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The Multiplier Effect

In the previous post "Keynesian Cross" we have received the expression for equilibrium level of income:
Y* = (C₀ + I₀)/(1-c), where c is marginal propensity to consume, 0 < c < 1, C₀ is autonomous consumption - the consumption expenditures that are unrelated to income and would occur even if household disposable income was zero. We assume that investment is a constant I = I₀

a) Closed private economy: AD(Y) = C₀ + I₀ + cY,
Y* = (1/(1-c)) *(C₀ + I₀), hence change (positive or negative) in C₀ or I₀ by x, result in a multiplied change in equilibrium level of income. Y* will change by (1/(1-c))*x.
(1/(1-c)) is multiplier.
For example, if c=0.8 and autonomous consumption C₀ increases by $10, the increase in equilibrium level of income is $50 {$10*1/(1-0.8)}.

b) Closed economy with government: AD(Y) = C₀ + I₀ + G₀+ c(Y - Tax), where G₀ - government spending, Tax - value of taxes (we consider only Lump-Sum tax that has to be paid regardless of the income level). Solve this equation with respect to Y:

Hence, the tax multiplier is (-c/(1-c)). Change in taxes affect the economy through change in consumption and the tax multiplier is differ from the regular multiplier.

When change in government spending G₀ occurs then we use the standard multiplier.

c) The balanced budget multiplier. The government can stimulate the economy without changing the budget deficit by increase in government spending and taxes by the same amount, i. e.

Hence,

Hence, the balanced budget multiplier is equal 1.

P.S.
GDP (gross domestic product) is the total market value of all goods and services produced within the political boundaries of an economy during a given period of time, usually one year. The aggregate expenditures approach to measurement of GDP reflects in the Basic Keynesian Equation GDP = C + I + G + NE, where C- consumption, I - gross investment, NE - net exports and G - government spending. I. e. we can consider the GDP in the conclusions above and the Y* is the equilibrium GDP that equalize aggregate supply (AS) and aggregate demand (AD).

Posted by mazoo at February 27, 2005 6:37 PM

Related posts:

Money multiplier. How does it work? Apr 19, 2005
Keynesian Cross Feb 27, 2005

Comments

Posted by: amjad ali at August 13, 2006 2:27 PM

Posted by: Mazoo at August 14, 2006 2:16 PM