High School

Maurice is a barbecue aficionado and loves hosting people at his ranch with his upright drum smoker. As a good host, he wants to create the perfect consumption bundle for his five guests but needs to operate under a reasonable hosting budget. Assume that ribs and brisket both cost $3 a pound. Each row of the table shows a consumption bundle as an alternative to other bundles and the associated utility when Maurice spends his whole budget on buying ribs and brisket.

| Pounds of Ribs | Utility for Ribs | Pounds of Brisket | Utility for Brisket |
|----------------|------------------|-------------------|---------------------|
| 1 | 22 | 8 | 114 |
| 2 | 40 | 7 | 113 |
| 3 | 57 | 6 | 106 |
| 4 | 72 | 5 | 96 |
| 5 | 82 | 4 | 84 |
| 6 | 91 | 3 | 66 |
| 7 | 97 | 2 | 46 |
| 8 | 100 | 1 | 16 |

If the goal is to maximize utility, which option will Maurice choose?

A. 3 lbs of ribs; 6 lbs of brisket
B. 6 lbs of ribs; 3 lbs of brisket
C. 1 lb of ribs; 8 lbs of brisket
D. 8 lbs of ribs; 1 lb of brisket
E. 4 lbs of ribs; 5 lbs of brisket

Answer :

To maximize utility, Maurice should choose option 5, which includes 4 lbs of ribs and 5 lbs of brisket, with a total utility of 168.

How to maximize utility

Maurice is a barbecue aficionado who wants to create

the perfect consumption bundle for his guests while operating under a reasonable hosting budget.

He needs to choose between different combinations of ribs and brisket to maximize utility.

Based on the provided table, we can calculate the total utility for each option:

1. 3 lbs of ribs; 6 lbs of brisket:

Total utility = 57 (ribs) + 106 (brisket) = 163

2. 6 lbs of ribs; 3 lbs of brisket:

Total utility = 91 (ribs) + 66 (brisket) = 157

3. 1 lb of ribs; 8 lbs of brisket:

Total utility = 22 (ribs) + 114 (brisket) = 136

4. 8 lbs of ribs; 1 lb of brisket:

Total utility = 100 (ribs) + 16 (brisket) = 116

5. 4 lbs of ribs; 5 lbs of brisket:

Total utility = 72 (ribs) + 96 (brisket) = 168

To maximize utility, Maurice should choose option 5, which includes 4 lbs of ribs and 5 lbs of brisket, with a total utility of 168.

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Final answer:

To maximize utility with his given budget, Maurice should choose the consumption bundle with 4 lbs of ribs and 5 lbs of brisket. This bundle gives the best combination of satisfaction for the overall pounds of food purchased.

Explanation:

In this problem, Maurice needs to find the utility-maximizing choice for his barbecue party. The utility-maximizing choice is the consumption bundle that provides the highest total utility within Maurice's budget. Here, the utility is measured by the satisfaction Maurice's guests derive from eating ribs and brisket.

The utility of each pound of ribs and each pound of brisket are presented in the table. By comparing each combination's total utility, Maurice can determine which choice gives the maximum benefit. Maximum utility is achieved when the ratio of the marginal utility to price for ribs is equal to the marginal utility to price for brisket.

By cross-referencing the utilities given in the problem with the respective weights of ribs and brisket, Maurice should choose the bundle with 4 lbs of ribs and 5 lbs of brisket. This bundle will allow him to spend his entire budget while maximizing the utility of his guests.

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