At a consumer optimum involving goods A and B, the marginal utility of good A is three
times the marginal utility of good B.
Part 2
The price of good B is $4.00
.
The price of good A is
Part 3
A.
$32.00
.
B.
$3
.00.
C.
$12.00
.
The answer is C. $12.00
How do I get to the answer?
To find the answer, we can use the concept of marginal utility and the principle of equalizing marginal utility per dollar spent.
We are given that at the consumer optimum, the marginal utility of good A is three times the marginal utility of good B.
Let's assume the marginal utility of good B is MU_B.
Then, the marginal utility of good A will be 3*MU_B.
Now, we know the price of good B is $4.00.
The principle of equalizing marginal utility per dollar spent tells us that the consumer will allocate their budget in such a way that the marginal utility per dollar spent is the same for both goods.
Since the price of good B is $4.00, the marginal utility per dollar spent for good B is MU_B/$4.00.
Now, let the price of good A be P.
The marginal utility per dollar spent for good A will be (3*MU_B)/P.
Since the marginal utility per dollar spent for both goods should be equal, we can set up the following equation:
MU_B/$4.00 = (3*MU_B)/P
Cross-multiplying, we get:
P = (12 * MU_B)/MU_B
P = 12
Therefore, the price of good A is $12.00. Hence, the answer is C. $12.00.
To get to the answer, you need to understand the concept of consumer optimization based on marginal utility and prices.
The consumer optimum occurs when the consumer allocates their budget in a way that maximizes their total utility. In this case, you are given that the marginal utility of good A is three times the marginal utility of good B.
To determine the optimal allocation of goods A and B, you need to compare the marginal utility per dollar spent on each good. This is referred to as the marginal utility per price ratio.
Let's denote the marginal utility of good A as MU_A, the marginal utility of good B as MU_B, the price of good A as P_A, and the price of good B as P_B. According to the given information:
MU_A = 3 * MU_B (1)
Also, you are given that P_B = $4.00.
Now, we need to determine the price of good A (P_A) to find the consumer optimum.
Assuming the consumer is optimizing their spending, they will allocate their budget in such a way that the marginal utility per dollar spent on each good is equal. Mathematically, this can be represented as:
MU_A / P_A = MU_B / P_B (2)
Substituting the values from equation (1) and P_B = $4.00 into equation (2), we have:
3 * MU_B / P_A = MU_B / $4.00
Cross-multiplying the equation, we get:
3 * MU_B * $4.00 = MU_B * P_A
Simplifying further, we have:
12 * MU_B = MU_B * P_A
Canceling out the common factor of MU_B, we get:
12 = P_A
Therefore, the price of good A (P_A) is $12.00. Hence, the correct answer is C. $12.00.
To find the answer, we need to consider the concept of marginal utility and consumer optimization.
Marginal utility refers to the additional satisfaction or benefit a consumer derives from consuming one additional unit of a good. In this case, it is given that the marginal utility of good A is three times the marginal utility of good B.
Consumer optimization occurs when a consumer allocates their limited budget in a way that maximizes their overall satisfaction or utility. In other words, the consumer spends their money in such a way that the marginal utility per dollar spent is equal across all goods.
Given that the price of good B is $4.00, we can determine the marginal utility per dollar spent on good B. We divide the marginal utility of good B by its price:
Marginal utility per dollar of good B = Marginal utility of good B / Price of good B
Next, we compare this to the marginal utility per dollar spent on good A. Since we know that the marginal utility of good A is three times the marginal utility of good B, the marginal utility per dollar of good A is three times the marginal utility per dollar of good B.
Therefore, we have:
Marginal utility per dollar of good A = 3 * (Marginal utility per dollar of good B)
To determine the price of good A, we divide the marginal utility of good A by the marginal utility per dollar of good A:
Price of good A = Marginal utility of good A / (3 * Marginal utility per dollar of good B)
Finally, we substitute the given price of good B ($4.00) into the equation to compute the price of good A:
Price of good A = Marginal utility of good A / (3 * (Marginal utility of good B / Price of good B))
= Marginal utility of good A / (3 * (Marginal utility of good B / $4.00))
= (Marginal utility of good A * $4.00) / (3 * Marginal utility of good B)
The correct answer is the price of good A, which is $12.00 (Option C).