Utility doubt ! Help !

[Anjali]

Mr. Jack has the utility function U = (x1)^1/2 + (x2)^1/2

a) Mr. Jack has lexicographic preferences c) Mr. Jack does not have homothetic preferences  b) Mr. Jack has homothetic preferences d) None of the above

[Dreyfus]

Mr jack has homothetic preferences....

[Arushi :))]

Its c ..

[Dreyfus]

Arushi.....why preferences are not homothetic?

[Akshay Jain]

@vaibhav....the function is not homogenous of deg 1 so not homothetic

[Dreyfus]

OK thanks......I mistakenly took multiplication....

[ishita1793]

this is homothetic according to amit sir! its homogenous of degre 1/2 right?

[X]

Yes! Indeed it is homogeneous of degree 1/2. And so is homothetic. We can also check dx2/dx1 does only depends only on the ratio of x1 & x2. Homotheticity is not the special property of homogenity of degree 1.

[Arushi :))]

 A homothetic function is a monotonic transformation of a function which is homogeneous of degree 1...
and for a fun of degree 1 homogenity .. the MRS depends on x/y.. when monotic transformations are taken then MRS remains same ..
So here  it is transformation of which fn in case its homothetic??

[Akshay Jain]

http://www.commerce.otago.ac.nz/econ/courses/econ371/secure/2003%5Csummary8_03.pdf
visit this pdf.....this may help

[Dreyfus]

Hey Akshay....I read somewhere that if utility fun is homogenous of degree 1 then it is homothetic but  acc to Nicholson if a function in general is homogenous of degree r den its rate of change will remain same even after the monotonic transformation and thus that function will be homothetic.....now real confusion I m facing is homothetic utility function and homothetic function are the same ?

[Amit Goyal]

Hi Arushi,

U(x) = (x1)^1/2 + (x2)^1/2  is the monotonic transformation of the following homogeneous function of degree 1: [(x1)^1/2 + (x2)^1/2]^2
Hence, U(x) is homothetic.

[Anjali]

Thank you so much sir . Your reply has indeed ended this debate of ours . Thanks again !

[X]

Sir, will you please provide me an example where function is not homogeneous of degree 1 as well as not homthetic? I think that "degree 1" requirement is unimportant as we can take monotonic transformation of a function which is not homogeneous of degree 1 to make it of degree 1, and monotonic transformation of homothetic function is homothetic.

Sir, please help!!