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.
Is Bridget making the utility maximizing choice? Why or why not?
Bridget is making the utility maximizing choice.
First, let’s define a utility function and how it impacts Bridget’s consumption choice:
U = u(X) = 40 – 50(X) = 30
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.
Bridget has decided to maximize her utility by consuming all four bottles of wine and all 10 pounds of cheese. Her total utility is 30 – 50(X) + 10 – 4(X), or 90 units at an average rate of $1 per unit.
Bridget’s choice is the optimal one.
The last bottle of wine added 50 units to Bridget’s utility, while the last pound of cheese added 40 units. This means that every time Bridget buys a bottle of wine or a pound of cheese, she is increasing her consumption beyond what she would have if she did not buy anything at all. She is consuming more units now than if she had not purchased any product at all.
The total amount of consumption that Bridget can get from consuming the same amount of money each week is called her marginal utility. For example, if you have $50 in your bank account and you spend $40 on food, then your marginal utility for food is 40 (Sharma, 2019). If you then spend another $20 on food, then your marginal utility for food would be 80.
In this case, since Bridget has only enough money to buy four bottles of wine and ten pounds of cheese, her marginal utility for wine is 50 because it consumes 50 units per week; her marginal utility for cheese is 40 because it consumes 40 units per week.
Bridget’s consumption choices are maximizing because they maximize her total consumption over time; they also maximize her total value
I believe Bridget is making the utility maximizing choice, because she is able to make a maximum of $40 worth of purchases with her limited income. She has two options: consuming 10 pounds of cheese or drinking four bottles of wine (Sharma, 2019). If she consumes both, she will end up with 30 units of utility. However, if she only consumes one, it will take her an extra half hour to get to and from work because she must stop at the store on the way home. Therefore, given this information and her limited time available for leisure activities, I believe that Bridget should consume the 10 pounds of cheese instead.
The price of each item affects my decision. The price of wine is $10 per bottle, meaning it costs $100 per bottle to buy all four bottles at once (4x$10). The price for cheese is much lower—only $4 per pound—meaning it costs less than half as much as wine ($80 per pound).
The reason for this is because she has a limited income and only certain things she can buy with that income. If she were to buy more cheese than wine, then she would have less money to spend on other things (Keya et al., 2018). However, if she were to buy more wine than cheese, then she would have less money to spend on other things.
Therefore, by choosing 4 bottles of wine and 10 pounds of cheese, Bridget is choosing the most optimal way to maximize her utility given her income constraints.
References
Sharma, B., Hickman, M., & Nassir, N. (2019). Park-and-ride lot choice model using random utility maximization and random regret minimization. Transportation, 46(1), 217-232. https://link.springer.com/article/10.1007/s11116-017-9804-0
Keya, N., Anowar, S., & Eluru, N. (2018). Freight mode choice: A regret minimization and utility maximization based hybrid model. Transportation Research Record, 2672(9), 107-119. https://journals.sagepub.com/doi/abs/10.1177/0361198118782256