Bob has utility function U(x,y)=x²+y over goods x and y a) Do we have a name for this type of utility function? Are Bob's preferences well-behaved? b) Let Bob have budget I=$60, and let prices be Px=$30, Py=$10. Find Bob's optimal basket of goods and y. Is this an interior or corner solution? c) What will happen if the price of good y doubles? [Think about: can we use this utility function to describe preferences over pet snakes and pet mice?]
Bob has utility function U(x,y)=x²+y over goods x and y a) Do we have a name for this type of utility function? Are Bob's preferences well-behaved? b) Let Bob have budget I=$60, and let prices be Px=$30, Py=$10. Find Bob's optimal basket of goods and y. Is this an interior or corner solution? c) What will happen if the price of good y doubles? [Think about: can we use this utility function to describe preferences over pet snakes and pet mice?]
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![Bob has utility function U(x,y)=x2+y over goods x and y
a) Do we have a name for this type of utility function? Are Bob's preferences well-behaved?
b) Let Bob have budget I=$60, and let prices be Px=$30, Py=$10. Find Bob's optimal basket of goods x
and y. Is this an interior or corner solution?
c) What will happen if the price of good y doubles?
[Think about: can we use this utility function to describe preferences over pet snakes and pet mice?]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa1f2822-8ee5-4468-b761-4648e25887d9%2Feeb15d72-cf36-4ae1-9b61-4e67919a5632%2F305dk7x_processed.png&w=3840&q=75)
Transcribed Image Text:Bob has utility function U(x,y)=x2+y over goods x and y
a) Do we have a name for this type of utility function? Are Bob's preferences well-behaved?
b) Let Bob have budget I=$60, and let prices be Px=$30, Py=$10. Find Bob's optimal basket of goods x
and y. Is this an interior or corner solution?
c) What will happen if the price of good y doubles?
[Think about: can we use this utility function to describe preferences over pet snakes and pet mice?]
Expert Solution
Step 1
Consumer preferences for a collection of products and services are measured using the utility function.
The benefit or satisfaction that consumers obtain is calculated in units called utils, which are abstract and difficult to pinpoint.
If a preference relation is monotonic and convex, it is said to be "well-behaved."
Monotonicity: It is always preferable to have more of any product (i.e. every product is a good, no satiation).
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