In the United States, the Earned Income Tax Credit $($EITC$)$ is a tax credit that supplements the earnings of low$-$income workers with children. For a qualifying single individual with one child, the structure of the EITC in the year $2023$ is as follows.

A $34\%$ credit on each dollar of income earned up to a maximum credit of $$3,995.$

The maximum credit is reduced by $15\mathrm{.}98\%$ for each dollar earned above $$21,560.$

Based on these parameters, please answer the following.

$($a$)$ What is the "phase in$"$ region for the EITC? In other words, what is the income range over which the earnings of this individual is subsidized? You may answer using a graph, an equation or using words. If you choose to characterize the phase$-$in region using words, then your answer must be very precise. $[6$ marks$]$

$($b$)$ What is the "break even" level of earnings above which a single worker no longer receives an EITC subsidy? $[6$ marks$]$

$($c$)$ Based on your answers to parts $($a$)$ and $($b$)$ and the parameters of the EITC, draw a figure showing the budget constraint of a single worker under the EITC. Your figure should clearly label the $x-$axis, $y-$axis and the income cutoffs $B_0,B_1$ and $B_2.[6$ marks$]$

$($d$)$ In one paragraph or less, explain how the EITC affects the incentive to work for $($i$)$ individuals with earnings below $B_0,($ii$)$ individuals with earnings between $B_0$ and $B_1,($iii$)$ individuals with earnings between $B_1$ and $B_2,$ and $($iv$)$ individuals with earnings above $B_2.[7$ marks$]$