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.