Cobb-Douglas Production Function Differentiation Example 

Very helpful! My textbook skipped over such steps, leaving me confused for hours on end. Thanks to you, I averted a nervous breakdown. Seriously...

Thanks for all the awesome content you create. Macro economics just got a little easier because of you, sir!

I don't understand any of this no matter how many times I read about it and watch videos on it.

Not having explained this function to students for a few years I was finding it difficult to explain it while still making any sense at all but this video is a very simple and powerful description. Great effort. I'm certainly giving this link to my students.

you are a gods send, u made me understand in 11 minutes something my lecturer has spend 2 weeks of class trying to make me understand!

So nice of you to say! As a fellow teacher of economics students, I can't recommend making videos like these things more. It's gotten to the point where if more than a few students ask me to clarify some oft tricky point, I'll start writing a video script.

I was going through the mathematical economics book by Chiang but literally wasted a lot of time but could not understand it. Thanks a lot,this video helped. 😊

THE BEST VID OF THE C.D. FUNCTION IVE WATCHED!! SIMPLY THE BEST!!

2. Assume a firm faces a Cobb-Douglas production function which takes the form Q= L1/2 K1/2 Where L and K are units of labor and capital respectively and further assume that -----of labor and capital are 20 birr and 30 birr respectively and total cost of production is equivalent to 3,000birr. Based on this information, answer the following questions I. Compute the equation for marginal product of labor (MPL) and capital (MPK). II. Compute marginal rate of technical substation of labor of capital (MRTSL,K) III. Determine the optimum level of labor and capital to be employed. IV. Compute the total output level to be produced at the optimum employment level.

Hey! Good video, though I think it is important to remark Alpha is not just some parameter. It is actually 'Output Elasticity' which is the parameter to which output level is influenced by the elasticity in Kapital and Labour respectively. Hence in this case presented Perfect Competition is assumed and that is why L parameter is 1-Alpha, since only in Perfect Competition Alpha (K parameter) + Beta (L parameter) = 1; hence Beta = 1 - Alpha just for perfect competition. Otherwise just use Beta. Cheers!

Thank You economicurtis because of your videos I have been able to gain significantly more knowledge on economics. Thank you.

You'd be surprised - in my experience the relatively simple algebra is the tricky part for most people. And in economics - outside of early problem sets, or perhaps simulations - you'll rarely plug in actual numbers. It's usually more useful to stick to the abstract. I'll do a couple where I plug in numbers. Thanks for the feedback

Thank you, professor. Thanks to you, I understood it easily.

Thank you so much, my man! I'm definitely subscribing and watching your stuff from now on! life saviour

Thank you so much for your video! My teacher directly gave us the result without any progress so it was so confusing, now i got it. Thanks!

This video is a lifesaver. Thanks a lot, you have no idea how much you helped me!

best vedio of cobb douglass function i have ever seen. dude if i were a girl i am gonna definetly marry you

Marvelous Finally after 3 year a got this concept 👍

Thanks for your comments. (in my defense, i feel there are tons of good print and online resources on this topic, i made this video after a section tutorial in which I tried to get through this example very quickly and I got twenty blank stares from students - thus I thought some people might like the long winded, slow, assume this is the first time people are seeing this material, and take nothing for granted approach - sorry if I failed even at that!)

Yes I started doing the same a few months ago. But this one was a touch beyond me I must admit....

The 1st and 2nd derivatives of the production function will usually show (this is usually an assumption anyway) that the marginal return to the factors of production (K and L) are positive but decreasing. The 1st derivative gives the MPL and MPK, it gives the marginal returns to the factors in the production function. And it shows they are positive. If you then take the 2nd derivative, you'll find it's negative, implying those marginal returns re decreasing. (implying a concave p.f.)

You just saved my life. Thank you Sir !!

thank you very much.. the intro reAlly help me to solve my Solow Model assignment even they are not really related..

You should be a teacher. This was beautiful! Thank you!

well explained the problem. if the Function is in intensive form Y= AL (k) where k= K/L small k show the capital per unit of effective labor. Show that the marginal product of labor

A positive 1st derivative (positive MPL and MPK) means that if you add a bit more of that factor of production, then you get a bit more output. (Makes sense). A negative 2nd derivative means that as you add more of a factor of production, it has less of an effect on output (are you familiar with the expression, "too many cooks in the kitchen?").

Thank you. You made me feel good about my self today!

If the sum of the exponents above the production function's factors (K and L here, but there might be other factors) is greater than one, then it will exhibit increasing returns to scale. That's a feature of the Cobb-Douglas production function. Having alpha above K and (1 - alpha) above L ensures constant returns to scale. Hopefully that was helpful!

Thank you! I found this very helpful

economicurtis you are a good tutor! I found it easy to follow your tutorial :) thanks cos i tried several videos and urs was the most useful.

I need to look for Cobb Douglas.

Clear and very well explained video, thank you.

Thanks a lot! This really helps me do my homework! Waiting for more videos from you :))

thank you very much for this video. iv been stuck on a very similar question for whole day this help me heaps. much appreciated :)

For each input (i.e. K & L) are there increasing or decreasing marginal returns? Thanks a lot for the video! Very helpful : )

Very helpful, cheers!

