Samantha is maximizing total utility while consuming food and clothing. Her marginal utility from food is 50, and her marginal utility from clothing is 25. If clothing is priced at $10 per unit, the price of food per unit must beGroup of answer choices$2.$2.50.$20.$5.
Question
Samantha is maximizing total utility while consuming food and clothing. Her marginal utility from food is 50, and her marginal utility from clothing is 25. If clothing is priced at 2.20.$5.
Solution
To find the price of food per unit, we need to use the concept of marginal utility per dollar spent. This should be equal for all goods for a consumer to maximize total utility.
The marginal utility per dollar spent is calculated as the marginal utility of the good divided by its price.
Given that Samantha's marginal utility from clothing is 25 and each unit of clothing costs $10, the marginal utility per dollar spent on clothing is 25/10 = 2.5.
For Samantha to maximize total utility, the marginal utility per dollar spent on food should also be 2.5.
Let's denote the price of food as P. Therefore, the marginal utility per dollar spent on food is 50/P.
Setting this equal to the marginal utility per dollar spent on clothing, we get:
50/P = 2.5
Solving for P, we find that P = 50/2.5 = $20.
So, the price of food per unit must be $20.
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