At a consumer optimum involving goods A and B, the marginal utility of good A is five times the marginal utility of good B.
Part 2
The price of good B is $2.50
.
The price of good A is
Part 3
A.
$12.50
.
B.
$5
.00.
C.
$10.00
To find the price of good A, we can use the concept of marginal utility and price ratios in consumer equilibrium.
Given that the marginal utility of good A is five times the marginal utility of good B, we can set up the following equation:
MUa = 5 * MUb
Let's say the price of good A is Pa and the price of good B is Pb. According to the law of diminishing marginal utility, the consumer will allocate their income in such a way that the marginal utility per dollar spent on each good is equal. In other words:
MUa / Pa = MUb / Pb
We know that Pb is $2.50, so we can substitute the values into the equation:
5 * MUb / Pa = MUb / $2.50
To simplify the equation, we can cancel out MUb from both sides:
5 / Pa = 1 / $2.50
Now, cross-multiply and solve for Pa:
5 * $2.50 = Pa
Pa = $12.50
Therefore, the price of good A is $12.50.
The correct answer for Part 3 is A. $12.50.
To determine the price of good A in the consumer optimum, we need to use the concept of marginal utility and the principle of consumer equilibrium.
The consumer equilibrium occurs when the consumer allocates their income in such a way that the marginal utility per dollar spent on each good is equal. In other words, the consumer maximizes their satisfaction by spending their money in a way that the additional utility gained from consuming each good is equalized.
In this case, we are given that the marginal utility of good A is five times the marginal utility of good B. Let's call the marginal utility of good B as MU_B. Then, the marginal utility of good A can be represented as 5 * MU_B.
Now, let's consider the prices of the goods. We are given that the price of good B is $2.50. To determine the price of good A, we need to compare the marginal utility per dollar spent on each good.
The marginal utility per dollar spent on good B can be calculated as MU_B / $2.50. Since we know that the marginal utility of good A is five times the marginal utility of good B, the marginal utility per dollar spent on good A can be represented as 5 * MU_B / P_A, where P_A is the price of good A.
Since consumer equilibrium requires the marginal utility per dollar spent on each good to be equal, we can set up the equation:
MU_B / $2.50 = 5 * MU_B / P_A
We can simplify this equation as follows:
P_A = 5 * $2.50
P_A = $12.50
Therefore, the price of good A in the consumer optimum is $12.50.
So, the correct answer for Part 3 is A. $12.50.
To determine the price of good A, we need to compare the marginal utilities and prices of both goods A and B.
Given that the marginal utility of good A is five times the marginal utility of good B, and the price of good B is $2.50, we can set up the following equation:
Marginal utility of A = 5 * Marginal utility of B
Since the price of good B is $2.50, we can assume that the marginal utility of B is equal to $2.50.
Therefore, the marginal utility of A would be:
Marginal utility of A = 5 * $2.50 = $12.50
Thus, the price of good A is $12.50.
Answer: A. $12.50