Derivation of Hicksian Demand Function from Utility Function

Derivation of Hicksian Demand Function from Utility Function
Learn how to derive a demand function form a consumer's utility function. In this problem, U = x(1)*X(2)^2
*Edit: Part (a) of this question should read the consumer's expenditure minimization problem*
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...

[@HaroldWalden]

**Edit: Part (a) of this question should read the consumer's expenditure minimization problem**

[@harmankhinda5743]

You explain econ so much better than everybody else on KZbin. Your work is neat and easy to read, and you also explain the meaning of the functions you derive. Best econ professor on YT by far. Keep up the good work sir!

[@HaroldWalden]

Thank you so very very much, I really appreciate the positive feedback. If you are having any problems with your economics work please let me know, I am always looking for new video ideas. Also, please make sure you subscribe to the channel and let your friends know about me, as a smaller KZbinr I need all the help I can get from viewers to get my videos in front of as many eyeballs as possible. Anyway, thanks again for the feedback ❤️

[@harmankhinda5743]

Harold Walden Yup will do. I’ll tell my classmates about this channel.

[@HaroldWalden]

Thanks ❤️❤️

[@jessp421]

I asked myself "I wonder where this bloke's from, he sounds like he could be from Perth", then I check the channel and there you go. Strange combo of skating and econs, but good video. Thanks from Germany!

[@HaroldWalden]

That is nuts! I don't know if Western Australia has a location specific accent but I am happy to be informed otherwise... I think the skateboarding is just something that I got addicted to as a kid, I am not very good but I still have heaps of fun going to the skatepark. Thanks for the positive feedback, I really appreciate it :)

[@jessp421]

Yeah I didn't know until I moved away, now I notice it because it sounds like default to me. It's a much better accent than Queenslanders anyway.

[@HaroldWalden]

Never has a truer word been spoken!

[@HaroldWalden]

Haha, that is pretty funny :)

[@Viancqa]

The best Hicksian vs Marshallian video I've ever found! Glad everything's now cleared up before my exam. Thank you so much for this :)

[@HaroldWalden]

Thank you for the kind words, I really appreciate it. :)

[@nanaluna6018]

thank you so much for all your economics videos. you help(ed) me a lot. I sometimes feel like I learn a lot more from watching your videos than from listening to my professor. keep it up!

[@KillswitchLtd1]

Thank you so much mate! My econ teacher is doing basically the same function some way more complicated way! You have given me faith that i will pass this course!

[@HaroldWalden]

Great! I hope it makes a little sense of what can be just a jumble of terms.

[@awadheshsireducationpoint4220]

It was very helpful video regarding to hicksian demand in comparison to other you tube videos, thank you sir...

[@davidturay4160]

Thanks for your professional lectures. I got it clear

[@HaroldWalden]

No worries, I am glad to be able to help people understand what is otherwise quite a confusing topic.

[@KiraAnandita]

Mate thank you so much for putting up this video. Very very helpful!!

[@HaroldWalden]

I am so stoked that you found what I have to say useful. The only reason I made this video is because I struggled so hard initially trying to wrap my head around the concept and I couldn't find anyone that had provided a suitable explanation of what you needed to do, step by step, to solve these kind of problems. If you need any other videos made, let me know please :)

[@Chigatera]

This has saved my life. Thank you.

[@HaroldWalden]

Thanks for taking the time to watch and leave a positive comment, I really appreciate it 🤓

[@dianacarillo5423]

the best video I've seen yet for this thank you

[@HaroldWalden]

Glad you liked it 🤓

[@wanjadouglas3058]

Thank you Harold. This was very helpful as I do Micro 1 for my PhD coursework.

[@HaroldWalden]

I am glad it was helpful, thanks for taking the time to leave a positive comment 🤓

[@douglasespindola5185]

Thank you! Greetings from Brazil!

[@HaroldWalden]

No worries, I hope it was helpful :-)

[@HaroldWalden]

Another optimisation problem that kinda forms the basis of modern economics.

[@izhanarif1542]

the best of the best, hands down.

[@HaroldWalden]

Don’t know about that but thank you ☺️

[@tallyskalynkafeldens1753]

You're the best! THANK YOU!

