Question

1. Briefly describe the expenditure multiplier and state how it is computed. How is it different from the Tax multiplier?

2. Discuss how spending and output influences equilibrium in a simple model where aggregate expenditure = consumption.

3. Describe how unplanned inventory can influence equilibrium in the model where AE=(C+I+G+(X-M))

Answer 1

1.

Expenditure multiplier(K) refers to the change in income due to a unit change in expenditure in the economy.

K= Change in Income(Y) / Change in expenditure(A)

Computation of Expentiure multiplier:

Let's take a 3 sector economy without tax:

Aggregate demand = Consumption expenditure(C)+Investment(I)+ Government expenditure(G)

AD= C+I+G

C= C*+MPC(Y)

Where C*= autonomous consumption

Y= income

MPC= Marginal propensity to consume

AD= C*+MPC(Y)+G+I

Equilibrium condition:

Y=AD

Y= C*+MPC(Y)+G+I

Y-MPC(Y)= A (A= C*+I+G)

Y= A/(1-MPC)

Differentiate Y with respect to A

dY/dA= 1/(1-MPC) Expenditure multiplier

Let's take a 3 sector economy with tax(T=T*+tY):

Aggregate demand = Consumption expenditure(C)+Investment(I)+ Government expenditure(G)

AD= C+I+G

C= C*+MPC(Y-T*-tY)

Where C*= autonomous consumption

Y= income

MPC= Marginal propensity to consume

t is the tax rate

T* is the autonomous tax

AD= C*+MPC(Y-T*-tY)+G+I

Equilibrium condition:

Y=AD

Y= C*+MPC(Y-T*-tY)+G+I

Y-MPC(Y)+MPCt(Y)= A+MPC(T*) (A= C*+I+G)

Y= A-MPC(T*)/(1-MPC+MPC(t*))

Differentiate Y with respect to T

dY/dT= MPC/(1-MPC+tMPC) Tax multiplier

Value of tax multiplier is negative which implies that tax and income have negative relationship which implies that to increase income it requires decrease in tax. While expenditure multiplier is positive which implies rise in expenditure is required to raise income.