a$.$ Incorporate government into the table $($in the gray$-$shaded cells$)$ by assuming that it plans to tax and spend $$20$ billion at each possible level of GDP$.$ Also assume that the tax is a personal tax and that government spending does not induce a shift in the private aggregate expenditures schedule.

Instructions: Enter your answers as a whole number.

$\backslash$table$[[\backslash$table$[[(1)$ Real Domestic$],[$Output $($GDP $=$ DI$),],[$Billions$]],\backslash$table$[[(2)$ Aggregate$],[$Expenditures$,],[$Private Closed$],[$Economy$,$ Billions$]],\backslash$table$[[(3)$ Exports,$],[$Billions$]],\backslash$table$[[(4)$ Imports,$],[$Billions$]],\backslash$table$[[(5)$ Net Exports,$],[$Billions$]],\backslash$table$[[(6)$ Aggregate$],[$Expenditures$,],[$Private Open$],[$Economy$,$ Billions$]],\backslash$table$[[(7)],[$Government$],[$Expenditures$,],[$Billions$]],\backslash$table$[[(8)$ Aggregate$],[$Expenditures$,],[$Open$],[$Economy with$],[$Government$,],[$Billions$]]],[$$$200,$$$240,$$$20,$$$30,$$$-10,$$$230,,],[250,280,20,30,-10,270,,],[300,320,20,30,-10,310,,],[350,360,20,30,-10,350,,],[400,400,20,30,-10,390,,],[450,440,20,30,-10,430,,],[500,480,20,30,-10,470,,],[550,520,20,30,-10,510,,]]$

b$.$ What is the change in equilibrium GDP caused by the addition of government?