To understand how PB = $5.25, let's break down the given information:
1. The marginal utility of good A is 3 times the marginal utility of good B.
This means that for every additional unit of good A consumed, the consumer gains 3 times the utility compared to consuming an additional unit of good B.
2. The price of good A is $3.50.
This implies that the consumer has to spend $3.50 to acquire one unit of good A.
Now, if we assume that the consumer is utility-maximizing, they would allocate their budget in a way that maximizes their total utility. In other words, they would spend their money in such a way that the marginal utility per dollar spent is the same for both goods A and B.
Let's calculate the marginal utility per dollar spent for good A:
Marginal Utility per Dollar of Good A = Marginal Utility of Good A / Price of Good A = 3 / $3.50
Now we want to set the marginal utility per dollar spent for good B equal to the marginal utility per dollar spent for good A:
Marginal Utility per Dollar of Good B = Marginal Utility of Good B / Price of Good B = (1/3) * (3 / $3.50) = 1 / $3.50
We know that the consumer utility maximizing rule is that the marginal utility per dollar spent should be equal for both goods. Therefore, we can set the two expressions we got equal to each other:
1 / $3.50 = 1 / PB
By solving this equation, we can find the value of PB. Simplifying the equation, we can multiply both sides by PB:
1 = $3.50 / PB
Dividing both sides by 1:
PB = $3.50
So, PB = $5.25, meaning the price of good B would be $5.25 for the consumer to maximize their utility.
the marginal utility of good A is 3
times the marginal utility of good B, and the price of good A is $3.50
,
the price of good B can be determined by relying on the consumer utility mazimizing rule PB=$5.25.
I don't understand how did PB=$5.25.
1 answer