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Pizza and Sprite Optimization: Maximizing Utility on a Budget


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Question: The following table shows​ William's utility from consuming slices of pizza and cans of Sprite. Part 2 Slices of Pizza Total Utility from Pizza Marginal Utility from Last Slice Cans of Sprite Total Utility from Sprite Marginal Utility from Last Can 0 0 ​- 0 ​- ​- 1 36 36 1 30 30 2 66 30 2 55 25 3 90 24 3 75 20 4 108 18 4 90 15 5 120 12 5 100 10 6 126 6 6 105 5 Part 3 Suppose William has ​$4.00 per week to spend on pizza and Sprite. The price of a slice of pizza is ​$1.00 and the price of a can of Sprite is ​$0.50. Part 4 If William wants to maximize his​ utility, he should buy    enter your response here ​slice(s) of pizza and    enter your response here ​can(s) of Sprite.

Asked by theunknown37

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To maximize utility, William should purchase the items in order of their marginal utility per dollar. The marginal utility per dollar for pizza and Sprite are as follow: For Pizza: -Marginal utility per dollar for the first slice is 36/1 = 36 -For the second slice is 30/1 = 30 -For the third slice is 24/1 = 24 -For the fourth slice is 18/1 = 18 -For the fifth slice is 12/1 = 12 -For the sixth slice is 6/1 = 6 For Sprite: -Marginal utility per dollar for the first can is 30/0.5 = 60 -For the second can is 25/0.5 = 50 -For the third can is 20/0.5 = 40 -For the fourth can is 15/0.5 = 30 -For the fifth can is 10/0.5 = 20 -For the sixth can is 5/0.5 = 10 Given William has $4.00 to spend and considering the marginal utility per dollar of each item, he should first buy 1 slice of pizza (cost $1.00) and 1 can of Sprite (cost $0.50). The total cost so far, is $1.50. Next, he should purchase another can of Sprite because its marginal utility per dollar (50) is higher than the marginal utility per dollar of a second slice of pizza (30). His total cost now is $2.00. Then, he should buy another can of Sprite (total cost now $2.50). Now, the marginal utility per dollar of the third sprite can and the second slice of pizza are the same (30), but Sprite is cheaper. So he buys the fourth can of Sprite (total cost $3.00) Now, with his remaining $1.00, William should buy a second slice of pizza because its marginal utility per dollar (30) is higher than that of a fifth can of Sprite (20). So if William wants to maximize his utility, he should buy 2 slices of pizza and 4 cans of Sprite.

Answered by gpt-4

Feb. 13, 2024, 7:28 p.m.

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This article was generated in part by one of OpenAI’s large-scale language-generation model, answering user theunknown37's question. Images were generated with OpenAI's AI model, DALL·E 2. The Internet takes ultimate responsibility for the content of this publication.
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Published: Tuesday, February 13, 2024

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