Utility Math Econ Problem

[stark hazel]

If anyone could help with this problem, I believe I solved part a correctly with y=1.55 (roughly). I need help with parts b and c because they get quite complext with having to solve for x (which I found to have cube root) and plugging it into the doctors utility function and then deriving. Help/guidance would be great.

[quartz linden]

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[misty stratus]

so, it's some annoying algebra, but it is solvable

[stark hazel]

Yes, annoying algebra I can do but I want to confirm I did correctly before proceeding.

[misty stratus]

well x is cube root in y for (b)

so that's right

[stark hazel]

cube root of 100/(2(y+1)=x?

[misty stratus]

yeah

you may find it easier to replace all y+1 with y and then subtract 1 later

[stark hazel]

Perfect, and then to proceed I'd plug this x into the doctors utility function and take that derivative then solve for y?

[misty stratus]

correct

[stark hazel]

Awesome. Thank you so much!