Função Utilidade Indireta do Consumidor (Cobb-Douglas)

Por
Rebeca Monteiro
-
266
1693

QUESTÃO CERTA: Considere que a função utilidade do consumidor do tipo Cobb-Douglas seja expressa na forma , em que x1 e x2 são as quantidades, respectivamente, dos bens 1 e 2, α ∈(0,1) é um escalar e p1 e p2 são os preços dos bens 1 e 2 respectivamente.

Considerando que w seja a renda do consumidor, julgue o item que se segue, relativo à teoria do consumidor. A função utilidade indireta do consumidor é expressa

por .

Como se calcular a função utilidade indireta do consumidor numa Coubb-Douglas: é a função de demanda do bem 1 elevada a potência do bem 1 multiplicada pela função de demanda do bem 2 elevada a potência do bem 2. Como assim? Já sabemos qual é a função do bem 1 que é:

Função de demanda do bem 1= aW/P1

Agora vou elevar essa função de demanda a potência do bem 1, logo:

[ a* W/P1 ] ^ a

a^a * [W/p1] ^a

a^a * [ W^ a / p1 ^a ]

Agora vou calcular a função de demanda do bem 2:

Função de demanda do bem 2= [X2/ X1+X2] * [ W/P2]

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Função de demanda do bem 2= [1-a/ a+(1-a)] * [ W/P2]

Função de demanda do bem 2= (1-a) * [ W/P2]

Agora vou elevar essa função de demanda a potência do bem 2, logo:

{(1-a) * [ W/P2]} ^ ( 1-a)

(1-a) ^ ( 1-a) * [ W/P2] ^ ( 1-a)

(1-a) ^ ( 1-a) *  [W ^ ( 1-a) / P2 ^ ( 1-a)]

Agora vou multiplicar ambas, para encontrar a função utilidade indireta:

{ a^a * [ W^ a / p1 ^a ] } * { (1-a) ^ ( 1-a) *  [W ^ ( 1-a) / p2 ^ ( 1-a)] }

{ a^a* (1-a) ^ ( 1-a)} [ W^ a / p1 ^a ] * [W ^ ( 1-a) / p2 ^ ( 1-a)]

{ a^a* (1-a) ^ ( 1-a)} [ W^ a * W ^ ( 1-a) / p1 ^a * p2 ^ ( 1-a)]

Nesse em negrito: repete a base, e some os expoentes

{ a^a* (1-a) ^ ( 1-a)} * [ W ^ a+ ( 1-a) / p1 ^a * p2 ^ ( 1-a)]

{ a^a* (1-a) ^ ( 1-a)} * [ W ^ a+-a+1  / p1 ^a * p2 ^ ( 1-a)]

{ a^a* (1-a) ^ ( 1-a)} * [ W ^1  / p1 ^a * p2 ^ ( 1-a)]

{ a^a* (1-a) ^ ( 1-a)} * [ W  / p1 ^a * p2 ^ ( 1-a)]

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Artigo anteriorO Que É Função Demanda? (com exemplos)
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Rebeca Monteiro

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  197. I’ve learned some new things from your blog post. One more thing to I have observed is that usually, FSBO sellers will reject people. Remember, they might prefer to not use your companies. But if you actually maintain a comfortable, professional romance, offering guide and remaining in contact for around four to five weeks, you will usually be capable to win an interview. From there, a listing follows. Thanks

  200. Oh my goodness! an amazing article dude. Thanks Nevertheless I’m experiencing problem with ur rss . Don?t know why Unable to subscribe to it. Is there anybody getting similar rss drawback? Anyone who is aware of kindly respond. Thnkx

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  207. When I initially commented I clicked the “Notify me when new comments are added” checkbox and now each time a comment is added I get three e-mails with the same comment. Is there any way you can remove me from that service? Thank you!

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  210. I would also like to add that in case you do not actually have an insurance policy or maybe you do not belong to any group insurance, you may well gain from seeking assistance from a health agent. Self-employed or those that have medical conditions usually seek the help of a health insurance brokerage. Thanks for your writing.

  211. Thanks for your post. One other thing is that often individual American states have their very own laws that affect people, which makes it very difficult for the the legislature to come up with a different set of guidelines concerning foreclosure on house owners. The problem is that every state provides own laws which may have impact in an unfavorable manner in regards to foreclosure guidelines.

  212. Hey, I think your website might be having browser compatibility issues. When I look at your website in Opera, it looks fine but when opening in Internet Explorer, it has some overlapping. I just wanted to give you a quick heads up! Other then that, wonderful blog!

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  219. One thing I’d really like to say is that before buying more laptop or computer memory, have a look at the machine within which it is installed. Should the machine is actually running Windows XP, for instance, the memory ceiling is 3.25GB. Installing in excess of this would merely constitute some sort of waste. Make sure that one’s mother board can handle the particular upgrade quantity, as well. Good blog post.

  223. Hello would you mind letting me know which webhost you’re using? I’ve loaded your blog in 3 different internet browsers and I must say this blog loads a lot quicker then most. Can you recommend a good web hosting provider at a reasonable price? Thanks a lot, I appreciate it!

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  226. The crux of your writing whilst appearing agreeable originally, did not work well with me after some time. Somewhere within the sentences you actually were able to make me a believer but only for a while. I still have a problem with your leaps in assumptions and you might do well to help fill in those gaps. If you actually can accomplish that, I will certainly be fascinated.

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  229. Hi! I know this is kinda off topic however , I’d figured I’d ask. Would you be interested in exchanging links or maybe guest authoring a blog article or vice-versa? My blog addresses a lot of the same topics as yours and I believe we could greatly benefit from each other. If you’re interested feel free to shoot me an email. I look forward to hearing from you! Wonderful blog by the way!

  235. I have observed that over the course of creating a relationship with real estate managers, you’ll be able to come to understand that, in each and every real estate contract, a commission amount is paid. Ultimately, FSBO sellers do not “save” the percentage. Rather, they fight to earn the commission by simply doing the agent’s work. In completing this task, they spend their money along with time to conduct, as best they could, the obligations of an adviser. Those assignments include displaying the home through marketing, offering the home to buyers, constructing a sense of buyer desperation in order to prompt an offer, arranging home inspections, controlling qualification assessments with the bank, supervising maintenance tasks, and assisting the closing of the deal.

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  242. Hello, Neat post. There is an issue along with your website in internet explorer, could test this? IE nonetheless is the market leader and a good element of folks will leave out your wonderful writing because of this problem.

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