Thanks. Helped alot

I haven't reviewed micro is a couple years, to be honest. And I don't understand the question -- I thought with a production function for a firm, we're assuming the firm uses the minimum amount of factors (labour, captial) to achieve that level of output - i.e. the firm is technically efficient. Maybe you're given a parameterized cobb-douglas and asked to plus in various combinations of capital and labor, and see the level of output?

Hi! Excellent video. U have made it crystal clear for me to understand. Could I ask how do we calculate changes over time for each of the respective variable.. suppose changes in dY(t) /d(t)? Really appreciate it! Thanks!

THANKYOU

Nicely done. Thank you sir!

awesome - happy to have helped you out.

awesome video helped me alot!! thanks for posting it on you tube

I'm pretty sure with the production function I used, it exhibits decreasing marginal returns for capital and labor. To show this, you need to take the first and second derivatives of the production function with respect to capital and labor, and for each show that the first derivative is positive, and the second derivative is negative (which, mathematically implies dmr). I'll make this winter break!

This was helpful!

You are a life savier. Thank you

Thank you so much for this video!!

Really really helpful, thanks a lot!

When alpha and beta equal 1, that's just a constant returns to scale production function. I'm pretty sure you follow the same steps as I do in the video.

Perfect explanation! Thank u so much! :)

Excellent video.Thanks

The video is great, very useful and easy to understand. Thank you @economicurtis .But for memorizing this kind of "complicated" things it is better to solve some problems. Maybe someone knows where i can find Cobb-Douglas production function problems?

Thank you for thanking me!

Nice discussion..

Its hard but this a lil helpful. Thank you!

thank you! great video

Suppose the conntracter wants to bulida budget and his objective function is given asQ=0.5 L1/2 k1/2 and the priceg labour wage (W) and 5 and then the cost out way is and 600 then find the aount of labour and captal which maximizes the out put and find the amount of labour and captal which minimizing cost subject out put 10%

very helpful, thank you

So useful, thank you very much sir :)

What if we've been given the production function to be alpa and beta

Thank you, will do!

and how do I get the average productivities and also elasticity of substitution of unity?

Thank you so much for your help :)

Thank you!

YOu explain in a cool way , would you please explain tralog function too.

Fantastic video. How do I solve this Y=100X1⅓X2⅔

why does no one explain what the rental rate of capital is. Thats like the most important bit. What are those variables - R and P. Does P mean Price or Production? So confusing. Everybody just tend to skip it for some bloody reason.

at 5.01 when u canceled the -1 where did u cancel it out from?

thanks mate

i have a problem related to the codd dogglas production function , i hope you will help me in finding solution to this problem the production function of an economy is given Y = K^0.4 L^0.6 . Growth rates of output, capital and labor are 5% , 8% and 2% respectively over a certain period . what would be the Growth rate accounted for by factor accumulation ??? thanks

I am asking if you can help me with this question: Theory of production by one only variable input and other fixed

How does the elasticity of substitution between capital and labor, σ, = 1?

Hey thank you. You should be paid for this humanitarian work to the beleaguered economic students out there haha!

Thank u so much sir!

You're welcome!

Thank you

Very informative. How would I use cobb douglas production function in agricultural finance? Having in mind, credit only affects the inputs indirectly. And how would i regress that function to find the correlation between credit and higher output? Kindly help.

Assume that all individual units of labour receive the same reward in real terms (we call this ‘the real wage’) and that this is equal to the marginal product of labour. Assume also that all individual units of capital receive the same reward in real terms (we call this ‘the real rental’) and that this is equal to the marginal product of capital. How can you show that if this is true and that all labour and capital income is spent on the goods and services produced in this economy then in real terms the total value of expenditure will be exactly equal to the total level of real output in this economy?

which is the software that you used for typing mathematical equation like in this video??

you're welcome!

this is great thanks for u/l

if you dont make money out of this, its really lame , thanx a lot great job !

whoa fast reply.. while ur here leme ask you.. i have a midterm on monday Use these data to measure the technical efficiency using Microsoft Excel and the methodology that employs the Cobb-Douglas production function and a table is given with labor - capital and output.. am suppose to use excel and get regression but no idea what to do next any idea? thanks

Thank u very much....u really did helped me.

For each input (K nd L), are there increasing or decreasing marginal returns? thanks

sorry how do u completely differentiate the cobb Douglas function when alpha + beta = 1? thx

u should do a calculus for beginers video

Can you answer me about how can I get the alpha and beta when I have got the K and L and A by using eviews 6.0

Awh. thank you.

welcome!

I was suggested to watch this o_0

you bet!

This is not helpful without an actual example in numbers. What exactly is ∆ its own??? You can have ∆y or ∆k ( or dy, dk) but d on its own is meaningless.

It's a great video but I have waited an example at the end..

What program are you using to write?

i think the way it is typed is very confusing.

Very good video, but you could be more direct. As Elvis would say "Little less conversation, a little more action, please".

is it okay to do that? 4:36

Why isn't in dy/dL= AK^a(1-a)/L^a

OK!