Economics/Math question ???

Question

Suppose that the Tax function for an economy is 0.2Y (there are no fixed taxes or transfers). What is the Consumption function if C was 900 when Y (GDP) was 1400 and C was 975 when Y was 1550?

Answer 1

C=Ca+MPC*Yd

Y - GDP

Yd - disposable income

Yd=Y-T

T=0.2Y

Tax = 0.2 = 20%

Yd=Y-0.2Y=0.8Y

Ca - autonomouse consumption

MPC - marginal propencity to consume/spend

C=Ca+MPC*0.8Y

Y=1400 C=900

Y=1550 C=975

900=Ca+MPC*0.8*1400

975=Ca+MPC*0.8*1550

900=Ca+MPC*1120

975=Ca+MPC*1240

Ca=900-MPC*1120

975=900-MPC*1120+MPC*1240

120*MPC=75

MPC=0.625

Ca=900-0.625*1120 = 900-700 =200

C=200+0.625*Yd

C=200+0.625*(0.8Y)

C=200+0.5*Y

Answ: C=200+0.5*Y