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
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
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.
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
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
@@EconomicsinManyLessons I got it, but using the multiplication rule for the powers was awesome
you rescued me from my math in econ exam. Thank you so much
Thank you, greeting from Colombia.
Are we multiplying by 5 because it’s the reciprocal of 1/5?
How did you get the -2 which raise to the power of both sides?
Exactly
He did magic
Does maximising output mean the same as maximising profit in this case?
You really helped me I was stuck
Thankyou
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??
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
If the firm chose 50 L and 250 K, wouldn't the output be bigger at same costs (1'000)?
Theliz no
how did you get -2 that you raise/ multiplied
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
What does the lambda mean tho? I dont really get it. Please help me explain..
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.
@@EconomicsinManyLessons what if the lambda is negative? What does it mean?
Both output maximization and cost minimization leads to same input combination?
pls they have the same input combination rather
How does 0.5 cancel 0.5
The coefficients I mean
Why -2 Raised?sir
you beautiful man
Thanks you for the comment!
CES stands for
Constant Elasticity of Substitution: The elasticity of substitution stays constant along an isoquant.