitution between masks and other goods (MRSmasks,other) at the given basket, under the assumption that her indifference curves are smooth and that the chosen bundle lies where the indifference curve is tangent to the budget line.

First, recall what the MRS represents: at any given bundle, MRSmasks,other is the rate at which Mary is willing to trade other goods for one more unit of masks while keeping utility constant. In a standard consumer choice model with a smooth indifference map and a linear budget constraint, the tangency condition says that the slope of the indifference curve (the MRS) equals the slope of the budget line, which is the ratio of prices p_mask/p_other (typically written as -p_mask/p_other, but we often talk about the positive ratio as the magnitude of the trade-off).

In this scenario, the reasoning in the prompt (and the accompanying illustration) indicates that the bundle (1 mask, 49.75 units of other goods) is on an indifference curve that is tangent to the budget line. When a bundle is at tangency, the MRS between masks and other goods equals the opportunity cost of one more unit of masks in terms of the other good, i.e., MRS = OC_mask,other = p_mask/p_other. The figure text explicitly states that OC_masks,other = 1/4 and that the MRS_masks,other at this basket is 1/4.

To break down why this is the case, consider:
- If Mary’s indifference curve is tangent to the budget line at this basket, the marginal rate at which she’s willing to substitute is exactly the rate implied by the prices. This makes MRS equal to the price ratio.
- The given OC (opportunity cost) of masks in terms of other goods is 1/4. This OC mirrors the slope of the budget constraint: sacrificing 1 unit of masks yields 4 units of other goods, or conversely, gaining 1 mask costs 1/4 of a unit of other goods, depending on the framing. In either case, the magnitude of the marginal trade-off is 1/4.

With that interpretation, the key idea is that the MRS at the tangency point matches the OC—in other words, the rate at which Mary is willing to trade masks for other goods equals the rate at which she must trade off other goods to obtain an additional mask, given the prices. When the OC is 1/4, the MRS is also 1/4 at that basket.

If you were to consider alternative possible options (had they been provided), the incorrect choices would typically misstate the trade-off by:
- Treating MRS as independent of the budget constraint or of the tangency condition, thereby disconnecting it from OC and price ratios.
- Reversing the direction of the trade-off (e.g., giving 4 instead of 1/4) or using an inappropriate unit, which would violate the tangency condition.
- Assuming a different interpretation of the bundle (e.g., thinking the MRS is determined solely by raw quantities without regard to prices and the budget line).

In short, at the tangency point where the indifference curve meets the budget line, the marginal rate of substitution between masks and other goods equals the opportunity cost of masking in terms of other goods, which in this setting is given as 1/4. The graphical intuition is that the slope of the indifference curve (MRS) must align with the slope of the budget line (OC), ensuring optimal consumer choice given prices and income.

Suppose that, under these circumstances, Mary chose to consume 1 mask per day and 49.75 units of other goods. What was Mary's numerical value of her MRSmasks,other at that basket? Assume that Mary's indifference curves are smooth curves.Single choice

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