For an economy to attain the equilibrium level of income, the aggregate demand must equal aggregate demand.
Therefore; Equilibrium income is given by; Y=
Where A = Consumption, I = Investments, G = Government Spending, b is the marginal propensity to consume, t is the tax rate
Therefore, Y (equilibrium income) =
=
= 64,285.70
(b)
If the government increases its spending in the economy by 20,000, the value of G will increase to 40,000.
The new equilibrium income would be;

Y (new equilibrium income) =

= 92,857.10
Equilibrium income, Y would have increased from 64,285.70 to 92,857.10, a difference of 28,571.40, which is lower than the expected increase of 30,000, although close
(c)
If the government must attain the targeted increase in equilibrium income of 30,000, it has to spend more than 20,000. The planned equilibrium income is
= 64,285.70 + 30,000
= 94,285.57
The level of government spending required to attain this income can be computed using the formula, as shown;
is referred to as a multiplier, and its value is 1.4286
94,285.57 =
94,285.57 =
Therefore, 0.7(94,285.57) = 25,000 + G
G = 66,000.00 – 25000
G = 41,000

And, therefore, the total government spending needed to attain a 30,000 increase in equilibrium income is 41,000. Thus, the government should increase its spending by 21,000 from the current 20,000.