Assuming both taxes and government spending increase by the same amount, derive an expression for the effect on equilibrium output.

Equilibrium output is where Aggregate Demand = Aggregate Supply

In a closed economy, Aggregate Demand = Consumption + Investment + Government Expenditure

Consumption = c + b Yd, where c = autonomous consumption, b = Marginal Propensity to Consume, Yd = Disposable income deducted tax ie Y - t

Aggregate Supply is analogous to total factor payments & factor incomes, so it is equal to national income Y

The equilibrium is where,

Y = C + I + G

• Assuming c = 100, MPC = 0.5, t = 10, G = 20 ; Equilibrium calculation is as follows

Y = 100 + 0.5 (Y - 10) + 20

Y = 100 + 0.5Y - 5 + 20

Y = 115 + 0.5Y

Y - 0.5Y = 115

Y = 115 / 0.5

Y = 230 [Equilibrium Income]

• Now, as both tax & government expenditure rise by 10 & become 20, 30 respectively

Y = 100 + 0.5 (Y - 20) + 30

Y = 100 + 0.5Y - 10 + 30

Y = 120 + 0.5Y

0.5Y = 120

Y = 120 / 0.5 = 240 [New Equilibrium Income]

• It hence shows that, when tax & government expenditure increase by same amount - equilibrium output also increase by same amount.