Money multiplier. How does it work?
Banks must have on reserve a certain percentage (the legal reserve requirement) of its total deposits. Banks keep these amounts (required reserves) on deposit at a Federal Reserve Bank.
If a bank's actual reserves exceed the required reserves, the difference is the excess reserves with which bank can extend loans. Therefore, the single bank creates money supple equal to its excess reserves.
The interesting fact is that money creation for the banking system as a whole (D) is a product of excess reserves by the Money Multiplier. D = E*m
So, the Money Multiplier is the maximum amount of money that the banking system generates with each dollar of excess reserves. The formula for money multiplier is
m = 1/r,
where r is the legal reserve requirement.
The answer is simple.
Assuming a required reserve ratio r=20%. The old woman deposited d=100$ in First bank. With a 20% requirement, the First bank has d*r = 20$ reserve requirement. The amount of excess reserves is
Continue reading "Money multiplier. How does it work?"
Posted by mazoo at 9:24 PM | Comments (4)
February 27, 2005
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 6:37 PM | Comments (4)
Keynesian Cross
1. Let's consider closed private economy without government spending and international trade. Hence, according to Keynesian theory, the aggregate demand is the sum of consumption and investment AD = C + I.
Keynes supposed that consumption is the function of disposable income Y: C(Y) = C0 + cY, 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. Next we assume that investment is a constant I = I0. Hence
AD(Y) = C0 + I0 + cY.
Let us denote C0 + I0 = A0.
2. Let equilibrium level of income Y* is the income at which the economy creates just enough spending to purchase the output produced. In other words, equilibrium occurs when aggregate demand (aggregate expenditures) AD(Y) is equal aggregate supply (aggregate domestic output) AS=Y:
Y* = AD (Y*), hence
Y* = A0/(1-c)
We can see this equilibrium on the upper graph called Keynesian cross.
3. Marginal propensity to consume is c - the proportion of each additional dollar of income that is used for consumption expenditures. The rest of income goes on savings S = Y - C. Hence,
S(Y) = -C0 + (1 - c)Y , and for equilibrium level of income:
S(Y*) = -C0 + (1 - c)A0/(1-c) = I0,
i. e. equilibrium occurs in the point where aggregate savings equal aggregate investment.
We can see this conclusion on the lower graph.
We'll consider the multiplier effect in the next post.
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 5:11 PM | Comments (6)