The accelerator effect in economics refers to a positive effect on private of the growth of the market economy (measured e.g. By a change in ).
Rising GNP (an economic boom or prosperity) implies that businesses in general see rising profits, increased sales and cash flow, and greater use of existing capacity. This usually implies that profit expectations and business confidence rise, encouraging businesses to build more factories and other buildings and to install more machinery. (This expenditure is called fixed investment.) This may lead to further growth of the economy through the stimulation of consumer incomes and purchases, i.e., via the effect. The accelerator effect also goes the other way: falling GNP (a ) hurts business profits, sales, cash flow, use of capacity and expectations. This in turn discourages fixed investment, worsening a recession by the multiplier effect.
The accelerator effect fits the behavior of an economy best when either the economy is moving away from or when it is already below that level of production. This is because high levels of hit against the limits set by the existing labour force, the existing stock of capital goods, the availability of natural resources, and the technical ability of an economy to convert inputs into products.
ADVERTISEMENTS: Some of the new theories of investment in macroeconomics are as follows: Contents:. The Accelerator Theory of Investment.
The Flexible Accelerator Theory or Lags in Investment. The Profits Theory of Investment. Duesenberry’s Accelerator Theory of Investment.
The Financial Theory of Investment. Jorgensons’ Neoclassical Theory of Investment.
Tobin’s Q Theory of Investment 1. The Accelerator Theory of Investment: 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. ADVERTISEMENTS: and I nt = v (Y t – Y t-1) I nt=K t– K t-1 = v∆Y t Where ∆Y t = Y t – Y t-1, and I nt is net investment. This equation represents the naive accelerator. In the above equation, the level of net investment is proportional to change in output.
If the level of output remains constant (∆Y = 0), net investment would be zero. For net investment to be a positive constant, output must increase. This is illustrated in Figure 1 where in the upper portion, the total output curve Y increases at an increasing rate up to t + 4 periods, then at a decreasing rate up to period t + 6. After this, it starts diminishing. The curve I n in the lower part of the figure, shows that the rising output leads to increased net investment up to t + 4 period because output is increasing at an increasing rate. But when output increases at a decreasing rate between t + 4 and t + 6 periods, net investment declines. When output starts declining in period t + 7, net investment becomes negative.
Define Agency Cost Theory
The above explanation is based on the assumption that there is symmetrical reaction for increases and decreases of output. In the simple acceleration principle, the proportionality of the optimum capital stock to output is based on the assumption of fixed technical coefficients of production. This is illustrated in Figure 2 where Y and Y 1 are the two isoquants. ADVERTISEMENTS: The firm produces T output with K optimal capital stock. If it wants to produce Y 1 output, it must increase its optimal capital stock to K 1.
The ray OR shows constant returns to scale. It follows that if the firm wants to double its output, it must increase its optimal capital stock by two-fold. Eckaus has shown that under the assumption of constant returns to scale, if the factor-price ratios remain constant, the simple accelerator would be constant.
Suppose the firm’s production involves the use of only two factors, capital and labour whose factor-price ratios are constant. In Figure 3, Y, Y 1 and Y 2 are the firms’ isoquants and C, C 1 and C 2 are the isocost lines which are parallel to each other, thereby showing constant costs. If the firm decides to increase its output from Y to Y 1, it will have to increase the units of labour from L to L 1 and of capital from K to K 1 and so on.
The line OR joining the points of tangency e, e 1 and e 2 is the firms’ expansion path which shows investment to be proportional to the change in output when capital is optimally adjusted between the iosquants and isocosts. 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, Koyck and Junankar.
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).
This is illustrated in Figure 4 where initially in period t 0, there is a fixed relation between the capital stock and the level of output. When the demand for output increases, the capital stock increases gradually after the decision and delivery lags, as shown by the K curve, depending on the previous levels of output. The increase in output is shown by the curve T.
