Thanks for this video and I hope I may ask a question too: Why did Arrow et al. in their 1961 paper write that sigma=1/1+rho, but now I mostly find the equation as you explained it sigma as 1/1-rho (which also seems more intuitive to me). Am I missing a point or did sth change over time?
Just a question, what program did you use to graph the function, is it just an adapted math program, or you used a language code program and you built the algorithms like python or java?
I used Maple, which unfortunately costs a lot of money (Maxima is a free alternative that isn't quite as good. I added a link in the video description to the Maple command file to make the graphs, and do some other things in the next video.
@@BurkeyAcademy okay, yes, its expensive. I saw too that the ces file is in maple, si a Im gonna find a converter for this. Thanks for sharing this content.
I'm not sure what you mean by "consideration about the Blue Line". If you are asking "Is the slope of the Blue line the same as the MRS", the answer is no. The MRS is the slope of the IsoQuant (the red curve) at a point. This could be represented by a tangent line to the red curve: but the blue ray is not tangent since it would go through the curve, the slope is positive (instead of negative) an in general the slopes will not be related in a simple way.
Please, in order to derive the Marshallian demand for n goods of the CES utility function, can you tell me how to write the general form of the function ? In the document below (page 6), the function is written but i don't understand. www2.econ.iastate.edu/classes/econ501/Hallam/documents/FunctionalForms.pdf Thanks a lot.
They are using a simplified form without the 1/p exponent. They are saying that CES= a*x^p + b*y^p + c*z^p ... and so on, for however many goods you have.
a couple of questions: 1) can you kindly tell the intuition behind this CES function? I mean, why do we divide the whole fringe by (roh) ? And what is the sense---like x^p, y^p mean? 2)and what is the benefit of having a constant elasticity in economic analysis?
1) I don't understand the question. Raising the inside factors to p, then raising the sum to 1/p just happens to give you a production function that has the property that it has "Constant Elasticity of Substitution". 2) The only benefit is that discovering this function added another somewhat easy function that people can try to estimate when they have actual data on production from a firm. When you first have data, you have no idea what kind of functional form might be the best "fit" to explain the data. So, using regression techniques you try various functional forms to see what fits the data the best, by estimating a, b, and p. However, there are many other functions you can try. At the time is was discovered, the CES function was cool because it is one function that actually contains several other common possibilities as special cases, as I discuss in the video. So, it saves you time!
I doubt it. Simply dropping (1/rho) is not a monotonic transformation. I know you're trying to simply the analysis by reducing the original utility to a less complex utility function. But that transformation doesn't preserve the ordering or preference. Given x>y>0, If rho=(-1/2), for example, then x^(-1/2)
Oh- you didn't say you were talking about CES Utility AND dropping the 1/p. For me, CES utility is not really what CES was invented for- I usually think of it in terms of production. So yes, if rho is negative, dropping 1/p is no longer a positive, monotonic transformation in the utility case. I have never worked with CES utility, or seen anyone else use it in research work- seems to be more of a math problem to torture economics students with. ☺
Yes, sir. I am working out a solution to the UMP of a CES utility function using lagrangian multiplier. It's part of homework for an advanced micro class. I don't know much about economics research cause I've not learned economics for long and I'm more focused on finance now. But I do remember CES has been extensively used as a utility function in research on International trade. I've never seriously thought about the rho in CES, though. My gut feeling is just like everyone else, which is just to treat rho as positive.
You blew my mind, amazing pedagogical skills
The final dynamic picture is amazing!! Thanks a lot!!
You were excellent dear. Loved it. Thanks a ton.
WOW a big thumbs up! This is my first comment ever on youtube, it is that helpful !
Thanks for your first ever comment! ☺
Thank you for yet another wonderful video. It would be extremely helpful if you could make a video for Translog production function.
Great explanation ...thank you for this.
Also, you sound a lot like Robert Downey Jr.
Excellent video, thanks!
Thank you! Best wishes and greetings from Costa Rica.
You are welcome! I just went to C.R. last month!
@@BurkeyAcademy ohh. nice, I hope you got a good stay, we have great distinguished economists in my institution.
Useful and the most skilful
Absolutely fantastic
huge help. thank you
Thanks for this video and I hope I may ask a question too:
Why did Arrow et al. in their 1961 paper write that sigma=1/1+rho, but now I mostly find the equation as you explained it sigma as 1/1-rho (which also seems more intuitive to me). Am I missing a point or did sth change over time?
