CES Intro: Constant Elasticity of Substitution Utility/Production Functions 

Thanks for your first ever comment! ☺

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.

Thanks for the feedback! Glad to have you here!

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.

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!

Yes, indeed. If σ=0, perfectly inelastic. Sorry for not saying that explicitly. So much to cover, so little time. ☺

did you find the derivation?

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-4aH-NeqDwgc.html Thank me later

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.

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

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.