Derivative Math for MicroEconomics

AiM

AiM

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I can't figure this one specific example out, I never took proper Calculus so I'm doing catchup here.... my exams are coming within a few days so I don't have time to ask the professor.

=============

"Suppose the production function of a firm is q = 10K^0.4 L^0.6 Find the MPL"
MPL = dq / dL
= 10K^0.4 L^0.6
= 10K^0.4 (.6)L^0.6 - 1

Now this is the part I don't understand...

Why does the 0.6 move to the 10?
= (0.6)10K^0.4 L^-0.4
= 6K^0.4 L^-0.4 <--- answer I have in my notes

Why doesn't the 0.6 move to L instead?
Shouldn't it be...
= 10K^0.4 0.6L^-0.4 <--- how I normally solve the other questions

============

Any help would be much appreciated :)
 
AiM said:
I can't figure this one specific example out, I never took proper Calculus so I'm doing catchup here.... my exams are coming within a few days so I don't have time to ask the professor.

=============

"Suppose the production function of a firm is q = 10K^0.4 L^0.6 Find the MPL"
MPL = dq / dL
= 10K^0.4 L^0.6
= 10K^0.4 (.6)L^0.6 - 1

Now this is the part I don't understand...

Why does the 0.6 move to the 10?
= (0.6)10K^0.4 L^-0.4
= 6K^0.4 L^-0.4 <--- answer I have in my notes

Why doesn't the 0.6 move to L instead?
Shouldn't it be...
= 10K^0.4 0.6L^-0.4 <--- how I normally solve the other questions

============

Any help would be much appreciated :)
Click to expand...

One is simplified, the other one is not. It is accustomed to write the coefficients in front of the rest of the expression, so that's why you multiply the 0.6 by 10.
 
I can't really tell you without knowing the full question.
Also I never took calculus. But it's definately not simplifying.
=10k ^ 0.4(0.6)L ^ 0.6 - 1
=(0.6)10k ^ 0.4L ^ 0.4
They are obviously not equal so either the equation is wrong or you wrote it out wrong or I'm missing something completely and I am stupid.
 
its basic D/DX[U^n]=nu^(n-1)u'

n in this case is =.6
u = 10
and the rest is history


when i saw this earlier i got confusedbecause i thought you would have to use the chain rule which would look more like this,
d\dx{u*v}=uv'+u'v

and then it would have gotten more confusing because you have to solve for the variables k and l so that k = k' and l = l'

ya.. really confusing without the whole question but i explain it up at top.. calculus is fun


edit: you do use the chain rule more specifically the general power rule.. your equation would make alot more sense if it was written like this"
q = (10K^0.4 L)^0.6 something like that

and general power rule graphics
If f(x) = [g(x)]n then, f '(x) = n[g(x)]n-1 ?g'(x).
 
Sorry if I confused you guys, let me clarify...

This is a MicroEconomics class that happened to use Derivative Math in order to find the Marginal Products of Labor (MPL). I typed out the full question "Suppose the production function of a firm is q = 10K^0.4 L^0.6 .... Find the MPL" but regardless, nofx's equation helped clarify it some for me, thanks guys! :)
 
great im glad you got something out of that, make sure you understand what derivatives are telling you.. for example say: you want to find the derivative of y = x^2
y is area
x is side

so x^n
so equals
y' = nx^n-1
y' = 2x^1 = 2x

the relationship is simple. lets call x^2 the area and 2x the derivative of the area. this relationship tells us at any given moment the area is growing at a rate that is 2x times fast as its side is lenghting

this might get confusing: "the derivative of a function, is basically another function. that describes that rate a dependent variable changes with respect to the rate the independent variable will change."

its easy to understand if you take it apart, and also you might want to invest in a book called Calculus made easy bythompson and gardner. the book will explain some calculus to you and how it's practical.
 
highlander said:
Me too :(
Click to expand...

ugh.jpg
 
A simple way to think of a derivative is just the change of a variable with respect to another. So for a simple relationship like pay = 8$/hr * time the derivative of pay with respect to time is just 8$/hr For any tiny increment of time in hours you will see a corresponding change in pay equal to 8$ times that increment in time. For more complex functions a derivative will not necessarily be a constant, but depend on the value of the variables at different locations.
 
AiM said:
I can't figure this one specific example out, I never took proper Calculus so I'm doing catchup here.... my exams are coming within a few days so I don't have time to ask the professor.

=============

"Suppose the production function of a firm is q = 10K^0.4 L^0.6 Find the MPL"
MPL = dq / dL
= 10K^0.4 L^0.6
= 10K^0.4 (.6)L^0.6 - 1

Now this is the part I don't understand...

Why does the 0.6 move to the 10?
= (0.6)10K^0.4 L^-0.4
= 6K^0.4 L^-0.4 <--- answer I have in my notes

Why doesn't the 0.6 move to L instead?
Shouldn't it be...
= 10K^0.4 0.6L^-0.4 <--- how I normally solve the other questions

============

Any help would be much appreciated :)
Click to expand...

Just carry the 1.
 
LOL, o yeah I'd've answered if it was on paper, no way in hell I'm bothering to read math (calculus in particular) that's been typed.
 
I like it how AiM tries to save his *** by claiming that

AiM said:
This is a MicroEconomics class that happened to use Derivative Math in order to find the Marginal Products of Labor (MPL). I typed out the full question "Suppose the production function of a firm is q = 10K^0.4 L^0.6 .... Find the MPL" but regardless, nofx's equation helped clarify it some for me, thanks guys
Click to expand...

Oh, so his problem is with Calculus and not with basic Math. More power to him!!!

Yet the part that he does not understand

AiM said:
Now this is the part I don't understand...

Why does the 0.6 move to the 10?
= (0.6)10K^0.4 L^-0.4
= 6K^0.4 L^-0.4 <--- answer I have in my notes

Why doesn't the 0.6 move to L instead?
Shouldn't it be...
= 10K^0.4 0.6L^-0.4 <--- how I normally solve the other questions
Click to expand...

involves basic multiplication and has nothing to do with Calculus.

AiM said:
I can't figure this one specific example out, I never took proper Calculus so I'm doing catchup here.... my exams are coming within a few days so I don't have time to ask the professor.
Click to expand...

Looks like proper Calculus is not the only class this prodigy skipped. Seriously, what's the point of signing up for a class you are so clueless about?
 
What the ****s your problem buddy?

I never voluntarily signed up for the class, it's a requirement and it's designed around the HK education system where most students have done 4 years of it in High School (which I never did). If it makes you happy, yeah I know Math is my major weakness, and the fact that the professor throws Derivatives at me and assumes I know it on the spot doesn't help. Whatever, if it makes you feel better about yourself, feel free to keep the insults coming... I don't give a shit.

====

nofx: Thanks man! Really appreciate you taking the time to explain it to me, can't thank you enough. :) I might check out that book for next Semester, but right now I should be able to do the Derivative questions posed in the MicroEconomics exam, which is all I can ask for.

Everyone else that tried to help.... :cheers:
 
My intent was not to feel good about mysef. My intent was to devaluate your ego, but I failed :)
 
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