Question

3. U = A^.5B^0..5

MU_A = 0.5A^-0..5B^0..5

MU_B = 0.5 A^0..5B^-0.5

P_A= 5

P_B = 2

I=100

1. Write down MRS function
2. Write down budget constrain
3. Write down tangency condition
4. Calculate the optimal consumption bundle.
5. What is the maximized utility level
6. At the optimal consumption bundle, calculate the MRS and explain using plain English the meaning of the MRS value.

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Answer 1

MRS is the ratio of MUA to MUB.
So, MRS =

MRS = B/A

Budget constraint: PA*(A) + PB*(B) = I
So, 5A + 2B = 100

Tangency condition is MRS = slope of budget constraint
And, slope of budget constraint = PA/PB
So, MRS = PA/PB gives,
B/A = 5/2
So, B = (5/2)A

Now putting this in budget constraint we get,
5A + 2(5/2)A = 100
So, 5A + 5A = 100
So, 10A = 100
So, A = 100/10 = 10
And, B = (5/2)A = (5/2)*10 = 25

Thus, optimal consumption bundle is A = 10, and B = 25

Maximized utility level = A^.5B^0..5 = (10)^0.5(25)^0.5 = (3.16)(5) = 15.8

MRS = B/A = 25/10 = 2.5
This means that 2.5 units of B have to be given up to gain an additional unit of A.