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 added 40 units.
A. Is Bridget making the utility-maximizing choice? Why or why not?
B. If not, what should she do instead? Why
To determine whether Bridget is making the utility-maximizing choice, we need to compare the marginal utilities to the prices of the goods.
A. Bridget's marginal utility for wine is 50 units per bottle, and the price of wine is $10. This means that the marginal utility per dollar spent on wine is 50/10 = 5 units per dollar.
Similarly, Bridget's marginal utility for cheese is 40 units per pound, and the price of cheese is $4. This gives us a marginal utility per dollar spent on cheese of 40/4 = 10 units per dollar.
Comparing the marginal utilities per dollar, we find that Bridget obtains higher utility per dollar spent on cheese than on wine. Therefore, she is not making the utility-maximizing choice, as she should allocate her budget in a way that maximizes the marginal utility per dollar for each good.
B. Bridget should consider reallocating her budget to increase the consumption of cheese and decrease the consumption of wine. By doing so, she can increase her total utility.
To find the optimal consumption, we need to compare the marginal utilities of wine and cheese. In this scenario, the marginal utility of cheese (40 units per pound) is higher than the marginal utility of wine (50 units per bottle).
Since the price of cheese is $4 per pound and the price of wine is $10 per bottle, we can see that the marginal utility per dollar spent on cheese is higher than on wine. Therefore, Bridget should increase her consumption of cheese and decrease her consumption of wine until the marginal utility per dollar spent on both goods is equal.
By adjusting her consumption, Bridget can achieve the utility-maximizing choice. This means she should buy fewer bottles of wine and more pounds of cheese, based on the marginal utilities and prices of the goods.