Question

given the following equation U=√X1 X2,. what would be the total effect of a price change when the price of one good reduces by 10% from shs. 30. the income of the consumer is shs. 6000 per month while the price of the good two is 40

Answer 1

U=√X1 X2

$U=X1^{0.5}X2^{0.5}$

$MU_{X1}=\frac{\delta U}{\delta X1}=0.5X1^{-0.5}X2^{0.5}$

$MU_{X2}=\frac{\delta U}{\delta X2}=0.5X1^{0.5}X2^{-0.5}$

The budget line is;

$P1\times X1 + P2\times X2= I$

$30X1+40X2=6000$ ……..equation 1

$X1=\frac{6000-40X2}{30}$

$X2=\frac{6000-30X1}{40}$

When price of good 1 reduces by $10\%$ from 30,equation 1 becomes;

$27X1+40X2=6000$

$X1=\frac{6000-40X2}{27}=222.22-1.48X2$

$X2=\frac{6000-27X1}{40}=150-0.675X1$

If the price of good 1 reduces by 10% from Ksh. 30, then the quantity of X1 consumed will increase, and the quantity of X2 consumed will decrease.

But the total effect of a price change will be positive, so the total utility will increase.