$1.$ Social Insurance $($please explain the math$)$

a$)[6$ points$]$ Suppose an individual was earning $\backslash (\backslash$$ $3000\backslash )$ a week and then becomes unemployed. The individual then has no labor market earnings but can borrow from family and friends. Suppose that the UI system provides $\backslash (\backslash$$ $800\backslash )$ a week in benefits. The table below summarizes the individual's situation. $\backslash ($ X $\backslash )$ and $\backslash ($ Y $\backslash )$ are unknown variables.

$($i$)$ What are $\backslash ($ X $\backslash )$ and $\backslash ($ Y $\backslash )$ if UI benefits don't affect borrowing from family and friends $($no crowd out$)?($ii$)$ What are $\backslash ($ X $\backslash )$ and $\backslash ($ Y $\backslash )$ if individuals stop borrowing by $\backslash (\backslash$$ $1\backslash )$ from family and friends for each dollar of UI benefits $($full crowd out$)?($iii$)$ What are $\backslash ($ X $\backslash )$ and $\backslash ($ Y $\backslash )$ if individuals reduce their borrowing from family and friends by $\backslash (50\backslash \%\backslash )$ for each dollar of benefits $($partial crowd out$)?$ You should provide numerical answers