Question

in the aggregate expenditure model for a closed economy assuming investment, government spending and taxes are exogenous, if the marginal prosperity to consume is 0.8, a simultaneous 50 unit increase in government spending and a 20 unit decrease in investment will change equilibrium income by?

Answer 1

We are assuming that investment, government spending and taxes are exogenous.

Say, Investment = I, Government Spending = G, Tax = T and Autonomous Consumption = C, equilibrum income= Y

Marginal Propensity to Consume is given as:

$MPC = 0.8$

At equilibrum,

$Y=C+I+G$

$Y = C + MPC(Y-T) + I +G.$

$Y = C + 0.8(Y) - 0.8(T) + I + G$

$0.2(Y) = C - 0.8(T) + I + G$

 Now, taking differential on both sides, we get

$0.2.∆Y = ∆C - 0.8(∆T) + ∆I + ∆G$

Now, Government Spending increases by 50 and Investment decreases by 20.

Tax and C remains constant.

Hence,

$∆G = 50, ∆I = -20, ∆T = ∆C° = 0$

Hence,

$0.2(∆Y) = -20 + 50$

$0.2(∆Y) = 30$

$∆Y = \frac{30}{0.2}$

$∆Y = 150$

The equilibrum income will change by 150 units.