If the marginal rate of substitution of X for Y is 2,the price of X is $3,and the price of Y is $1,a utility-maximizing consumer should
A)be indifferent between 1X and 2Y.
B)prefer 3Y to 1X.
C)choose less X and more Y.
D)choose more X and less Y.

Question

Quizplus · Accepted Answer

The marginal rate of substitution (MRS) of X for Y represents the amount of Y that the consumer is willing to give up for one additional unit of X while remaining at the same level of utility. In this case, the MRS of X for Y is 2, which means the consumer is willing to give up 2 units of Y for one additional unit of X.

Given the prices of X and Y, the consumer should allocate their budget in a way that the marginal utility per dollar spent on both goods are equal.

MUx/Px = MUy/Py

Where MUx is the marginal utility of X, Px is the price of X, MUy is the marginal utility of Y, and Py is the price of Y.

Since Px = $3 and Py = $1, we can rewrite the equation as:

MUx/3 = MUy/1

Simplifying this expression, we get:

MUx = 3MUy

Since the MRS of X for Y is 2, we know that:

MUx/MUy = 2

Substituting MUx = 3MUy, we get:

3MUy/MUy = 2

MUy cancels out and we're left with:

3 = 2

This is a contradiction, which means the consumer cannot afford to consume the combination of goods that give an MRS of 2. Instead, the consumer should aim for an MRS equal to the price ratio of the two goods (i.e., Px/Py = 3/1).

At the optimal consumption bundle, the consumer's MRS of X for Y is equal to the price ratio of X and Y. This means the consumer is willing to give up 3 units of Y for one additional unit of X. Since the MRS is greater than 2, the consumer should consume less X and more Y until the MRS equals 2. Therefore, the consumer should choose less X and more Y.

If the Marginal Rate of Substitution of X for Y