Sir, Please make a video on translog cost function and production function.
Simply amazing!
Thanks! Really helps a lot!! ♡
hi, can you share the derivation of sigma = (1/1-rho)?
did you find the derivation?
th-cam.com/video/4aH-NeqDwgc/w-d-xo.html
Thank me later
Please how does the degree of homogeneity relate to elasticity of substitution?
Is ces utility function different from ces production function
Just a question, what program did you use to graph the function, is it just an adapted math program, or you used a language code program and you built the algorithms like python or java?
I used Maple, which unfortunately costs a lot of money (Maxima is a free alternative that isn't quite as good. I added a link in the video description to the Maple command file to make the graphs, and do some other things in the next video.
@@BurkeyAcademy okay, yes, its expensive. I saw too that the ces file is in maple, si a Im gonna find a converter for this. Thanks for sharing this content.
9:20 consideration about blue line...isn't it the same as MRS?
I'm not sure what you mean by "consideration about the Blue Line". If you are asking "Is the slope of the Blue line the same as the MRS", the answer is no. The MRS is the slope of the IsoQuant (the red curve) at a point. This could be represented by a tangent line to the red curve: but the blue ray is not tangent since it would go through the curve, the slope is positive (instead of negative) an in general the slopes will not be related in a simple way.
saved my life:)
You should teach me instead of my professor. Your explanation is 100x better than his
Thanks for the feedback! Glad to have you here!
Please, in order to derive the Marshallian demand for n goods of the CES utility function, can you tell me how to write the general form of the function ? In the document below (page 6), the function is written but i don't understand.
www2.econ.iastate.edu/classes/econ501/Hallam/documents/FunctionalForms.pdf
Thanks a lot.
They are using a simplified form without the 1/p exponent. They are saying that CES= a*x^p + b*y^p + c*z^p ... and so on, for however many goods you have.
Thank you very much.
Very helpful...thank you so much
a couple of questions:
1) can you kindly tell the intuition behind this CES function?
I mean, why do we divide the whole fringe by (roh) ?
And what is the sense---like x^p, y^p mean?
2)and what is the benefit of having a constant elasticity in economic analysis?
1) I don't understand the question. Raising the inside factors to p, then raising the sum to 1/p just happens to give you a production function that has the property that it has "Constant Elasticity of Substitution". 2) The only benefit is that discovering this function added another somewhat easy function that people can try to estimate when they have actual data on production from a firm. When you first have data, you have no idea what kind of functional form might be the best "fit" to explain the data. So, using regression techniques you try various functional forms to see what fits the data the best, by estimating a, b, and p. However, there are many other functions you can try. At the time is was discovered, the CES function was cool because it is one function that actually contains several other common possibilities as special cases, as I discuss in the video. So, it saves you time!
@@BurkeyAcademy .Now i get it. That is just givin me a production function. Thankyou for the second answer. It makes sense ! thanks!
Perfectly inelastic
Yes, indeed. If σ=0, perfectly inelastic. Sorry for not saying that explicitly. So much to cover, so little time. ☺
you are great...
saludos
Thanks!!!
helpful. thank you very much
what if rho is smaller than 0? Why nobody talks about this?
There is nothing weird if rho
I doubt it. Simply dropping (1/rho) is not a monotonic transformation. I know you're trying to simply the analysis by reducing the original utility to a less complex utility function. But that transformation doesn't preserve the ordering or preference. Given x>y>0, If rho=(-1/2), for example, then x^(-1/2)
Oh- you didn't say you were talking about CES Utility AND dropping the 1/p. For me, CES utility is not really what CES was invented for- I usually think of it in terms of production. So yes, if rho is negative, dropping 1/p is no longer a positive, monotonic transformation in the utility case. I have never worked with CES utility, or seen anyone else use it in research work- seems to be more of a math problem to torture economics students with. ☺
Yes, sir. I am working out a solution to the UMP of a CES utility function using lagrangian multiplier. It's part of homework for an advanced micro class. I don't know much about economics research cause I've not learned economics for long and I'm more focused on finance now. But I do remember CES has been extensively used as a utility function in research on International trade. I've never seriously thought about the rho in CES, though. My gut feeling is just like everyone else, which is just to treat rho as positive.
" seems to be more of a math problem to torture economics students with" My professor gotta read it