U(x, y)=(x^(1/2)+y^(1/4))^(1/2) | Ux(x, y)/Uy(x, y)

[idontknowcookie]

Hi!

U(x, y)=(x^(1/2)+y^(1/4))^(1/2)

How do I solve this equation? Demanded is (-dy/dx)|dU=0, U_x(x, y)/U_y(x, y) respectively. The whole power matter confuses me, I don't know where to start to solve this.

The same for U(x, y)=x^(1/2)y.

 

[stapel]

U(x, y)=(x^(1/2)+y^(1/4))^(1/2)

How do I solve this equation? Demanded is (-dy/dx)|dU=0, U_x(x, y)/U_y(x, y) respectively.

What do you mean by "solving" this functional statement? What do you mean by "demanded"? You posted this to algebra; why are ("partial"?) derivatives involved? What do you mean by "respectively"?

Please reply with the full and exact text of the exercise, the complete instructions, the type of course you're in (calculus? beginning algebra? something else?), and a listing of recent topics of study. Thank you!

 

[idontknowcookie]

hello stapel

Given is the utility function U(x, y)=(x^(1/2)+y^(1/4))^(1/2). I have to calculate the marginal rate of substituion (subject microeconomics). How I do that is to insert the x and y from the utility function into the first order condition ((-dy/dx)|_dU=0 or U_x(x, y)/U_y(x, y), it's the same).

So why I posted it here is because I know what the steps are but I lack knowledge in algebra.

What is (x^(1/2))^(1/2)? -> "A"
What is (y^(1/4))^(1/2)? -> "B"
Do I have to apply binomial formulas since the structure is (...+...)^x?

What is the result of the division of "A/B"? How do I solve that efficiently without getting confused?

With so much power calculation my brain is just overloaded. Are there any tricks or easy steps?

The result is 2y^(3/4)x^(-1/2).

Thank you very much.