Sorry, but this calculation is awkward. Just divide MUx by MUy and you`re done! This trick works always by CD-utility. I don not this instructor knows this!

I appreciate your comment!

Thanks!

I appreciate that. Thank you!

Himadri Nag Yeah I was wondering about that as well!

I feel like this is more of a CES method.

@@yifanbao8264 utility is ordinal, so it does not matter if you take x^0,5*y^0.25 or x^2*y or x^(2/3)*y^(1/3) try. But only the last one is homothetic which leads in an aggregation for social welfare to a concave utility possibility curve, but all this important stuff is not said in the video, it is just stupid calculation with no explanaition!

Show me result

You are very welcome!

Probably too late to know, but deriving it results in: x^.25 * .5y^.5-1, but you can move that all the way to the front of the equation, it won't make a difference. It's just much easier to work with that way.

No!!!! Because the why is missing! It is just stupid wicked calculation, with no deeper inside!

Example. Let U = XY + Y. Take Partial derivative of U with respect to X (we treat Y as a constant). For the sake of argument, say Y = 5 (a constant) and replace Y with 5 in the equation above, so U = 5X + 5. Take the derivative of this last equation wrt to X: dU/dX = 5 + 0 = 5. Now, replace 5 with Y, so dU/dX = Y and you get the correct partial derivative of the utility function with respect to X.

You are welcome!

Thank you so much!

This video should help:kzfaq.info/get/bejne/e7KoitJhytmwqqM.html

The exponents do not need to sum to 1; each exponent only needs to be a positive constant.

NO!!!!!!!!!!!!!!!! utility is ordinal, therefore the exponents does not need to add up to 1!!! You Prof should have told you!

That is great!

I'm sure it is far too late for you to get this answer now, but I wanted to respond. The Cobb-Douglas equation is a really big deal in advanced economics classes. Its form is: Y=A*Labor^(beta)*Capital^(alpha). In this case, they changed the formula a bit to become U=X^a*Y^b (with a and b being constants). It has a lot of uses, for instance to show how to continue to grow a business when efficiency really can't be improved (machines and workers can only work so fast). There are entire books written about that formula and entire programs of study in masters degrees devoted to it. It is really not possible to go into enough detail here, as this formula is really the mac-daddy of economics equations.

how do you get the beta and alpha though still very confused on this equation.

@@billyoung8118 Sorry but CD first semester and has nothing to do with advanced stuff. Its just the geometric mean, or you ask for a function with substitution elasticity of 1

Happy Turtle The 4 is outside the fraction and it's implied that it is multiplying the whole thing but that is an astute observation

@@jpratt8676 but he never actually multiplies with the 4 on the left side. My question is why doesn't cross multiplying not work.

It's fine if the exponents do not sum to 1--the example is still in Cobb-Douglas format. I multiplied both sides by 4 to get rid of the 4 in the denominator on the right hand side of the equation; on the left hand side, 4 x 0.25 = 1.

No, only if your instructor requires it.

u=x^a*y^b m=p_x*x+p_y*y -> x*=[a/(a+b)]/p_x and x*=[b/(a+b)]/p_y this should have been told you in your first semester in microeconomics! Do not forget this!!!

There is no requirement for the exponents on a Cobb-Douglas function to sum to 1. The exponents only need to be positive.

do you know the difference between cardinality und ordinality look it up!

The exponent on the X variable after the derivative is X^(0.25 - 1), which simplifies to X^(-0.75)

Thank you. Also, this video really helps me. ❤️

A utility function can take on many different forms. U = square root of X*Y is just another example of a Cobb-Douglas utility function. The general Cobb-Douglas form can be written as U = (X^a)(Y^b).

thanks