Supposing that a society is divided between a rich class and a poor class. Also supposing that $0<k<1$ is the proportion of GDP going to poor class and $(1-k)$ of the GDP going to the richer section.
Now I've been ask to find out the Government expenditure multiplier and comment on its economic significance.
Now I assumed that tax is not proportional, investment is autonomous and got the equilibrium income equation as follows: $Y= (C¹+I¹+G¹+c*T¹)/(1-c)$ where $c=(c_1+c_2)$ is MPC and the capital letters in the numerator are autonomous components of aggregate demand plus tax.
From this equation we get $∆Y=∆G/(1-c_1-c_2).$
Is this correct? Now how do I use the given details of proportion of GDP for different classes?.