Question

There are two goods X and Y. Tabithas Utilities are given by U = 1/3X2 + 2 Y1/2. If the price of X is $2 and the Price of Y is $0.75 What is Tabithas optimum bundle?

Answer 1

$U= 1/3 x^2 + y^{1/2}$

 and 

x=2, y=0.75=3/4

$MR_{s} = \frac {MU_{x}}{MU_{y}} = \frac {2/3x}{\frac{2}{2}y^{1/2}} =\frac {2/3x}{y^{1/2}}$

=$\frac {2}{3} xy^2$

MR_s is not Diminishing

if x is consumed then,

• if x is consumed then

$x'=\frac{m}{p_{x}}$ x` $=$ $\frac {m}{P_{x}}$$=$ $\frac {2}{p_{x}}$

$U= 1/3(\frac{m}{2})^2 = \frac {m^2}{12}$

• if y is consumer then,

$y` =\frac {m}{p_{y}} = \frac {m}{0.75} = \frac {4}{3} m$

$U= 2 (\frac {4}{3}m)^{1/2} = 4 \sqrt (\frac{m}{3})$