Assuming the two good case.  When a person is attempting to maximize utility and the price of one of the two goods increases, then:   The budget constraint will contract (rotate towards the origin), shifting the budget line inward indicating more choices are now affordable and a lower utility level is now possible.   The budget constraint will contract (rotate towards the origin), shifting the budget line outward indicating fewer more are now affordable and a higher utility level is now possible.   The budget constraint will contract (rotate towards the origin), shifting the budget line inward indicating fewer choices are now affordable and a lower utility level is now possible.

Microeconomics A Contemporary Intro
10th Edition
ISBN:9781285635101
Author:MCEACHERN
Publisher:MCEACHERN
Chapter6: Consumer Choice And Demand
Section: Chapter Questions
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Assuming the two good case.  When a person is attempting to maximize utility and the price of one of the two goods increases, then:
 
The budget constraint will contract (rotate towards the origin), shifting the budget line inward indicating more choices are now affordable and a lower utility level is now possible.
 
The budget constraint will contract (rotate towards the origin), shifting the budget line outward indicating fewer more are now affordable and a higher utility level is now possible.
 
The budget constraint will contract (rotate towards the origin), shifting the budget line inward indicating fewer choices are now affordable and a lower utility level is now possible.
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