A) Computer Marys MRSxy at consumption bundle A. What does this number tell me?

Question

A) Computer Marys MRSxy at consumption bundle A. What does this number tell me?

B) If Mary chose consumption bundle B, her MRSxy would be higher or lower? Explain please?

C) Marys preference is transative, could two of marys IC's intersect? Explain with a graph please?

D) Please explain why to maximize utility Mary should chose a consumption bundle where MRSxy = Px/Py

E) If Px = $2, Py = $5, and income I = $200, compute Marys utility maximizing consumption bundle. Show the utility maximizing consumption bundle on a graph please?

Explanation / Answer

MRS stands for MARGINAL RATE OF SUBSTITUTION

U(x,y)=(6)[x^(1/3)][y^(2/3)]

at A, U(x,y)=60 (sustituting x=10 and y=10)

at B, U(x,y)=60 (substituting x=40 and y=5)

since,U(x,y) A=U(x,y) B, they provide the same amount of utility

Thus, A and B lie on a indifference curve

A)MRSx,y=(-dy/dx)=(MUx/MUy) where MU is the marginal utility and (dy/dx) is the slope of the indifference curve

U(x,y)=(6)[x^(1/3)][y^(2/3)]

differentiating we get,

4[x^(1/3)][y^(-1/3)]dy+ 2[y^(2/3)][x^(-2/3)]dx=0

(-dy/dx)=(1/2)(y)(1/x)

AT A,x=10,y=10

therefore,MSRx,y= (-dy/dx)=0.5

MSRx,y at A=0.5

B) MRS decreases down a indifference curve

Point B lies below point A

therefore,if Mary chooses B, MRSx,y would be lower

C)indifference curves can never intersect becauseif they do , the point of intersectio would imply two different levels of satisfaction which is impossible

D)REFER: in the link(http://en.wikipedia.org/wiki/Marginal_rate_of_substitution)-simple mathematical analysis

E) MUx/MUy=(Px/Py)=0.4 (considering equillibrium of the consumer)

MRSx,y=MUx/MUy=0.4

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