Q$1$:The price of x is $1$ and the price of y is $2.$ An individual with well$-$behaved preferences and a fixed money income consumes $10$ units of each in equilibrium. If the price of x increases to $2$ and the price of y increases to $3$ while her money income increases to $50,$ her consumption of y will not fall. True or false?

To answer this question start with the following:

i$)$ Find initial income Y $($cost of initial bundle$).$ Plot initial BL and indicate the optimal bundle. Draw appropriate IC$.$

ii$)$ Draw the new BL$.$ Be very specific as to where the BL$$s cross: is the old bundle above, on$,$ or below the new BL$.$

iii$)$ Look at the new BL and initial choice: how should consumer adjust their consumption of the goods?