Question

7. MRS and utility maximization Rina lives in Dallas and loves to eat desserts. She spends her entire weekly allowance on pudding and pie. A bowl of pudding is priced at $1.00, and a piece of pumpkin pie is priced at $4.00. At her current consumption point, Rina's marginal rate of substitution (MRS) of pudding for pie is 3. This means that Rina is willing to trade three bowls of pudding per week for one piece of pie per week.

Does Rina's current bundle maximize her utility—in other words, make her as well off as possible? If not, how should she change it to maximize her utility?

Rina's current bundle maximizes her utility, and she should keep it unchanged.

Rina could increase her utility by buying more pudding and less pie per week.

Rina could increase her utility by buying less pudding and more pie per week.

Answer 1

At utility maximization bundle : MRS= MU_pie/ MU_pudding = P_pie/ P_pudding

Here we can see at the current consumption bundle : MU_pie/ MU_pudding = 3

And P_pie/ P_pudding = 4/1 = 4

Because MRS < Price ratio . So, this means that Rina is currently not maximizing her utility . Rina could increase her utility by buying more pudding and less pie per week. Because by increasing the consumption of pudding , marginal utility from it decreases and by buying less pie , marginal utility from pie increases. As a result , MRS increases and Rina reach to the utility maximization bundle. Hence,option(C) is correct.