Simple Keynesian model

It is given that economy is at equilibrium at $Y_0$ = 1000. If Government undertakes a fiscal change so that tax rate $t$, increases by 0.05 and government spending increases by 50, will the budget surplus go up or down?

I tried doing it this way:

$$Y = C( Y - tY ) + I + G$$

Differentiating the above equation I got

$$dy = \frac{di+ dg - c'y dt}{1- c'(1-t) }$$

Where $c'$ is mpc, $t$ is tax rate.

Also,

$$BS = ty-G- TR$$

So,

$$dBS = tdy +ydt-dg-dtr$$

Now, $Y=1000, dt = 0.05, DG= 50$. Plugging these first into $dy$ and then using $dy$ in $dBS$, I got the following:

$$dBS = \frac{50t(1-c') }{(1-c'(1-t) }$$

Therefore the budget surplus goes up. Is my method correct? Also, what could be the economic intuition behind this? This is not a homework assignment. I am currently preparing for an upcoming entrance exam and was trying out a few back questions from dfs for conceptual clarity.

• TR means "transfers" ? but it does not appear in your disposable income... Could you either develop or remove it?
– Yann
Nov 8 '18 at 23:23

Consider the following with MPC = 0.3, t = 0.2 and Y = 1000 and dt = 0.5: 