the marginal utility of good A is 3 imes the marginal utility of good B, and the price of good A is $4.50
Use consumer utility mazimizing rule ( MU A / P A) =(MUB/ PB) to solve. The answer is $6.75.
To solve this problem using the consumer utility maximizing rule, we can start by setting up the equation:
(MU A / P A) = (MU B / P B)
Given that the marginal utility of good A is 3 times the marginal utility of good B, we can rewrite the equation as:
(3MU B / $4.50) = (MU B / P B)
Next, we can cross multiply to get:
3MU B * P B = MU B * $4.50
Simplifying further, we can divide both sides of the equation by MU B to get rid of it:
3P B = $4.50
Finally, we can solve for P B:
P B = $4.50 / 3
P B = $1.50
Therefore, the price of good B is $1.50.
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.
To solve the problem using the consumer utility maximizing rule, we need to determine the price of good B (PB) and use the given information of the marginal utilities. Here's how:
Step 1: Write down the given information:
The marginal utility of good A (MUA) is 3 times the marginal utility of good B (MUB).
The price of good A (PA) is $4.50.
Step 2: Set up the equation using the consumer utility maximizing rule:
(MUA / PA) = (MUB / PB)
Step 3: Substitute the given values into the equation:
(3MUB / $4.50) = (MUB / PB)
Step 4: Simplify the equation:
Cross-multiply to eliminate the fractions:
3MUB * PB = MUB * $4.50
Step 5: Cancel out MUB from both sides of the equation:
3 * PB = $4.50
Step 6: Solve for PB:
Divide both sides of the equation by 3:
PB = $4.50 / 3 = $1.50
Step 7: Calculate the price of good B (PB) as $1.50.
Therefore, the price of good B is $1.50.