Differentiating: Y = A[K^?][L^(1-?)/2][H^(1-?)/2], 0 < ? < 1

[annalynne]

Hey everyone,

I have 3 questions surrounding this equation:
Y = A[K^?][L^(1-?)/2][H^(1-?)/2] where 0 < ? < 1

1. What Is ?Y/?L?
2. What Is APL (APL = Y/L)?
3. What Is ?APL/?L

Any help would be appreciated! Thanks!?

 

[tkhunny]

Y = A[K^?][L^(1-?)/2][H^(1-?)/2]

Ignore this part: A[K^?][H^(1-?)/2] and give that partial derivative a go.

Please be more clear with your notation. You have written this: H^(1-?)/2 A most technical reading would decode that as \(\displaystyle \frac{H^{1-\alpha}}{2}\). Is that your intent?

 

[Deleted member 4993]

I have 3 questions surrounding this equation:
Y = A[K^?][L^(1-?)/2][H^(1-?)/2] where 0 < ? < 1

1. What Is ?Y/?L?
2. What Is APL (APL = Y/L)?
3. What Is ?APL/?L

What are the constants - what are the variables?

 

[BigGlenntheHeavy]

\(\displaystyle If \ a \ is \ a \ constant, \ then \ D_L[L^{a}] \ = \ aL^{a-1}\)

\(\displaystyle but \ if \ a \ is \ a \ variable \ then \ D_a[L^{a}] \ = \ ln(L)L^{a}.\)

 

[annalynne]

What are the constants - what are the variables?

Sorry everyone!
The constants are: A, L, H
The variable is: ?

 

[Deleted member 4993]

I have 3 questions surrounding this equation:
Y = A[K^?][L^(1-?)/2][H^(1-?)/2] where 0 < ? < 1

1. What Is ?Y/?L?
2. What Is APL (APL = Y/L)?
3. What Is ?APL/?L

What are the constants - what are the variables?

Sorry everyone!
The constants are: A, L, H << In that case ?Y/?L does not exist