Government Expenditure Multiplier

Government Expenditure Multiplier

 The government spending multiplier is an estimate of the extent to which an increase in government spending leads to an increase in the overall level of income (GDP) in an economy. It represents the amount by which the increase in government spending raises the overall level of economic activity in the economy. The multiplier effect of government spending is believed to be greater than 1, meaning that an increase in government spending leads to multiple increases in the economy's income level.

The government spending multiplier is based on several key assumptions, including:

The economy is operating below its potential: If the economy is already at full employment, an increase in government spending may not result in a corresponding increase in output and income.

Leakages in the spending cycle are minimal: The multiplier effect assumes that a large portion of the increase in government spending will be re-spent by households and businesses, leading to a chain of spending and income generation. However, the multiplier will be smaller if there are substantial leakages in the form of taxes, imports, or saving.

The price level remains constant: The multiplier assumes that prices do not change in response to the increase in spending. If prices do rise, this could dampen the multiplier effect by reducing consumers' purchasing power.

The economy is closed: The multiplier assumes that there is no international trade so any increase in demand generated by government spending will be met by domestic production.

The economy is in the short-run: The multiplier assumes that the economy is in the short-run, in which factors of production such as capital and labor are fixed, but prices and output can change.

Government spending includes the purchase of goods and services and salaries paid to government employees.

Transfers are payments made by the government with no direct service in return, such as unemployment insurance and welfare benefits.

Taxes on property, goods, and income are used to finance transfers and expenditures.

An increase in government spending or a decrease in net tax revenues leads to an increase in output.

The government can influence output through changes in taxes, transfers, and spending.

Output is in equilibrium when it equals consumption, investment, and government spending using the spending approach or when net tax revenues plus savings equals investment and government spending using the leakage/injection approach.

Net tax revenues (Tn) are calculated as gross tax receipts(Tg) minus transfers(Tr). i.e Tn = Tg - Tr

Let Y = C + I +G + X – M  

or, Y = a + b Y + I + G + X – M------- (i)

Y1= C1+ I + G1 + X – M 

or Y = a + b Y1+ I+ G1 + X – M ----(ii) (Since I, X, and M are assumed to be constant)

From (i) and (ii)

Y1 – Y = a + b Y1+ I+ G1 + X – M – (a + b Y + I + G + X – M)

or, ΔY =  b Y1– b Y+ G1– G

or, ΔY = b (Y1–  Y) +( G1– G)

or, ΔY = b ΔY + ΔG

or, ΔY – b ΔY = ΔG

or, ΔY(1 – b) = ΔG

or, ΔY/ ΔG = 1/(1 – b)

or, Km =  1/(1 – b) = ΔY/ ΔG  

or, Km ( Multiplier) =  1/(1 – b) = ΔY/ ΔG  

or, Km (Government expenditure multiplier) = 1/ (1 – MPC)   (since MPC = marginal propensity to consume)

or, Km (Government expenditure multiplier) = 1/ (1 – MPC) = ΔY/ ΔG  =Change in income/ Change in government expenditure.

Tax Multiplier

When there is a government sector, there is a lump-sum tax multiplier and a balanced budget multiplier in addition to an expenditure multiplier.

C = a + b Yd, Yd = Y – Tn ,  Tn = Tg –Tr , I= Contant , G = Constant For equilibrium

Let Y = C + I +G = a + b Yd + I + G = a + b (Y– Tn)  + I + G ---- (i)

Y1= C1+ I + G + X – M = a + b Yd1+ I+ G = a + b (Y1– Tn1)  + I + G ----(ii)

From (i) and (ii)

Y1–  Y = a + b (Y1– Tn1)  + I + G – [a + b (Y– Tn)  + I + G]

or, ΔY = b Y1– bTn1 – b Y+ b Tn    

or, ΔY = b Y1– bTn1 – b Y+ b Tn    

or, ΔY = b Y1– – b Y–  bTn1 + b Tn    

or, ΔY = b (Y1 – Y) –  b (Tn1– Tn)    

or, ΔY = b ΔY –  b ΔTn

or, ΔY– b ΔY = – b ΔTn

or, ΔY(1– b) = –b ΔTn

or, ΔY/ ΔTn = –b /(1– b) 

The lump-sum tax multiplier Kt = ΔY/ ΔTn = –b /(1– b)

Kt = ΔY/ ΔTn = Change in income / Change in net tax

Kt = ΔY/ ΔTn = –b /(1– b) = – mpc/ (1- mpc)

The negative sign of the tax multiplier indicates that an increase in tax hurts the equilibrium level of national income.

The balanced budget multiplier

When a government adopts a balanced budget policy, it spends as much as it collects through taxation.

C = a + b Yd, Yd = Y – Tn ,  Tn = Tg –Tr , I= Contant , G

Let Y = C + I +G = a + b Yd + I + G = a + b (Y– Tn)  + I + G ---- (i)

Y1= C1+ I + G + X – M = a + b Yd1+ I+ G = a + b (Y1– Tn1)  + I + G1 ----(ii)

From (i) and (ii)

Y1–  Y = a + b (Y1– Tn1)  + I + G1 – [a + b (Y– Tn)  + I + G

or, ΔY = b Y1– bTn1 – b Y+ b Tn + G1 –  G   

or, ΔY = b (Y1 – Y) –  b (Tn1– Tn) + ΔG  

or, ΔY = b ΔY –  b ΔTn + ΔG

or, ΔY– b ΔY = ΔG – b ΔTn

or, ΔY(1– b) = ΔG –b ΔTn 

or, ΔY= [ΔG –b ΔTn]/(1– b)

The change in equilibrium output for an equal change in G and Tn [i.e., ΔG = ΔTn]

Now, ΔY= [ΔG –b ΔTn]/(1– b)

or, ΔY= [ΔG –b ΔG]/(1– b)

or, ΔY= ΔG(1 –b)/(1– b)

or, ΔY= ΔG

The multiplier for an equal change in G and Tn is

  The balance budget multiplier Kg = ΔY/ΔG = 1    [since ΔY= ΔG]

Thus the increase in national income is always equal to an increase in government expenditure.