Utility function $U(x_1 , x_2) = x_1 + 4 * x_2 $
$ p_1 = 3, p_2 = 8, m =120 $
$p_2$ changes from $8$ to $10 $
How can I calculate the income and substitution effect.
I first thought about calculating the MRS making the partial derivatives of the Utility function which resulted in $MRS = 1/4$ which means that the consumer will always prefer at any given moment good $x_2$ thus only buying that good. At first he can only buy $m/p_2 = 120/8 = 15$ so the bundle would be $(0,15)$ and after the price change it would be $(0,12)$ (not sure about that).
I also calculated the utility at the previous point by plugging $(0,15)$ into $U(x_1 , x_2) = x_1 + 4 * x_2 $ which resulted in $60$
$60/p'_2 - 60/p_2 $ = $60/10 - 60/8= - 1.5$ = substitution effect
I am not sure if what I have done is correct and if the substitution effect is 1.5. Is there any way to visualize this graphically ? I thought about doing linear equations with $m/p_2$ and $m/p'_2$ as seen below:
Am I missing something ? Any help is appreciated