The dotted line K is the optimal capital stock which equals the actual capital stock K in period t. Koyck’s Approach: Koyck’s approach to the flexible accelerator assumes that the actual capital stock depends on all past output levels with weights declining geometrically. Accordingly, 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 periodThe coefficient (1 – λ) tells us how rapidly the adjustment takes place. If λ= 0 i.e.
(1 – λ) = 1 then adjustment takes place in the unit period”. To conclude, the flexible accelerator is a very important contribution to the theory of investment which solves the problem of lags in investment demand. It not only incorporates the effects of lags but also of depreciation and excess capacity in the capital stock adjustment. It’s Comparison with Naive Accelerator: Since the flexible accelerator and naive accelerator are both accelerators, their long-run response of investment to a change in output will be similar. Let us consider a situation where output (Y) is rising at a decreasing rate and ultimately stops rising at a high level.
In the case of the flexible accelerator, net investment will increase during several periods before the negative effect of the increased capital stock outweighs the positive effect of further increases in output and ultimately net investment will become zero. This is shown in Figure 5. On the other hand, in the case of the naive accelerator, net investment will be decreasing continuously and will also become zero, as shown in Figure 6. In both the accelerators, gross investment will be equal to depreciation. The Profits Theory of Investment: The profits theory regards profits, in particular undistributed profits, as a source of internal funds for financing investment.
Investment Theory
Investment depends on profits and profits, in turn, depend on income. In this theory, profits relate to the level of current profits and of the recent past. If total income and total profits are high, the retained earnings of firms are also high, and vice versa, Retained earnings are of great importance for small and large firms when the capital market is imperfect because it is cheaper to use them.
Thus if profits are high, the retained earnings are also high. The cost of capital is low and the optimal capital stock is large. That is why firms prefer to reinvest their extra profit for making investments instead of keeping them in banks in order to buy securities or to give dividends to shareholders. Contrariwise, when their profits fall, they cut their investment projects. This is the liquidity version of the profits theory.
Another version is that the optimal capital stock is a function of expected profits. If the aggregate profits in the economy and business profits are rising, they may lead to the expectation of their continued increase in the future. Thus expected profits are some function of actual profits in the past, K t = f( t-1) Where K is the optimal capital stock and f ( t-1) is some function of past actual profits. Edward Shapiro has developed the profits theory of investment in which total profits vary directly with the income level. For each level of profits, there is an optimal capital stock. The optimal capital stock varies directly with the level of profits.
The interest rate and the level of profits, in turn, determine the optimal capital stock. For any particular level of profits, the higher the interest rate, the smaller will be the optimal capital stock, and vice versa. This version of the profits theory is explained in terms of Figure7. The curve Z in Panel (A) shows that total profits vary directly with income. When the income is Y 1, profits are P 1 and with increase in income to Y 2 profits rise to P 2.
Panel (B) shows that the interest rate and the profits level determine the capital stock. At P 2 profits levels and r6% interest rate, the actual capital stock is K 2 and at the lower profits level P and interest rate r6%, the actual capital stock declines to K 1. In Panel (C), the MEC curve is drawn for each level of profits, given the actual capital stock and the rate of interest. As such, the curve MEC 1 relates the profits level P 1 to the optimal capital stock K 1 when r6% is the interest rate. The higher curve MEC 2 relates the profit level P 2 to the higher optimal capital stock K 2, given the same rate of interest r 6%.
Suppose that the level of profits is P 1, the market interest rate is r6% and the actual capital stock is K 1. With this combination of the variables, the optimal capital stock in Panel (C) is K so that the actual capital stock, K 1 = K 1 the optimal capital stock. As a result, net investment is zero. But there is still I 1 replacement investment at r6%, as indicated by MEI 1 curve in Panel (D).
The combination of I 2 investment and Y 1 income level establishes point A on the investment curve I in Panel (E) of the figure. Now begin with P 2 level of profits and Y 2 income level in Panel (A) so that at r6% interest rate in Panel (C), the optimal capital stock is K 2. Assuming again that the actual capital stock is K 1, the optimal capital stock is greater than the actual, K 2 K 1 at this profit-income combination. Here the MEC 2 is higher than r6% interest rate by RM. As a result, the MEI 1 curve shifts upward to MEI 2 in Panel (D). Since K 2 K 1 net investment is positive. This is shown by I 1 – I 2 in Panel (D).
