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Who is good at Economics?
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| Tudo Beleza |
I got a question for my project and i can not get it.
it reads
Her income is $9 and the prices of X and Y are $2 and $1, respectively.
a. What quantities of each good maximize utility and what will be the total utlity achieved?
b. Suppose the price of X falls to $1. What quanttiies of X and Y now maximize utilty?
How would you do this question
With the graph being
Units of X Marginal Utilty X Units of Y MUy
1 10 1 8
2 8 2 7
3 6 3 6
4 4 4 5
5 3 5 4
6 2 6 3
If anyone could help it would be great.
The data is also in the excel file. |
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| IronDragon |
I would need to know your utility function.
From there I could just set the partial derivative of that function equal to the MRS (in this case 2 since MRS here is 2/1)
Umm....and that data I think you're trying to make a graph of x vs y, but I can't make heads or tails of what you're trying to do with that graph. |
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| vmc |
| I'll try to solve it later, but I don't promise |
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| zzleeper |
U=U(X,Y)=U(X)+U(Y)
Px=2 ; Py=1
1) We assume you spent all your 9 bucks.
2) As the functions are not continual, we cannot derivate. So we just try to find the combination of X and Y that maximizes U.
3) There are several technics for doing this. I'll give you just one.
4) The idea behind this is to spend EACH BUCK on the good that gives you the more utility. That is, we DON'T CARE ABOUT MARGINAL UTILITY, we just care about THE MARGINAL UTILITY OF ONE DOLLAR SPENT ON X or Y.
a) U have 9 bucks. If you spend your 1st buck on Y you get 9 utils per buck. If you spend it on X it gives you only 10/2=5 utils per buck. Obviously, you buy one Y.
b) You have 8 bucks. Now Y has a marginal utility per buck of ..... you buy Y again.
...
..
the order would be
Y
Y
Y
Y
X
Y
X
Y
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Y=6 ; X=2
You spend 6 + 2*2 = 10.
Utility= 8+7+6+5+4+3 + 10 + 8
Ps: If you need further help with the intuiton behind this (THAT IS, TO "THINK MARGINALLY"), ask if u want. |
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| TranceGiant |
| Thank your for successfully convincing me NOT to study Economics :wtf: |
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| zzleeper |
| quote: | Originally posted by TranceGiant
Thank your for successfully convincing me NOT to study Economics :wtf: |
lmao!
actually, compared to what i'm studying now, this is like solving crosswords..
btw, it's not that hard.. it's like learning uuhh HTML.. if you see | 
name="Map"> it looks hard, but it isn't..
bye! ;) |
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| Tudo Beleza |
But isn't maximizing ulity achieved when you have equal Marginal Utilites, the answer my group got was 3 and 3 that was the only one that had similar marginal utilites and fit within the cost structure.
3x2=6
3x1=3
=9
Marginal Utility
mux = 10+8+6=24
muy = 8+7+6=21
mux+muy=45
Total Utility of 45 |
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| zzleeper |
| quote: | Originally posted by Tudo Beleza
But isn't maximizing ulity achieved when you have equal Marginal Utilites, the answer my group got was 3 and 3 that was the only one that had similar marginal utilites and fit within the cost structure.
3x2=6
3x1=3
=9
Marginal Utility
mux = 10+8+6=24
muy = 8+7+6=21
mux+muy=45
Total Utility of 45 |
sorry dude, next time trust me ;)
well what i was trying to tell u was that "Marginal Utilites Per Unit" DONT MATTER really, what matter is the "Marginal Utilities Per Dollar".
Oh and i made a mistake too, since the restriction was 9 bucks and not 10.
Correct answer:
Y
Y
Y
Y
X
Y
X
Y --> NOT ANYMORE
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Y=5 ; X=2
You spend 5 + 2*2 = 10.
Utility= 8+7+6+5+4+ + 10 + 8 =48
ps: don't worry, we all make mistakes.. |
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| yujie__ |
A. maximize utility is achieved when MUofX=MUofY. So total units produces is 3x3=9
B. what is the original price of both units? i need to know to do it. |
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| Tudo Beleza |
zzleeper
Thanks for question my logic, it really helped me to find your answer. Thanks again, and sorry for questioning you, but through your answer i understand it. I got it right. |
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| arjoderoon |
ah i liked these questions. had loads of them last year at university, but wasnt it just like getting the most utility out of your basket?
kind of math... finding the unknown with 2 variables...
and keep in mind... more is always better.. |
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