the marginal utility of good A is 3 imes the marginal utility of good​ B, and the price of good A is ​$4.50

Question

Use consumer utility mazimizing rule ​( MU A / P A) =(MUB/ PB) to solve. The answer is $6.75.

Answer 1

To solve this problem, we need to use the consumer utility maximizing rule:

(MU A / P A) = (MU B / P B)

We are given that the marginal utility of good A is 3 times the marginal utility of good B, and the price of good A is $4.50.

Let's assume that the marginal utility of good B is MU B.

Therefore, the marginal utility of good A is 3MU B.

We also know that the price of good A is $4.50.

Plugging these values into the consumer utility maximizing rule, we get:

(3MU B / $4.50) = (MU B / PB)

Cross-multiplying, we get:

(3MU B) * (PB) = (MU B) * ($4.50)

Simplifying, we get:

3MU B * PB = MU B * $4.50

Dividing both sides by MU B, we get:

3PB = $4.50

Dividing both sides by 3, we get:

PB = $1.50

Therefore, the price of good B is $1.50.

Finally, to find the price of good A, we can plug the price of good B into the consumer utility maximizing rule:

(MU A / $4.50) = (MU B / $1.50)

Since we know that MU A is 3 times MU B, we can substitute 3MU B for MU A:

(3MU B / $4.50) = (MU B / $1.50)

Cross-multiplying, we get:

(3MU B) * ($1.50) = (MU B) * ($4.50)

Simplifying, we get:

4.5MU B = 1.5MU B

Dividing both sides by MU B, we get:

4.5 = 1.5

Therefore, the equation does not hold true and there may be an error in the original question or provided answer.

Please double-check the information and equations given to ensure accuracy in solving the problem.