Consider the preference represented by the following utility function:

u(x,y)= (x^)/ + (y^)/

where1,=0.

1. (5)Derive the marginal rate of substitution for this utility function.
2. (5) Does this preference have the characteristic of diminishing marginal rate of substitu- tion? Explain your answer for full credits.
3. (5) Is this preference homothetic? Explain your answer for full credits. Be sure to explain what homothetic means.
4. (5)Propose a monotonic transformation g() that converts the above utility functionu(x,y) to a different utility function v(x, y) so that they represent the same preference. Verify that g() converts u(x,y) to v(x,y) and show that it is order preserving.