I know there are some geniuses on this forum.. figured I'd ask this question here. My professor isn't responding to emails, and this homework is due in 5 hours. All my friends are idiots. I'm getting desperate lol.
If you can provide an answer, and explain it, reps for life..
1. Given the CobbDouglas utility function U = X^1/2 Y^1/2 and income (I) is $100, answer the following questions.
A. Find the utility maximizing consumption bundle if the price of good X (Px) is $1 and the price of good Y (Py) is $1.
B. Find the utility maximizing consumption bundle if the price of good X (Px) is $4 and the price of good Y (Py) is $1.
C. What proportion of the consumers budget was spent of each of the goods in questions A and B.


02192013, 10:21 AM #1
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Econ Bros : Help! Cobb Douglas Equation..
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02192013, 10:24 AM #2

02192013, 10:25 AM #3

02192013, 10:27 AM #4

02192013, 10:33 AM #5
int'l econ student checking in. gonna take a stab at this, but take this with a grain of salt bc i haven't studied this part of cobbdouglas
simplifying the cobbdouglas equation (googled this) we get
x*, y* = [ (a/a+b)(m/px), (b/a+b)(m/py) ]
x* and y* are optimal amounts of x and y
a and b are the exponents in your function (1/2 in both cases)
m is the budget constraint
px and py are prices or x and y
putting your equations into this:
A: x*, y* = [ (.5/1)(100/1), (.5/1)(100/1) ]
simplifying, x*,y* = [50,50]
B: x*, y* = [ (.5/1)(100/4), (.5/1)(100/1) ]
simplifying, x*,y* = [12.5, 50]
C: just need to figure out the proportion. in A, the consumer spent 50% on both x and y, in B the consumer spent (12.5)(4)=50% on X and 50% again on y

02192013, 10:35 AM #6

02192013, 10:37 AM #7
I believe you take the partial derivative of x and y, set each to 0 and plug it back in. Also don't forget about the budget constraint PxX + PyY=I
So for the first one
dx/dy= 1/2*x^(1/2) + y^(1/2) = 0 y^(1/2) = 1/2 * (1/2x)
dy/dx= x^(1/2)= 1*2 (1/2y)
I don't feel like doing the rest but you should be able to figure it out from here
EDIT: ^^ That post gives you the correct answer but the process is a lot more important. This is something you want to know how to do for your exams, it is one of the basic equations of micro econ

02192013, 10:39 AM #8
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My notes, maybe they can help. They're from an example where p1=5, p2=4 and m=200

02192013, 10:39 AM #9

02192013, 10:40 AM #10

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02192013, 10:44 AM #12
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Hey brah . you can either use lagrange method
objective function U=x^1/2 y^1/2
ST= Px *(x) + Py *(y)=100
so set up the lagrange. substitute the given prices in for the constraint.
To find the proportion of income just do Px*X/100 for proportion of income spent on good X
Py*Y/100for proportion of inccome spent on good y40: 4.6
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02192013, 10:48 AM #13

02192013, 10:51 AM #14
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