At a consumer optimum involving goods X and Y, the price of good X is $4
per unit, and the price of good Y is $8
per unit.
The marginal utility of good Y is enter your response here
times of the marginal utility of good X.
The marginal utility of good Y is 2 times the marginal utility of good X.
To find the relation between the marginal utility of good Y and the marginal utility of good X at the consumer optimum, we need to use the concept of marginal utility ratio. The marginal utility ratio (MUR) is the ratio of the marginal utility of one good to the marginal utility of another good.
Given that the price of good X is $4 per unit and the price of good Y is $8 per unit, we can assume that the consumer is maximizing utility subject to these prices.
At the consumer optimum, the consumer will allocate their income in a way that maximizes the total utility. This happens when the marginal utility per dollar spent is equal for both goods. In other words:
MUR (Y to X) = Marginal Utility of Y / Marginal Utility of X
Let's assume that the marginal utility of good X is "Ux" and the marginal utility of good Y is "Uy". According to the given information, the price of good X is $4 per unit and the price of good Y is $8 per unit.
Therefore, at the consumer optimum, MUR (Y to X) = Uy / Ux = 8/4 = 2.
So, the marginal utility of good Y is 2 times the marginal utility of good X.
To determine the marginal utility of good Y in relation to the marginal utility of good X, we need more information. Specifically, we need to know the quantities of goods X and Y consumed at the consumer optimum.
The consumer optimum occurs when the ratio of the marginal utility of good X to its price is equal to the ratio of the marginal utility of good Y to its price. In other words, the consumer will allocate their budget in such a way that the additional satisfaction obtained per dollar spent on each good is the same.
Let's assume that at the consumer optimum, the consumer is consuming q units of good X and p units of good Y. Based on the given prices, the consumer is spending 4q dollars on good X and 8p dollars on good Y.
Now, to find the marginal utility of good Y in terms of the marginal utility of good X, we can use the ratio of their prices:
marginal utility of good X / price of good X = marginal utility of good Y / price of good Y
Assuming the marginal utility of good X is denoted as MUx and the marginal utility of good Y is denoted as MUy, we can write the equation as:
MUx / 4 = MUy / 8
To find the exact ratio or multiple between the two marginal utilities, we would need the specific values of MUx and MUy. Without that information, we cannot provide a precise answer to the question.