Derivation of Marshallian Demand Functions from Utility Function

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Derivation of Marshallian Demand Functions from Utility Function

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Deriving Marshallian Demand Functions from Generalised Cobb Douglas Utility Function
Derivation of Marshallian Demand Functions from Utility Function
Learn how to derive a demand function form a consumer's utility function. In this problem, U = x^a*y^b
This video introduces the Cobb-Douglas utility function for two goods and demonstrates some of its properties.
I demonstrate how to compute marginal rate of substitution for Cobb Douglas utility. I use the resulting expression to show why Cobb Douglas indifference curves have constant slope along rays out of the origin.
I also demonstrate how to solve for consumer demand using the Cobb-Douglas utility function. After deriving Cobb-Douglas demand, I show that the alpha share parameter in Cobb-Douglas utility functions actually represents the consumer's expenditure share on that good.
This video uses calculus to compute MRS, but after that, the rest is just algebra. If you are a viewer who doesn't know calculus, you can take me at my word, skip the computation of MRS, and the rest of the video can still be worthwhile.
Economics Playlist
Derivation of Marshallian Demand Functions from Utility Functions: • Derivation of Marshall...
Derivation of Marshallian Demand Functions from Utility Functions (II): • Derivation of Marshall...
Derivation of Hicksian Demand Functions from Utility Functions:
• Derivation of Hicksian...
Deriving Marshallian and Hicksian Demand Functions (compensated and uncompensated demand):
• Deriving Marshallian a...
Derivation of a Generalised (n-good) Marshallian Demand Function from Utility Function.
• Derivation of a Genera...
Deriving Hicksian (compensated) Demand Using the Slutsky Equation:
• Deriving Hicksian (com...
Deriving Marshallian Demand From a Stone-Geary Utility Function:
• Deriving Marshallian D...
I hope the video helps :)

Пікірлер: 59

@lingyanzhang9253 11 ай бұрын

Thank you so much for this tutorial!

@HaroldWalden 11 ай бұрын

You are so welcome! Glad it helped!

@PumpkinEatSpice 6 жыл бұрын

Fantastic explanation. Really helped me refresh my knowledge of Marshallian demand functions! Thanks!

@HaroldWalden 6 жыл бұрын

I am glad it helped :)

@PromdiMeets 6 жыл бұрын

Hey Harold. I don't comment much on videos around youtube. But THANK YOU FOR THIS VIDEO. It is very helpful! Subscribed also :)

@HaroldWalden 6 жыл бұрын

Thanks for the comment, it is really encouraging to hear people are getting value from these videos. If you are ever having problems with a concept or problem, let me know, I am always looking for new video ideas :)

@faithtushabe Жыл бұрын

Very helpful video, thank you

@HaroldWalden Жыл бұрын

I am glad the video helped, let me know if there are any concepts that need more of an explanation. I am always looking for new video ideas 🤓

@4frenkie4 2 жыл бұрын

thanks. this is absolutely useful. With love from Surrey

@HaroldWalden 2 жыл бұрын

Glad it helped! Thanks for taking the time to leave a positive comment. I really appreciate it 🤓

@adamw2030 4 жыл бұрын

Really appreciate the help, have a final tomorrow!

@HaroldWalden 4 жыл бұрын

Great, good luck mate. I hope the video helped 🤓

@greenangelssky 6 жыл бұрын

Thank you so much-this cleared up all my questions!! You're a star

@HaroldWalden 6 жыл бұрын

Glad I could be of assistance :) If you ever need any help with concepts like this - send me a message. I am always looking for new video ideas.

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@damaridamien3367 3 жыл бұрын

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@rbvmooneesawmy1940 6 жыл бұрын

thanks bro.. you are a savior

@HaroldWalden 6 жыл бұрын

No worries mate, glad it helped :)

@nicholasbloom2414 5 жыл бұрын

Hey Harold, really enjoying the videos and helping a lot with my advanced Microeconomics course. I have one question, in your other video deriving the Marshallian demand from the utility function you use -Lamda but here you use +lamda in the lagrange multiplier, is there a reason for this change in the CD utility function. Many thanks from a thankful subscriber

@HaroldWalden 5 жыл бұрын

Good question, I guess it depends what mood I am in. It doesn’t effect the solution at all. This is because when you divide the first two first order conditions by each other to get rid of the lambda coefficient the negative signs (if you have them) will cancel each other out anyway. It is really nice to hear that people are getting value out of these videos. I have been flat out in my real life outside KZfaq so I haven’t posted any videos lately - I really to change that ASAP. Also great to hear that you are a subscriber, just make sure if your finding the videos helpful please tell your mates about my channel. Cheers for taking the time to leave a comment, I really appreciate it ❤️ Harold 🤓

@zouH2807 3 жыл бұрын

thank you so much great explanation! helped me alot

@tamilbiblestories 3 жыл бұрын

Dear Sir, Great explanation. Pls clarify how to solve the langragian when there is another quantity restriction on one of the goods.

