Equilibrium level of income question

Question

Question:

In the 2012 tax year,

Consumption= (85% of income after tax) + (Autonomous Consumption)

Taxation rate= 20%

Autonomous consumption= 175 million

Investment= 485 million

Government Expenditure= 1100 million

a) find equilibrium level of income

b) investment doubles in 2013 tax year, other quantities unchanged. find new equilibrium and level of multiplier

c) Calculate the government deficit or surplus in each of 2012 and 2013

d) Determine the rate of taxation the government would need to charge to ensure a balanced budget (ie a zero deficit/ surplus) in 2013 and calculate the national income in this case.

My answer:

a) Y=5500

b)Y=7015.63 K= 1.47

I don't know how to do part c and part d, can anyone help me please?

Answer 1

$Y_{2012} = 5500 $ so $tY_{2012} = 0.2*5500 = 1100$ A balanced budget in 2012.

$Y_{2013} = 7015.63$ $tY = 1403.13$ The budget is $1403.13-1100 = 303 $ surplus.

Part d)

$tY$ must equal $1100$ for a balanced budget. Autonomous spending is 2245. So $$ Y - 0.85(Y[1-t]) = 2245$$

$$ 0.15Y + 0.85tY = 2245$$ Sub in the 1100 for tY and you get $Y \approx8733 $

$t8733 = 1100$ so $t \approx 12.6\%$