# Government expenditure multiplier in a class divided society

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?.

• Only the first line of your question was visible (hence the close votes). I have edited it to make the whole thing visible but you might check it still says what you intended – Henry Apr 2 '18 at 9:31
• Thanks. I've been trying to correct it but wasn't able to do so for some reason. – Shoaib Ashraf Apr 6 '18 at 2:06