Question

Given α is non-income tax, β is income tax, δ is marginal propensity to consume, γ is autonomous consumption, T (tax), Y (national income), I0 (investment) and G0 (government expenditure).


a) Formulate the equations needed to find the reduced form of equilibrium income (Ye).

Answer 1

$Ye=C+I+G$

$C=Ca+MRC\times Yd$

$Yd=Ye-T+TR$

$T=Ta+t\times Ye$

substitute these designations into the equation

$T=α+β\times Ye$

$Yd=Ye-T+TR=Ye-(α+β\times Ye)$

$C=Ca+MRC\times Yd=γ+δ((Ye-(α+β\times Ye))$

$Ye=C+I+G=γ+δ((Ye-(α+β\times Ye))+I0 +G0$

$Ye=γ+δ((Ye-(α+β\times Ye))+I0 +G0$