Bridget has a limited income and consumes only wine and cheese; her current consumption choice is four bottles of wine and 10 pounds of cheese. The price of wine is $10 per bottle and the price of cheese is $4 per pound. The last bottle of wine added 50 units to Bridget's utility, while the las pound of cheese added 40 units
a. Is Bridget making the utility-maximizing choice, Why or Why not?
b. If not, what should she do instead?
I'm not sure what these utility units are, but think of the following:
$10 bottle of wine = 50
This is $.20/unit.
$4 of cheese = 40
This is $.10/unit.
Does this help with your problem?
To determine whether Bridget is making the utility-maximizing choice, we need to compare the marginal utilities per dollar spent on wine and cheese.
a. To calculate the marginal utility per dollar spent on wine and cheese, we can use the following formulas:
Marginal Utility per dollar of Wine = Marginal Utility of Wine / Price of Wine
Marginal Utility per dollar of Cheese = Marginal Utility of Cheese / Price of Cheese
Given that the last bottle of wine added 50 units to Bridget's utility and the price of wine is $10 per bottle, the marginal utility per dollar of wine can be calculated as:
Marginal Utility per dollar of Wine = 50 / 10 = 5 units per dollar
Similarly, the marginal utility per dollar of cheese can be calculated using the last pound of cheese, which added 40 units to Bridget's utility, and the price of cheese which is $4 per pound:
Marginal Utility per dollar of Cheese = 40 / 4 = 10 units per dollar
Since the marginal utility per dollar of cheese (10 units per dollar) is greater than the marginal utility per dollar of wine (5 units per dollar), Bridget is not making the utility-maximizing choice. She is not allocating her limited income efficiently because she can get more utility by spending more on cheese rather than wine.
b. To make the utility-maximizing choice, Bridget should reallocate her consumption to maximize the marginal utility per dollar spent on wine and cheese. This means she should spend more on cheese and less on wine. By doing so, she can increase her overall utility.
To determine the optimal consumption, Bridget needs to compare the new marginal utility per dollar of wine and cheese. By incrementally increasing the consumption of cheese and reducing the consumption of wine, Bridget can find the point where the marginal utility per dollar spent on both wine and cheese is equal. At this point, her consumption choice will be utility-maximizing.