(advanced analysis) the accompanying equations are for a mixed open economy. the letters y, ca, ig, xn, g, and t stand for gdp, consumption, gross investment, net exports, government purchases, and net taxes, respectively. figures are in billions of dollars. if the economy's tax schedule was t = 0.2y rather than t = t0 = 30, the equilibrium gdp would be

Equilibrium GDP = C+ I+ G+ X

Where:             Y = GDP

                        C = Ca = a+bYd

                         I  = Ig

                        G = G

                        X =  Xn

                     Yd  = Y-T

                        T =  0.2Y

                       Y  =  C+ I+ G+ X

                       Y  = a + bYd + I +G + X

                       Y  = a + b(Y-T) + I +G + X

                       Y  = a + bY - bT + I +G + X

                       Y  = a + by - b(0.2Y) + I +G + X

                       Y  = a + bY - 0.2Yb + I +G + X

                       Y  =  a + 0.8Yb + I +G + X

         Y - 0.8Yb  =  a + I +G + X

         Y(1 - 0.8b) =  a + I +G + X

                        Y = (a + I +G + X)/(1 - 0.8b)

That is the equilibrium GDP is Y = (a + I +G + X)/(1 - 0.8b)

Explanation:

Equilibrium GDP is also called equilibrium level of national income. This is the condition that must prevail for planned expenditure to exactly equals planned income or output in an economy. this is represented by the general equation of Y  =  C+ I+ G+ X-M but for the purpose of this question M which represent import was not introduced.

The consumption function of C = Ca = a+bYd is a Keynesian consumption function, it shows aggregate planned expenditure by household

Ig represents investment expenditure of the firm

Xn represents export while

G represents government expenditure on goods and services

T represents tax which varies with income level