A utility function is homothetic if
A utility function is homothetic if
- A) the marginal utility depends on the average of the goods
- B) the total utility depends on the sum of the goods
- C) the marginal rate of substitution for the function depends only on the ratio of the amount of the two goods
- D) the MRS for the function depends on the total quantities of the two goods
Correct Answer: C) the marginal rate of substitution for the function depends only on the ratio of the amount of the two goods
Explanation
This Economics question is asking about a type of utility function called homothetic. A utility function is a mathematical equation that represents an individual's preferences for different goods or services. Homothetic utility functions have a unique property that can help economists understand how people make choices.
The question is giving us four options to choose from, and we need to select the correct one. Option A says that the marginal utility depends on the average of the goods. Option B says that the total utility depends on the sum of the goods. Option C is the correct answer, and it says that the marginal rate of substitution (MRS) for the function depends only on the ratio of the amount of the two goods. Option D says that the MRS for the function depends on the total quantities of the two goods.
Let's focus on Option C, which is the correct answer. The MRS refers to the rate at which a person is willing to trade one good for another while keeping their overall level of satisfaction constant. In other words, how much of one good someone is willing to give up for a little more of the other good. For a homothetic function, the MRS only depends on the ratio of the two goods, not their absolute quantities. This means that a person's preferences between two goods remain the same regardless of how much of each good they have.
Understanding homothetic utility functions is important because it allows economists to make predictions about how people will behave when faced with different choices. For example, if someone's utility function is homothetic, we know that they will always be willing to trade the same amount of one good for another, regardless of how much of each good they have.
In summary, this Economics question is asking about homothetic utility functions, and the correct answer is Option C. Homothetic utility functions have the unique property that the MRS for the function depends only on the ratio of the amount of the two goods. This means that a person's preferences between two goods remain the same regardless of how much of each good they have.