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.
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. 😊
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
you can do it, man, I started saw this video 3 months ago, didn't understand it, then I went to check partial derivatives, didn't get them either, then I went below that algebra and its rules, and after three months of making problems over and over, I finally understand this and it's not that hard I swear, write me back if you need help!
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.)
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?").
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!)
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!
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.
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
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!
It's really tough to balance making a tightly focused tutorial while hitting all the important points, so I'm sorry that I glossed something folk will find useful. Sorry and thanks Jonathan Violante Pica!
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!
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.
economicurtis Help solve this.Q=f(KL)=AL^2/.K^1/2. Compute MPl. MPk and MRTS. 2.determine degree of return to scale when both k and l are increase by half.
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%
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!
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?
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
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
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?
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.
Alpha is a parameter. -With a cobb douglas production function, if the exponents above the factors (K & L) sum to one, then you've got constant returns to scale. -Thus with alpha above K, and (1-alpha) above L, you know you got CRS with this production function. (CRS comes in handy elsewhere). - Alpha also stands for other stuff. With CRS - and assuming alpha is above K - alpha is going to give you the share of income that goes to Capital. - That also means that 1-alpha is the Labor share of income (look up those terms of you're not familiar. - best o'luck out there.
economicurtis And to add a bit more, with CRS (see prev comment) alpha is the "capital share of income"... which is a little tricky to explain in a YT comment thread!
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?
Lachlan K TheMatez6 tey jian phern hipPoPiing Andrew G Haha, ok, I haven't touched Macro since 2012, but by popular demand: For notation, call the MPL w , and the MPK k . The "total value of expenditure" is just {L*w + K*r}. We have formulations for both of those solved in this video. Plug those guys into your "total value of expenditure" equation. Now look closely at what you have, do you see anything canceling out? What you're left with is just equal to Y. Y is output, or the "total level of real output in this economy". Hope that gets you on the right path. Now please help me find a tenure track professorship job!
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.
Very helpful! My textbook skipped over such steps, leaving me confused for hours on end. Thanks to you, I averted a nervous breakdown. Seriously...
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!
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.
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. 😊
Thanks for all the awesome content you create. Macro economics just got a little easier because of you, sir!
THE BEST VID OF THE C.D. FUNCTION IVE WATCHED!! SIMPLY THE BEST!!
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 economicurtis because of your videos I have been able to gain significantly more knowledge on economics. Thank you.
Yes I started doing the same a few months ago. But this one was a touch beyond me I must admit....
I don't understand any of this no matter how many times I read about it and watch videos on it.
I'm so sorry to hear that
+Lost cause Man don't Give up! This video is amazing because any person can understand! Including me! Great Video thx economicurtis
lost cause lmfao
you can do it, man, I started saw this video 3 months ago, didn't understand it, then I went to check partial derivatives, didn't get them either, then I went below that algebra and its rules, and after three months of making problems over and over, I finally understand this and it's not that hard I swear, write me back if you need help!
Marvelous
Finally after 3 year a got this concept 👍
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!
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.)
This video is a lifesaver. Thanks a lot, you have no idea how much you helped me!
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?").
THANKYOU
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!)
Thank you so much, my man! I'm definitely subscribing and watching your stuff from now on! life saviour
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!
best vedio of cobb douglass function i have ever seen. dude if i were a girl i am gonna definetly marry you
Thank you, professor. Thanks to you, I understood it easily.
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.
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
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!
It's really tough to balance making a tightly focused tutorial while hitting all the important points, so I'm sorry that I glossed something folk will find useful.
Sorry and thanks Jonathan Violante Pica!
You should be a teacher. This was beautiful! Thank you!
thank you very much.. the intro reAlly help me to solve my Solow Model assignment even they are not really related..
thank you very much for this video. iv been stuck on a very similar question for whole day this help me heaps. much appreciated :)
I need to look for Cobb Douglas.
Thank you. You made me feel good about my self today!
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.
Thank you! I found this very helpful
Clear and very well explained video, thank you.
Thank you for saying that!
awesome video helped me alot!! thanks for posting it on you tube
You just saved my life. Thank you Sir !!
awesome - happy to have helped you out.
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!
You are a life savier. Thank you
Thanks a lot! This really helps me do my homework! Waiting for more videos from you :))
Very helpful, cheers!
Excellent video.Thanks
Nicely done. Thank you sir!