So when profits increase to P 2 with the rise in income to Y 2, the optimal capital stock K 2 being greater than the actual capital stock K 1 at r6% interest rate, investment increases from I 3 to I 4 in Panel (E) which is equal to net investment I 1I 2 in Panel (D). The combination of I 4 and Y 2, establishes point B on the upward sloping I curve. To sum up, in the profits theory of investment, the level of aggregate profits varies with the level of national income, and the optimal capital stock varies with the level of aggregate profits. If at a particular level of profits, the optimal capital stock exceeds the actual capital stock, there is increase in investment to meet the demand for capital.
But the relationships between investment and profits and between aggregate profits and income are not proportional. It’s Criticism: The theory is based on the assumption that profits are related to the level of current profits and of the recent past.
But there is no possibility that the firm’s current profit of this year or of the next few years can measure the profits of the next year or of the next few years. A rise in current profits may be the result of unexpected changes of a temporary nature. Such temporary profits do not induce investment. Duesenberry’s Accelerator Theory of Investment: J.S. Duesenberry in his book Business Cycles and Economic Growth presents an extension of the simple accelerator and integrates the profits theory and the acceleration theory of investment.
Duesenberry has based his theory on the following propositions: (1) Gross investment starts exceeding depreciation when capital stock grows. (2) Investment exceeds savings when income grows. (3) The growth rate of income and the growth rate of capital stock are determined entirely by the ratio of capital stock to income. He regards investment as a function of income (Y), capital stock (K), profits and capital consumption allowances (R). All these are independent variables and can be represented as I = f(Y t-1, K t-1, t-1, R t) Where t refers to the current period and (t-1) to the previous period. According to Duesenberry, profits depend positively on national income and negatively on capital stock. =aY- bK Taking account of lags, this becomes =aY t-1– b K t-1 Where t refers to profits during period t, Y t-1 and K t-1 are income and capital stock of the previous period respectively and a and b are constants.
Capital consumption allowances are expressed as R, = kK t-1 The above equation shows that capital consumption allowances are a fraction (k) of capital stock (K t-1). Duesenberry’s investment function is a modified version of the accelerator principle, I t = αY t-1 + βK t-1. (1) where investment in period t is a function of income (X) and capital stock (K) of the previous period (t—1). The parameter (a) represents the effect of changes in income on investment, while the parameter ((3) represents the influence of capital stock on investment working through both the marginal efficiency of investment and profits. Since the determinants of investment also affect consumption, the consumption function can be written as, C t = f (Y t-1 – t-1 – R t-1+ d t) Where d t stands for dividend payments in period t.
Since = f (Y, K), R = kY and d=f (∏), these independent variables can be subsumed under Y and K. Thus C t = a Y t-1 + bK t-1.
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(2) The parameter, a, in equation (2) is MPC and it also reflects increase in profits. This increase is reduced by the effect of profits on dividends and the effect of changes in dividends on consumption.
The influence of changes in capital stock on consumption is reflected by the parameter b. This influence results from the influence of capital stock on profits through the influence of profits on dividends on consumption. The capital stock is represented by the following equation which is an identity, The a (MPC) in equation (7) will be much smaller than MPC out of disposable income because it reflects the influence of changes in income on profits and business savings. Simultaneously, the a in the above equation will be much less than the average capital-output ratio which is the accelerator in simple multiplier- accelerator models. An increase, say, $100 in income, with capital stock constant, will increase the rate of business investment by an amount which is not much larger than the increase in business savings resulting from $100 increase in income. It will be only, say, $25.
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Thus an increase in income will have a smaller immediate effect on expenditure than would occur in a simple multiplier-accelerator model. On the other hand, the negative effect of an increase in capital stock, with income constant, will be much smaller than in the simple multiplier-accelerator model. If there is an increase in business capital stock of say, $100, income being constant, it will reduce profits by a very small amount and will have correspondingly a small effect on business investment.