@HaroldWalden 3 жыл бұрын

So do you have a situation in which you have 3 goods or do you have 2 different restrictions?

@jamesbullock5713 6 жыл бұрын

Awesome vid. Thanks mate.

@HaroldWalden 6 жыл бұрын

I am glad it helped :)

@nanditanair6168 5 жыл бұрын

This was so helpful! Thank you very much. I particularly appreciate how you break down your methods of simplification. How would we adapt this for a utility function for perfect complements? e.g. u(x,y) = min{αx, βy} Thank you again!

@HaroldWalden 5 жыл бұрын

So for perfect compliments, there is only one optimal solution due to the fact that regardless of the price of one good, you also need the other good as well. The way I think about is to consider if you needed to buy shoes individually - in this scenario, the shoes are perfect compliments; you're not going to buy 5 left foot shoes without buying the corresponding 5 right foot shoes. Because there is only one optimal solution, we don't need to optimise it using calculus. At the optimal point; αx = βy which we can rearrange to make y in terms of x; y = αx/β. Substituting into the budget constraint M=(p_x*x)+(p_y*y) we get M=(p_x*x)+(p_y*(αx/β)) Factorising right-hand side by x: M=x[p_x+αp_y/β] Allowing x to become the subject; x*= M/[p_x+αp_y/β] Which the Marshallian demand for x. To get y it is exactly the same but you rather than rearranging to make y=something, you make x=something Hope that helps, let me know if anything needs clarifying :)

@HaroldWalden 5 жыл бұрын

Also, thanks for the positive feedback, I really appreciate it.

@nanditanair6168 5 жыл бұрын

Hi! I was wondering if I could bother you for a bit of help on this question: Calculate the demand functions of u(x1; x2) = ln x1 + x2 and the price and income elasticity of demand for each good. How would you work it out for a quasilinear function?

@HaroldWalden 5 жыл бұрын

Yeah no worries, I’ll get to that today. I hope that’s alright. :)

@HaroldWalden 5 жыл бұрын

@@nanditanair6168 Here is a link to a PDF which details my explanation to your question. If you need any clarification on what I have said, please don't hesitate to let me know. :) drive.google.com/file/d/1JbMhyd5gVOgc7gfrlDLZeMsdbfvu8XsM/view?usp=sharing

@leeorianna5797 3 жыл бұрын

Very useful!!! Thanks!

@haoran1996ify 4 жыл бұрын

Great help, thank you so much

@HaroldWalden 4 жыл бұрын

No problem, I am so glad that the video helped 🤓

@zainmalik4323 2 жыл бұрын

*Truly Awesome!* Can you recommend me a book in which these types of derivations are given?

@carlawalden 6 жыл бұрын

Great video, thanks :)

@intankhoirulaulia5281 2 жыл бұрын

thank you so much! This was so helpful!

@HaroldWalden 2 жыл бұрын

Thanks for taking the time to leave a positive comment. I really appreciate it 🤓

@supermec131 6 жыл бұрын

If I were unable to guarantee that the solution were not on the y or x axis (y or x = 0), then would I need to include restrictions of non-negativity in the lagrangian function? Likewise, if I had a utility function that was not monotonous, or even one with negative goods whose level curves grow inwards rather than outwards, I wouldn't be able to guarantee that the income restriction would be active at the optimal point: we could have an optimal inside the affordable set and not on the line described by the equality PyY + PxX = I, and instead we'd have to use: PyY + PxX

@HaroldWalden 6 жыл бұрын

Have a read of this, if I was going to answer your question I would be essentially be copying what it says anyway. business.illinois.edu/nmiller/documents/notes/yktay.pdf Hope it helps 🤓

@supermec131 6 жыл бұрын

thanks!

@HaroldWalden 6 жыл бұрын

No worries :) if you need me to elaborate on anything let me know 😁

@muhammedlaminceesay7881 5 ай бұрын

thanks a lot

@amushkamohammed2064 Жыл бұрын

Why did you replace 1 with alpha/alpha at 9.10

@HaroldWalden 11 ай бұрын

You do that so you can express what is in the brackets as a single fraction. It is just an algebraic move which sometimes helps you down the line. I usually do stuff like that out of habit because I think I might need the simplified version later. I hope that clears it up.

@obaidurrahman2405 4 жыл бұрын

I think there are some mistakes in the question,It should look like marshallian Demand Function x(Px,I) And y(Py,I)

@HaroldWalden 4 жыл бұрын

The question is asking for the Marshallian demand function in terms of income and a vector of both prices - not simply the single good case.

@HaroldWalden 4 жыл бұрын

This is probably a more realistic example of how consumer choice works because in real life your demand function will be determined by both the price of the good in question as well as the price of all of the other goods that you you can derive utility from by purchasing.