[@HaroldWalden]

Thanks for taking the time to leave some positive feedback. I really appreciate it. :) I am guessing that this video helped you out a little?

[@brianlu5651]

Thank you so much! -A confused first-year university student.

[@HaroldWalden]

This is a little beyond the scope of a first year university course. You watching these for your own interest???

[@Sui_Generis0]

@@HaroldWalden we had to do this in our first year micro course at cambridge. Came back again this year so this video was a good refresher

[@HaroldWalden]

@@Sui_Generis0 It's good to hear that the video was helpful. Thanks for taking the time to leave a positive comment.

[@sardarnaeemhakimzai4237]

Many many thanks sir.

[@jaredhee4194]

love seeing aussies on youtube - keep up the great work

[@HaroldWalden]

Thanks for taking the time to leave a positive response mate, I really appreciate it. :)

[@maggiewu9946]

very clear! thank you!

[@GMan-um1pi]

You need to explain the step where you actually put together the Hicksian demand @12:30. I have no idea how you got what you did...

[@GMan-um1pi]

After looking more closely I was able to tell what you did, but the expenditure function part got real confusing with you converting to brackets.

[@HaroldWalden]

@Grady thanks for the comment. You are right, my explanation for how I got to the Hicksian Demand functions for good one and good two is bloody hopeless. Basically all I have done is simplified the optimum levels good x1 and x2 that we find after satisfying the first order conditions of the initial Lagrange function and then inputing these values into the consumers utility function. Because in Hicksian demand the individuals total utility is fixed this allows us to find, in terms of a given utility and price (p1 and p2), the quantities of x1 and x2 that we need to buy to minimise the amount that we spend getting to this utility. After we find x1 and x2 in terms of a fixed utility and price we just substitute these individual demand functions back into the expenditure function to see what the individuals minimum total spend will be. I hope this helps.

[@GMan-um1pi]

Thanks for the response - I've never been so confused going into a midterm but your video definitely helped!

[@HaroldWalden]

I hope the midterm went ok.

[@apoionuz]

I think the question you answered in part "a)" should be "Set up the expenditure minimization problem", isn't it?

[@ice_bearie3818]

agree

[@HaroldWalden]

You're right, I did have a **Edit** in the video description but I'll pin a comment to the top as well. Good spot! Sometimes I go into autopilot when I make these videos and I had just made a corresponding Marshallian Demand tutorial so I must have accidentally cut and pasted a little too much... It happens to the best of us. Thanks for keeping me honest :)

[@ilknur53123]

thanks a lot for video! it is really helpful

[@HaroldWalden]

+ilk nur no worries, it is greats to hear that the videos are helping people. Do me a favour and recommend my channel to people that you think might find the videos useful please. Thanks :)

[@ilknur53123]

Don't worry, i will :))

[@HaroldWalden]

Thanks xx

[@Explorer982]

Great videos Do you have any plans to do some of the corresponding graphs?

[@nxa74]

When setting up the lagrangian in this case, why is it + lambda instead of - lambda as in when deriving marshallian demand functions?

[@HaroldWalden]

It doesn’t matter whether you plus or minus lambda, it works out the same in the end. Check if you like.

[@wanjadouglas3058]

@@HaroldWalden True.

[@muhammedabidemi2622]

@@HaroldWalden it matter, reason behind it is that. The sign, your dependent variable in subjective function after equating it to zero determine the sign you will attributed to your lambda.

[@ambroseezzat2703]

Could you explain why you wrote the constraint in the negative form in the Lagrangian? Shouldn't it be U - Ubar in the brackets after lambda ?

[@HaroldWalden]

It doesn't really matter if you add it or subtract the constraint. you get the same answer in the end anyway.

[@tenzinnamdhak]

Have u got a video on N-good cobb douglas utility function to find the marshallian demand function? Just curious!! thanks for the information anyways. I am grateful..

[@HaroldWalden]

+Tenzin Namdhak I'll put one together today :)

[@HaroldWalden]

kzbin.info/www/bejne/rYbEcn6GpL2ee80 Hope it helps :)

[@dibissaejeta4447]

Find MRS for the following u(x1,x2)=max(ፀx1, x2)

[@Ferdinaand]

thanks a bunch mate

[@HaroldWalden]

+Fern B it is always nice to hear that the videos are helping, thanks :)

[@Kashyapkiduniya92]

Can we take this example as CES demand function?!

