Deriving Marshallian and Hicksian Demand Functions (Compensated and Uncompensated Demand)

Deriving Marshallian and Hicksian Demand (Compensated and Uncompensated Demand)
Consider the utility function U(x,y)=xy subject to an Income constraint; M=px+py
Find the Marshallian and Hicksian Demand Functions for good x and good y .
These two types of demand functions compliment each other. Hicksian Demand concerns minimising the costs associated with attaining a particular level of utility, Marshallian Demand concerns maximising utility for a given level of income.
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 it helps :)

[@bruno2011gmail]

I've learned more on this subject with this video than in an entire semester at college. You rock!

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[@HaroldWalden]

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Loved it... It still baffles me how I couldn't derive these functions before. Thank u so much. Easy explanation, easy calculations. God bless you!

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Harold you are probably contributed my knowledge on economics more than my professor. Really appreciate. but i have a question: i lost my second good(y) in first order cond. process so i only can find the x and not the y. what should i do if i lost one of my goods in lagrange process?

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The best explanation on the subject I've seen.

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Thanks for that man, I appreciate the positive feedback, if you have any ideas for future videos, don’t hesitate to let me know. Thanks again :)

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[@HaroldWalden]

Had a few positive comments on these compensated and uncompensated demand derivations using the method of Lagrange. Fairly important that you know how to do this stuff if you want to continue towards a career in microeconomic modelling.

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Glad you liked it!

[@realkosherpork9223]

Is there a difference between them when deriving perfect substitutes?

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Thank you

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[@HaroldWalden]

Thanks for the nice words, I really appreciate it. If you’re having trouble with any of these topics, just let me know. I am always looking for new video ideas. 🤓

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@@HaroldWalden that's really kind of you, actually there are less videos commented MRS or preferences about monotonic transformation of utility function like your amazing methed teaching with basic sample. I think I just can learn economics with your method

[@HaroldWalden]

@@arefemamian Again, that's very kind of you. But just so you know, if you are having difficulty with any specific problems, let me know and I would be more than happy to try and put a video together on it. Until that time, keep enjoying your economics :)

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Thank you!

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Very well explained

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[@devangeib7864]

Hey Harold, Great video! Quick question: after you do the partials for each demand function, we get to y= and x=. What are x and y telling us? You mentioned something about MRS... is that the equation for MRS for good x? And once the x and y are optimized (with *) those are our demand functions for those goods right? Lastly, where does the lagrange multiplier come into play? We use it to set these up but it doesnt come up again? What does lambda tell us in these problems? Thanks so much!

[@bruno2011gmail]

Well, I can answer the MRS stuff: basically, solving this problem through Lagrange is one way to look at it. The other one is MRS=Px/Py (keep in mind that MRS is equal to marginal utility of X/marginal utility of Y, meaning you derive partially with respect to X and Y, and take MUx/MUy = Px/Py), and taking the results of this process and applying them to the budget constraint will give us the Marshallian demand for good X or Y, depending on which one you isolate. That is why he got to the MRS equation for good X in the middle of the process. I have never tried the MRS process with the Hicksian demand, so I'm not sure if it works or if you can only solve it through Lagrange. As to the Lagrange multiplier, It sure has an economic meaning, which I still do not know :/ Anyway, I know it's been 11 months, but maybe this might help.

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Glad I could help 🙂

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[@sundayagbonjinmi6773]

Thanks for this video. However, kindly assist with this below request Marshallian and Hicksian derivative function is needed with (X1 and X2 with power)raise to power function is needed.

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[@HaroldWalden]

No... you are awesome! Thanks for stopping by and taking the time to leave a positive comment, I really appreciate it 🤓

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Hi, thank you so much!! your videos are really beneficial. Can you please make a video on compensating variation and equivalent variation. and how we calculate them.

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That’s a good idea, when I get a moment, I’ll put one together and give you a like if you like. 🤓

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Great video! Could you please tell me for this two goods is gross substitute or gross complement? net substitute or net complement?

[@HaroldWalden]

Sorry it has taken a moment to respond, i have been crazy busy on my end. Have a look at this explanation: economics.stackexchange.com/questions/4579/gross-substitutes-vs-net-substitutes

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Sir I am a bigener ,why Lagrangian function is used in such cases?

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Great to hear that the video helped 🤓

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What if the utility function = x^2+y^2? The answer would be the same since the constants will be cancelled out?

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Check out this video I did, I feel like it may help answer your question. kzbin.info/www/bejne/pWrGfH-JoKZ5ZtU Let me know if you need any more help :)

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If you can be more specific that would really help :)

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@tapaswini mishra I would love to but I have no idea what your referring to with those acronyms 😢

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I think the first two stand for compensated variation and equivalent variation

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