Yes, the preferences represented by the utility function U(x, y) = 3x + 2y are homothetic.

Here's why:

Homothetic preferences are those for which the marginal rate of substitution (MRS) is the same along any ray from the origin. In other words, if you multiply all goods by the same positive number, the ratio of the marginal utilities does not change.

The MRS is the ratio of the marginal utility of x to the marginal utility of y, which in this case is MUx/MUy.

The marginal utility of x (MUx) is the partial derivative of the utility function with respect to x, which is 3.

The marginal utility of y (MUy) is the partial derivative of the utility function with respect to y, which is 2.

So, the MRS is 3/2, which is a constant.

Therefore, the preferences represented by this utility function are homothetic because the MRS is the same along any ray from the origin.

Question

Yes, the preferences represented by the utility function U(x, y) = 3x + 2y are homothetic.

Here's why:

Homothetic preferences are those for which the marginal rate of substitution (MRS) is the same along any ray from the origin. In other words, if you multiply all goods by the same positive number, the ratio of the marginal utilities does not change.

The MRS is the ratio of the marginal utility of x to the marginal utility of y, which in this case is MUx/MUy.

The marginal utility of x (MUx) is the partial derivative of the utility function with respect to x, which is 3.

The marginal utility of y (MUy) is the partial derivative of the utility function with respect to y, which is 2.

So, the MRS is 3/2, which is a constant.

Therefore, the preferences represented by this utility function are homothetic because the MRS is the same along any ray from the origin.

Knowee AI · Accepted Answer

Yes, the preferences represented by the utility function U(x, y) = 3x + 2y are homothetic.

Here's why:

Homothetic preferences are those for which the marginal rate of substitution (MRS) is the same along any ray from the origin. In other words, if you multiply all goods by the same positive number, the ratio of the marginal utilities does not change.

The MRS is the ratio of the marginal utility of x to the marginal utility of y, which in this case is MUx/MUy.

The marginal utility of x (MUx) is the partial derivative of the utility function with respect to x, which is 3.

The marginal utility of y (MUy) is the partial derivative of the utility function with respect to y, which is 2.

So, the MRS is 3/2, which is a constant.

Therefore, the preferences represented by this utility function are homothetic because the MRS is the same along any ray from the origin.

Are the preferences represented by the utility function U (x, y) = 3x+2y homothetic?

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Are the preferences represented by the utility function U (x, y) = 3x + 2y homothetic?

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