[@Theisrarhasan]

I did not understand the hicksian equation part.

[@HaroldWalden]

With Hicksian Demand, we are trying to minimise the cost of attaining a particular predetermined amount of utility --> We want to answer the question; given that we want to be this particular level of happiness, what is the cheapest way to get there? The Hicksian Demand equations come from satisfying the first order conditions of the Lagrangian expression. ie. dL/dx(1)=0, dL/dx(2)=0 Following that you get the amount of a good you will demand given the price of both goods and the amount of the other good demanded. Then you substitute these equations into the utility function so you can get the utility in terms of the prices of both goods but only the quantity consumed of one good. Finally you rearrange the utility function to get the quantity consumed of a particular good in terms of the prices of both goods and the consumer's predetermined level of utility - which is what Hicksian demand is. I hope that helps :)

[@oskarjonsson7010]

When you eliminate Landa by dividing dL/dx1 with dL/x2, what is the rule for doing so? Is it that we know the MRS = U1/U2?

[@HaroldWalden]

Correct 🤓

[@oskarjonsson7010]

@@HaroldWalden Thx for answering and for your video!

[@HaroldWalden]

No problemo 😊

[@naomihalubimba878]

how do you derive a Hicksian and Marshellian demand function given a utility function that has 10 as the coeffient of X raised to the power 2

[@tajpeterson3111]

For other videos, can you please "x" & "y" instead of "x1" and "x2". It would cut down on some confusion and would minimize the use of "x". Just a suggestion. Thank you

[@HaroldWalden]

Good idea,. From what I remember, I was just using an example question that a viewer emailed me. You’re right though, it is way to crazy with the x1 and x2’s. Next time I’ll definitely have a think about how I can make it more simple to follow. I don’t want to leave people more confused after watching the video than they were prior to hitting play. Thanks for leaving some good feedback, I really appreciate it :)

[@tajpeterson3111]

Harold Walden thank you sir. I have a Micro midterm tomorrow and your videos are helping me a lot.

[@HaroldWalden]

TaJ Peterson good luck mate, glad to hear the videos are having a positive impact 🤓

[@tenzinnamdhak]

What if there is three prices and X's?

[@HaroldWalden]

The method is exactly the same just with another First Order Constraint. Here is an okay example that I found: jrm-research.blogspot.com.au/2008/12/solving-three-good-utility-function.html If you would like me to do a video on a three good cost minimisation problem just let me know. Hope that helps :)

[@tenzinnamdhak]

well it's just the marshallian demand function and not the hicksian.

[@ansazaiba3795]

Hello.sir how we find relationship between price and quantity by taking log?

[@luisschneider5617]

do you also do tutoring?

[@Theisrarhasan]

How is it cubed?

[@HaroldWalden]

Which part are you referring to specifically?

[@HaroldWalden]

If you are referring to the cubed part at 9:47 then it is cubed because you have (x_2)^2 being multiplied by x_2 so it becomes (x_2)^3. I hope that helps :)

[@diamonddogsgaming7059]

I have a question here.. when we setup our Lagrange multiplier, I see in the derivation of the hicksian demand, lambda is being added to the constraint, where as in the derivation of the marshallian demand, the lambda is being subtracted from the constraint. However, in another video on derivation of both hicksian and marshallian demand functions such as this link kzbin.info/www/bejne/nmXKZpJjgreXoc0 I see this guy adding lambda to the constraints in both hicksian and marshallian. so who is right? could you please clarify?

[@HaroldWalden]

It doesn’t matter. If you do the calculations both ways and you’ll see.

[@BigLoaf]

12:00 for x1, I got the same answer but to the power of 1/4. Please can you explain to me where the 1/3 came from?

[@BigLoaf]

nevermind I forgot the additional x1 to make x1^3

[@23rt2308u24tkhg]

cool

[@HaroldWalden]

Nice username 😜

[@Boellemids]

Thank you for this!

[@carlawalden]

Bjorn Utzon it was exactly the question I was after!

[@HaroldWalden]

No problem mate, I am glad it helped! Thanks for taking the time to leave a positive comment, I really appreciate it :)