Suppose that a consumer has the utility function $\mathrm { U } = 5 \mathrm { X } + 7 \mathrm { Y }$. The $\mathrm { MRSx } , \mathrm { y }$ is:
A) $7 / 5$
B) $5 / 7$
C) $1.00$ since $\mathrm { X }$ and $\mathrm { Y }$ are perfect substitutes.
D) 0 since $\mathrm { X }$ and $\mathrm { Y }$ are perfect complements.

Question

Quizplus · Accepted Answer

The MRSx,y is the marginal rate of substitution of X for Y, which is the amount of Y a consumer is willing to give up for an additional unit of X, while remaining indifferent (keeping the utility level constant). It is calculated as the ratio of the marginal utility of X to the marginal utility of Y. In this case, since the utility function is linear, the marginal utility of X and Y is constant and equal to the coefficient in front of each variable, which is 5 for X and 7 for Y. Therefore, the MRSx,y is 5/7. The consumer is willing to give up 7 units of Y in exchange for 5 units of X, while remaining indifferent.

Since the consumer's budget is not given, we cannot determine the specific bundle of X and Y that maximizes the consumer's utility or the affordability of each good. The MRSx,y is the marginal rate of substitution of good X for good Y. It measures how much of good Y a consumer is willing to give up in order to obtain an additional unit of good X, while remaining at the same level of utility.  
In this case, MRSx,y= MUx/MUy, where MUx and MUy are the marginal utilities of X and Y respectively.  
Since the utility function is linear, the marginal utility of each good is constant. Therefore, MRSx,y is a constant as well. In this case, MRSx,y=5/7.

To find the best choice, we need to look for the point where the consumer's budget constraint is tangent to their indifference curve (i.e. where MRSx,y equals the ratio of prices of the two goods). If the price ratio is greater than the MRSx,y, the consumer should buy more of good X; if the price ratio is lower, they should buy more of good Y. If the price ratio equals MRSx,y, the consumer is already at the best choice.

Unfortunately, we don't have any information about the prices of the goods or the consumer's budget, so we can't determine the best choice. We can only determine the MRSx,y, which is B, and use that to make a decision.

Suppose That a Consumer Has the Utility Function U=5X+7Y\mathrm { U } = 5 \mathrm { X } + 7 \mathrm { Y }U=5X+7Y

Suppose That a Consumer Has the Utility Function $\mathrm { U } = 5 \mathrm { X } + 7 \mathrm { Y }$