Lagrangian: Maximizing Output from CES Production Function with Cost Constraint

[@bellomisquah9153]

I don't understand the part where you got L=1/25k
It's like you did magic
L is supposed to be 2.5k or 5k

[@EconomicsinManyLessons]

Let me simplify this in more detail: L^-0.5 = 5(K^-0.5)
I raise both sides of the equation to the -2 power. On the left hand side of the equation, note that (L^-0.5)^-2 = L^(-0.5 x -2) = L^1 = L
On the right hand side of the equation: [5(K^-0.5)]^-2 = (5^-2)(K^-0.5)^-2. Note that 5^-2 = 1/25 and (K^-0.5)^-2 = K^(-0.5 x -2) = K^1 = K. Putting this side together: (1/25)K.
Overall, we get L = (1/25)K

[@Kentucky_Fried_Man]

@@EconomicsinManyLessons I got it, but using the multiplication rule for the powers was awesome

[@user-ej6kj3rv1b]

you rescued me from my math in econ exam. Thank you so much

[@GascaPdCanal]

Thank you, greeting from Colombia.

[@cmulz2372]

Are we multiplying by 5 because it’s the reciprocal of 1/5?

[@mambojackson8245]

You really helped me I was stuck
Thankyou

[@gjinkalla7121]

Does maximising output mean the same as maximising profit in this case?

[@lyttiegrabamak1563]

How did you get the -2 which raise to the power of both sides?

[@bellomisquah9153]

Exactly
He did magic

[@abegailmendez4569]

Why is it that if you solve it the other way around the results are not the same, i mean the isolated L or K

[@lobowatz5274]

If the firm chose 50 L and 250 K, wouldn't the output be bigger at same costs (1'000)?

[@tripledee4439]

Theliz no

[@justnothing1067]

I dont understand the part u multiplied only 1 side by 1/5. I mean K^0.5+L^0.5 can be multiplied by 1/5 too. Why did u left it??

[@sarahakin02]

how did you get -2 that you raise/ multiplied

[@EconomicsinManyLessons]

I raise both sides by -2 because when you multiply the exponent on L and K, which is -0.5, by - 2 you are left with just L and K. For example, L^[(-0.5)(-2)] = L

[@vanshitaverma9095]

Both output maximization and cost minimization leads to same input combination?

[@benedictamanu1594]

pls they have the same input combination rather

[@justry_right9766]

What does the lambda mean tho? I dont really get it. Please help me explain..

[@EconomicsinManyLessons]

In this video, Lambda tells us how much output will increase by if the constant in the constraint was increased by 1-unit. In other words, the increase in output from spending an additional dollar on inputs.

[@yeon9595]

@@EconomicsinManyLessons what if the lambda is negative? What does it mean?

[@minnaasia3371]

How does 0.5 cancel 0.5

[@minnaasia3371]

The coefficients I mean

[@arunkumarsabar7906]

Why -2 Raised?sir

[@-RayQuaZa]

you beautiful man

[@EconomicsinManyLessons]

Thanks you for the comment!

[@kittykhan7581]

CES stands for

[@EconomicsinManyLessons]

Constant Elasticity of Substitution: The elasticity of substitution stays constant along an isoquant.