Question

a) If Maria’s utility function is U = A Xayb what is his marginal utility functions for X and Y? Find the MRS between x and y.
b) What is his marginal rate of substitution between X =3 and Y=4? If A=1, a = 0.4 and b = 0.5.

Answer 1

a) $MRSxy=\frac{MUx}{MUy}$

$MUx=\frac{\delta U}{\delta X}=AaX^{a-1}Y^b$

$MUy=\frac{\delta U}{\delta Y}=AbX^aY^{b-1}$

$MRSxy=\frac{MUx}{MUy}=\frac{AaX^{a-1}Y^b}{AbX^aY^{b-1}}=\frac{aX^{a-1}Y^b}{bX^aY^{b-1}}$

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b)$MRSxy=\frac{MUx}{MUy}=\frac{AaX^{a-1}Y^b}{AbX^aY^{b-1}}=\frac{aX^{a-1}Y^b}{bX^aY^{b-1}}=\frac{0.4\times3^{0.4-1}4^{0.5}}{0.5\times3^{0.4}\times4^{0.5-1}}=1.067$