Lecture No. 7
(2) Flexible Acceleration Theory of Investment
(1) Kt = aB [Qt + (1-B) Qt-1 + (1-B) 2 Qt-2 + (1-B) 3 Qt - 3……]
A: Acceleration Co-efficient
B: Is a fraction less than one.
It denotes the weight assign to output.
1-B ` = Successively one time period behind
1-B2 = Successively two time period behind
1-B3 = Successively three time period behind
We can have lags equation by one time period behind to get Kt-1 and multiplying both the sides buy 1-B of equation No (1). So we get equation (2)
(2)___ (1-B) (Kt-1) = aB (1-B (Qt-q)) + (1-B) 2 Qt-1 + (1-B) 3 Qt-3
Subtract equation 1 from Equation (2) we have equation (3)
(3) ___ Kt-(1-B) (Kt-1) = ab (Qt) OR
Kt-(1-B) (Kt-1) - ab Qt
The equation (3) can be written as below:
(4) Kt = aBQt + (1-B) (Kt-1)
By definition net investment is equal to the change in capital stock between two successive time periods, which can be written as
(5): In = kt – Kt - 1
Therefore net investment can be written down as in equation (6)
(6) ln = – kt– 1
Equation (6) can be written as equation (7)
(7) ln = aBQt – B (Kt-1)
(8) ln = B[aQt – (Kt-1)]
Equation (8) is the equation of flexible acceleration which explain that net investment is a function of current output as well as output in the past time period with given weight to every output in successfully given time period. This equation is differently from simple acceleration theory of investment
In the above equation this is also shown that relationship between investment and change in output during the same period is not given by the average capital output rate (a), fraction of this ratio B. In this way flexible acceleration is different from simple theory of investment. According to flexible theory of investment business man do not adjusted their capital stock in only current output.
Simply to the current level of demand for their product but to whole pattern of past output. This is the process which is called expected normal output. According to flexible acceleration investment is a function of present as well as fast output. So, A difference must be made between short run marginal capital output ratio and long run equilibrium amount of capital which will be added for each unit of permanent income use in output in an economy with unchanging Technology. we can make a comparison between simple acceleration theory of investment and flexible acceleration theory of investment with the help of diagram:
(2) Flexible Acceleration Theory of Investment
This theory has been given by L.M koyck in an article (distributed lags and Investment analysis) given in 1954. In simple acceleration theory of investment relationship between desired capital stock and correct output in assume to take place in time period only. But in flexible acceleration theory change in output do not immediately leads to a change in the level of capital Stock nor is a desire to change the capital immediately reflected in actually investment. According to L.M. koyck stock of capital is adjusted not only to current output. But also to the past output with a declining weight given to successively earlier time period. This can be explain with the help of following equations 18 equal
A: Acceleration Co-efficient
B: Is a fraction less than one.
It denotes the weight assign to output.
1-B ` = Successively one time period behind
1-B2 = Successively two time period behind
1-B3 = Successively three time period behind
We can have lags equation by one time period behind to get Kt-1 and multiplying both the sides buy 1-B of equation No (1). So we get equation (2)
(2)___ (1-B) (Kt-1) = aB (1-B (Qt-q)) + (1-B) 2 Qt-1 + (1-B) 3 Qt-3
Subtract equation 1 from Equation (2) we have equation (3)
(3) ___ Kt-(1-B) (Kt-1) = ab (Qt) OR
Kt-(1-B) (Kt-1) - ab Qt
The equation (3) can be written as below:
(4) Kt = aBQt + (1-B) (Kt-1)
By definition net investment is equal to the change in capital stock between two successive time periods, which can be written as
(5): In = kt – Kt - 1
Therefore net investment can be written down as in equation (6)
(6) ln = – kt– 1
Equation (6) can be written as equation (7)
(7) ln = aBQt – B (Kt-1)
(8) ln = B[aQt – (Kt-1)]
Equation (8) is the equation of flexible acceleration which explain that net investment is a function of current output as well as output in the past time period with given weight to every output in successfully given time period. This equation is differently from simple acceleration theory of investment
In the above equation this is also shown that relationship between investment and change in output during the same period is not given by the average capital output rate (a), fraction of this ratio B. In this way flexible acceleration is different from simple theory of investment. According to flexible theory of investment business man do not adjusted their capital stock in only current output.
Simply to the current level of demand for their product but to whole pattern of past output. This is the process which is called expected normal output. According to flexible acceleration investment is a function of present as well as fast output. So, A difference must be made between short run marginal capital output ratio and long run equilibrium amount of capital which will be added for each unit of permanent income use in output in an economy with unchanging Technology. we can make a comparison between simple acceleration theory of investment and flexible acceleration theory of investment with the help of diagram:
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