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.
This was helpful!
Great video thank you!
You're welcome!
economicurtis
Help solve this.Q=f(KL)=AL^2/.K^1/2.
Compute MPl. MPk and MRTS.
2.determine degree of return to scale when both k and l are increase by half.
Nice discussion..
extremely helpful! thank you so much
So useful, thank you very much sir :)
Really really helpful, thanks a lot!
Perfect explanation! Thank u so much! :)
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%
Thank you !
and how do I get the average productivities and also elasticity of substitution of unity?
Thank you, will do!
Thank you for thanking me!
Its hard but this a lil helpful. Thank you!
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!
YOu explain in a cool way , would you please explain tralog function too.
For each input (i.e. K & L) are there increasing or decreasing marginal returns?
Thanks a lot for the video! Very helpful : )
Thank you so much for your help :)
very helpful, thank you
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?
at 5.01 when u canceled the -1 where did u cancel it out from?
sorry how do u completely differentiate the cobb Douglas function when alpha + beta = 1?
thx
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
you're welcome!
thanks mate
How does the elasticity of substitution between capital and labor, σ, = 1?
Thank u so much sir!
Thank u very much....u really did helped me.
yeah....wena
yoh complicated nje ingiphathisa nekhada
hopefully
Thank you (hopefully).
I'm guessing you have an exam soon, good luck!
Kahleni ukusibhalela into engakhulumi bantabami. Impukane zani manje lezi???
Thank you
this is great thanks for u/l
if you dont make money out of this, its really lame , thanx a lot great job !
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
For each input (K nd L), are there increasing or decreasing marginal returns?
thanks
Hey thank you. You should be paid for this humanitarian work to the beleaguered economic students out there haha!
Fantastic video. How do I solve this Y=100X1⅓X2⅔
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
welcome!
u should do a calculus for beginers video
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?
you bet!
What if we've been given the production function to be alpa and beta
I am asking if you can help me with this question: Theory of production by one only variable input and other fixed
is it okay to do that? 4:36
Awh. 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.
did you manage to find out? Would be interested to know aswell
I unfortunately haven't.
Very good video, but you could be more direct. As Elvis would say "Little less conversation, a little more action, please".
It's a great video but I have waited an example at the end..
which is the software that you used for typing mathematical equation like in this video??
Kien Dinh its just microsoft word, using the equation editor
What program are you using to write?
Just MS word. It actually has a pretty good type-as-you-go equation editor.
what does alpha mean and what does it stand for?
Alpha is a parameter.
-With a cobb douglas production function, if the exponents above the factors (K & L) sum to one, then you've got constant returns to scale.
-Thus with alpha above K, and (1-alpha) above L, you know you got CRS with this production function. (CRS comes in handy elsewhere).
- Alpha also stands for other stuff. With CRS - and assuming alpha is above K - alpha is going to give you the share of income that goes to Capital.
- That also means that 1-alpha is the Labor share of income (look up those terms of you're not familiar.
- best o'luck out there.
economicurtis And to add a bit more, with CRS (see prev comment) alpha is the "capital share of income"... which is a little tricky to explain in a YT comment thread!
months later u reply
cheers anyway m8
make videos on a regular basis
I was suggested to watch this o_0
OK!
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?
hipPoPiing i need answer for your question, can someone answer this?
hipPoPiing i need answer too please
hipPoPiing di dyou get the answer i need it for tomorrow lol
TheMatez6 did you get the answer?
Lachlan K TheMatez6 tey jian phern hipPoPiing Andrew G Haha, ok, I haven't touched Macro since 2012, but by popular demand: For notation, call the MPL w , and the MPK k . The "total value of expenditure" is just {L*w + K*r}. We have formulations for both of those solved in this video. Plug those guys into your "total value of expenditure" equation. Now look closely at what you have, do you see anything canceling out? What you're left with is just equal to Y. Y is output, or the "total level of real output in this economy". Hope that gets you on the right path. Now please help me find a tenure track professorship job!
i think the way it is typed is very confusing.
Why isn't in dy/dL= AK^a(1-a)/L^a
I'm not 100% sure, but I'm pretty sure dy/dL is AK^a(1-a)/L^a.
That is to say, AK^a(1-a)/L^a is equivalent to the solution I showed above.
It's just also handy to show the MPL and MPK in relation to Y.
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.
you do know that without actual figure this makes no sense