Hi there, could you please provide some perspective to this question concerning the multipler effect.

For this question, assume the economy currently has a recessionary output gap and that the marginal propensity to consume is 0.8.

Consider a three-sector Keynesian model in which the only form of taxation is exogenous taxes (that is, the tax rate, t, is zero). Note that a three sector model comprises households, firms and the government (there are no exports or imports). Suppose the government increases its expenditure by $1 billion, financed through an increase in exogenous taxes of $1 billion. Derive the formula for the multiplier needed to analyse the effect of this fiscal policy on equilibrium GDP. Calculate thevalue of the change in equilibrium GDP.

I know the multipler equation is simply 1/(1-x) but I don't know how it incorporates in the Keynesian model I derived below from my teaching nor what formula to analyse the effect of this fiscal policy.

The three sector economy economy is what I simplified already taking into effects taxes in the consumption function.
Y=PAE=C+I+G
Y=C bar + cY +I + G
T=C bar +c (y-t) + I + G
Y- cY= c bar - cT + I + G
Y=(1-c) = c bar - cT + I+ G
therefore Y= 1/(1-c) x (c bar-cT + I + G)

Thanks much appreciated.

Wait I'm confused, what does the multiplier used in this context mean. Is it a simple equation to analyse the effect on this fiscal policy?