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 last 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? Why

?

a. No, Bridget is not making the utility-maximizing choice. The marginal utility of the last bottle of wine (50 units) is higher than the marginal utility of the last pound of cheese (40 units). This indicates that Bridget should be consuming more wine and less cheese in order to maximize her utility.

b. Bridget should increase her consumption of wine and decrease her consumption of cheese in order to maximize her utility. She should purchase five bottles of wine and nine pounds of cheese, as this will give her the highest utility. This is because the marginal utility of the last bottle of wine (50 units) is higher than the marginal utility of the last pound of cheese (40 units).

a. To determine if Bridget is making the utility-maximizing choice, we need to compare the marginal utility per dollar spent on wine to the marginal utility per dollar spent on cheese.

The marginal utility per dollar spent on wine can be calculated by dividing the increase in utility (50 units) by the price of wine ($10), resulting in a marginal utility of 5 units per dollar.

Similarly, the marginal utility per dollar spent on cheese can be calculated by dividing the increase in utility (40 units) by the price of cheese ($4), resulting in a marginal utility of 10 units per dollar.

Since the marginal utility per dollar for cheese is higher than the marginal utility per dollar for wine, Bridget is not making the utility-maximizing choice.

b. To maximize utility, Bridget should reallocate her consumption by buying more cheese and less wine. Buying more cheese will yield a higher marginal utility per dollar spent compared to wine.

By reallocating her consumption, Bridget can increase her total utility. However, to determine the exact quantity of wine and cheese that will maximize her utility, we would need information on her total income or budget constraint.

To determine if Bridget is making the utility-maximizing choice, we need to calculate the marginal utility per dollar for both wine and cheese.

a. To determine if Bridget is making the utility-maximizing choice, we need to compare the marginal utilities per dollar for both wine and cheese. The formula to calculate marginal utility per dollar is:
Marginal Utility per Dollar = Marginal Utility / Price

For wine:
Marginal Utility per Dollar of Wine = 50 / $10 = 5 units per dollar

For cheese:
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 higher than that of wine (5 units per dollar), Bridget can increase her total utility by consuming more cheese and less wine. Therefore, she is not currently making the utility-maximizing choice.

b. Bridget should consume less wine and more cheese to maximize her utility. By reallocating her spending, she can increase her overall satisfaction. She should compare the marginal utilities per dollar for wine and cheese and adjust her consumption until they are equal.

Let's assume Bridget wants to increase her cheese consumption by one pound. She would have to decrease her wine consumption by $10 since the price of wine is $10 per bottle. The marginal utility gained from one pound of cheese is 40 units. Therefore, her marginal utility per dollar for cheese will remain the same (40 / 10 = 4 units per dollar), and her marginal utility per dollar for wine will decrease to 4 units per dollar (50 / $10 = 5 units per dollar) since she is consuming one bottle less.

Bridget should continue reallocating her spending until the marginal utilities per dollar for wine and cheese are equal. At that point, she will have reached the utility-maximizing choice.