Consumer optimum requires that consumers make purchases so for that the last dollar spent on all goods, the ratio of marginal utility to the price of the good is
equal
.
Part 2
We know the marginal utility of good A is three
times the marginal utility of good B, and the price of A is $4.50
.
Since we know the price of good A is three times the price of good B. In this case the price of good B would be $ 6.75.
I don't understand how to get $6.75?
the price of good B can be determined by relying on the consumer utility mazimizing rule ( MU A / P A) =(MUB/ PB) --> (8/4.50) =(12.00/PB).
Do you know where the 8 on (8/4.50) come from? and the 12.00 on (12.00/PB) come from?
In the given information, it is mentioned that the marginal utility of good A is three times the marginal utility of good B. This means that the ratio of the marginal utilities can be expressed as MU(A)/MU(B) = 3/1.
In the utility maximizing rule (MU(A)/P(A)) = (MUB/PB), we can substitute the given values to find the price of good B.
We are given that the price of good A is $4.50. Plugging in these values, we have:
(3/1)/(4.50) = (MUB/PB)
Simplifying the left side of the equation, we get:
(3/4.50) = (MUB/PB)
To find the price of good B, we can cross-multiply and solve for PB:
3 x PB = 4.50 x 1
3 x PB = 4.50
Dividing both sides by 3 gives us:
PB = 4.50/3 = $1.50
Therefore, the price of good B would be $1.50.
I'm not sure where the numbers 8 and 12.00 are coming from in the question you provided. It seems there might be a mistake or misunderstanding in the given information.
To understand where the numbers come from in the equation (8/4.50) = (12.00/PB), let's break it down step by step:
1. We are given that the marginal utility of good A is three times the marginal utility of good B. So if we assume the marginal utility of good B as x, then the marginal utility of good A will be 3x.
2. The price of good A is given as $4.50.
3. According to the consumer utility maximizing rule, the ratio of marginal utility to the price of a good should be equal for all goods. So we can set up the following equation: (MU A / P A) = (MUB / PB).
4. Substituting the values we know, we have (3x / $4.50) = (x / PB).
5. Simplifying the equation, we multiply each side by PB and get: (3x * PB) = (x * $4.50).
6. Now, if the price of good A is three times the price of good B, we can represent the price of good B as x * 3, which gives us: (3x * PB) = (x * $4.50) = ($x * 3).
7. Canceling out x from both sides of the equation, we are left with 3 * PB = $4.50.
8. Rearranging the equation, we divide both sides by 3: PB = $4.50 / 3.
9. Simplifying the division, we find that PB = $1.50.
Therefore, the price of good B (PB) would be $1.50, not $6.75. It seems there was an error in the given information.
To determine the price of good B, we can use the consumer utility maximizing rule, which states that the ratio of the marginal utility of a good to its price should be equal for all goods in the consumer's optimal bundle.
In this case, we are given that the marginal utility of good A is three times the marginal utility of good B. The price of good A is $4.50. We want to find the price of good B (PB).
Now, let's break down the problem step by step:
Step 1: Set up the equation
According to the consumer utility maximizing rule, we have:
(MU A / P A) = (MUB / PB)
Step 2: Substitute the given values
We know that MU A = 3(MUB) and P A = $4.50. Substituting these values into the equation, we get:
(3(MUB) / $4.50) = (MUB / PB)
Step 3: Simplify the equation
To simplify the equation, we can cancel out the common factor of MUB:
3 / $4.50 = 1 / PB
Step 4: Solve for PB
To solve for PB, we'll invert both sides of the equation:
$4.50 / 3 = PB
Step 5: Calculate the result
Performing the calculation, we get:
PB = $1.50
Therefore, the price of good B would be $1.50, not $6.75.
Apologies for the confusion caused by the incorrect values mentioned earlier. The correct calculation yields a price of $1.50 for good B.