Utilizar herramientas virtuales para fortalecer los procesos de aprendizaje y mejorar

The accelerator principle states that an increase in the rate of output of a firm will require a proportionate increase in its capital stock. The capital stock refers to the desired or optimum capital stock, K*. Assuming that capital-output ratio is some fixed constant, v, the optimum capital stock is a constant proportion of output so that in any period t,

K_t* = vY_t ……….. 1

Where K_t* is the optimal capital stock in period t, v (the accelerator) is a positive constant, and Y_t is output in period t.

Any change in output will lead to a change in the capital stock. Thus

K_t* - K*_t-1 = v (Y_{t –} Y_t-1) ……….2 and I_nt = v (Y_{t –} Y_t-1) ………. 3 [ I_nt = K_t* - K*_t-1] = v Y_t ……….4 where Y_t = Y_t – Y_t-1 and I_nt is net investment.

In the above equation, the level of net investment is proportional to change in output. If the level of output remains constant ( net investment would be zero. For net investment to be a positive constant, output must increase.

Self Assessment Exercise (SAE)

i. Discuss major determinant of investment in accordance to accelerator theory 3.2 THE FLEXIBLE ACCELERATOR THEORY OR LAGS IN INVESTMENT

The flexible accelerator theory removes one of the major weaknesses of the simple acceleration principle that the capital stock is optimally adjusted without any time lag. In the flexible accelerator, there are lags in the adjustment process between the level of output and the level of capital stock. This theory is also known as the capital stock adjustment model. The theory of flexible accelerator has been developed in various forms by Chenery, Goodwin and Koyck. But the most accepted approach is by Koyck. Junankar has discussed the lags in the adjustment between output and capital stock. He explains them at the firm level and extends them to the aggregate level. Suppose there is an increase in the demand for output. To meet it, first the firm will use its inventories and then utilise its capital stock more intensively. If the increase in the demand for output

is large and persists for some time, the firm would increase its demand for capital stock. This is the decision-making lag. There may be the administrative lag of ordering the capital. As capital is not easily available and in abundance in the financial capital market, there is the financial lag in raising finance to buy capital. Finally, there is the delivery lag between the ordering of capital and its delivery. Assuming ―that different firms have different decision and delivery lags then in aggregate the effect of an increase in demand on the capital stock is distributed over time … This implies that the capital stock at time t is dependent on all the previous levels of output, i.e.

K_t = f (Y_t, Y_t-1, …., Y_{t - n}).”……… 5 The Koyck’s Approach

Koyck‘s approach to the flexible accelerator assumes that the actual capital stock depends on all past output levels with weighs declining geometrically.

Accordingly,

……. 6 …

Where, 0 < < 1. If there is no change in income and it is equal to ̅, the expected volume of output also remains unchanged, then

̅ ̅ ̅ ̅ ̅

= ̅ ……….. 7

Where = 1/ are the weights in geometric series and equation (7) becomes

̅ ̅ ……… 8

Or ̅ ……… 9

If equation (6) is valid, then is also true. Therefore, we can rewrite equation (6) as

………. 10 Multiplying by we have

………… 11

…

Subtracting equation (10) from equation (6), we get

……….12 Since the term tends to zero, the above equation becomes

……….. 13

or ……… 14 This process of rewriting equation (6) as equation (11) is called the Koyck transformation.

Net investment is the change in the stock of capital, Therefore, subtract from both sides of the equation to get the expression net investment,

……….. 15 I_nt =

or I_nt = ……….. 16 The net investment ( is called the distributed lag accelerator which is inversely related to the capital stock of the previous period and is positively related to the output level. On the other hand, gross investment equals net investment plus depreciation. Depreciation is proportional to the capital stock and is estimated by . By adding this to net investment, gross investment is

………

17

By substituting the value of in the above equation, we have

………..

18

……… . 19 The above equation reveals that ―gross investment will rise when the level of income rises because in that case more capital is required. It also shows that the existing capital stock plays a dual role. Since the term is negative, a large existing capital stock implies excess capacity and therefore less investment.

On the other hand, is positive so that the larger the existing capital, the greater the required amount of replacement investment.‖

In the long run equilibrium, the capital stock reaches its optimal so that

K_t* = ……… 20 Substituting equation (14) in equation (11), we have

K_t* = ……… 21 Substituting equation (15) in equation (12) we get

or ………...… 22 This equation represents the flexible accelerator or the stock adjustment principle. This suggests that ―net investment is some fraction of the difference between planned capital stock and actual capital stock in the previous period ….

The coefficient tells us how rapidly the adjustment takes place. If [i.e. = 1] then adjustment takes place in the unit period‖..

Self Assessment Exercise (SAE)

i. Differentiate between accelerator theory and flexible accelerator theory.