But a part of the decline in business investment will be offset by a reduction in business saving. Such changes will reduce the effect on an increase in income on expenditure for some time because investment will decline slowly, as capital accumulates, provided there is no further increase in income.
The system will therefore, be much more stable than a simple multiplier-accelerator system. The Financial Theory of Investment: The financial theory of investment has been developed by James Duesenberry. It is also known as the cost of capital theory of investment. The accelerator theories ignore the role of cost of capital in investment decision by the firm. They assume that the market rate of interest represents the cost of capital to the firm which does not change with the amount of investment it makes. It means that unlimited funds are available to the firm at the market rate of interest. In other words, the supply of funds to the firm is very elastic.
In reality, an unlimited supply of funds is not available to the firm in any time period at the market rate of interest. As more and more funds are required by it for investment spending, the cost of funds (rate of interest) rises. To finance investment spending, the firm may borrow in the market at whatever interest rate funds are available. Sources of Funds: Actually, there are three sources of funds available to the firm for investment which are grouped under internal funds and external funds. These are: (1) Retained earnings which include undistributed profits after taxes and depreciation allowances are internal funds.
(2) Borrowing from banks or through the bond market; and borrowing through equity financing or by issuing new stock (shares) in the stock market are the sources of external funds. Retained Earnings: Retained earnings are the cheapest source of funds because the cost of using these funds is very low in the short run. There is no risk involved in spending these retained earnings or to repay debt. In fact, the cost of using these funds is the opportunity cost which is the return that the firm could obtain to repay debt or to buy the shares of other companies. The opportunity cost of internal funds will be less than the cost of external funds. When the firm lends these funds to other borrowers, it usually earns the market rate of interest.
If it borrows funds from banks or through the bond market, it has to pay a higher interest rate. This difference in interest rate is the opportunity cost to the firm.
Borrowed Funds: When the firm needs funds more than the retained earnings, it borrows from the banks or through the bond market. The cost of borrowed funds (rate of interest) rises with the amount of borrowing. As the ratio of debt service to earnings from investment of funds rises, the marginal cost of borrowed funds rises. This is because the opportunity cost (risk) of not repaying debt increases. Equity Issue: A third source is equity financing by issuing new shares in the stock market. The imputed cost of equity funds is more costly than the opportunity cost of retained earnings or borrowed funds. Duesenberry points out that “the yield cost of equity finance is usually of the order of 7 to 10 percent for large firms.
To this must be added floatation costs plus any reduction in the value of existing shares resulting from the issue. The differential is further increased by the differential tax treatment of bond and equity finance.” Cost of Funds: The cost of capital to the firm will vary according to its source and how much funds it requires.
Keeping these considerations in view, we construct the marginal cost of funds curve MCF in Figure 8 which shows the various sources of funds. The cost of funds is measured on the vertical axis and the amount of investment funds on the horizontal axis. Region A of the MCF curve shows financing done by the firm from retained profits (RP) and depreciation (D).
In this region, the MCF curve is perfectly elastic which means the true cost of funds to the firm is equal to the market rate of interest. The opportunity cost of funds is the interest forgone which the firm could earn by investing its funds elsewhere. No risk factor is involved in this region. Region B represents funds borrowed by the firm from banks or through the bond market. The upward slope of the MCF curve shows that the market rate of interest for borrowed funds rises as their amount increases.
But the sharp rise in the cost of borrowing is not only due to a rise in the market rate of interest but also due to the imputed risk of increased debt servicing by the firm. Region C represents equity financing. No imputed risk is involved in it because the firm is not required to pay dividends. The gradual upward slope of MCF curve is due to the fact that as the firm issues more and more of its stock, its market price will fall and the yield will rise.
The cost of funds may vary from firm to firm and consequently the shape and position of the MCF curve will differ from one firm to another. But in general, it will be like the MCF curve of Figure 8. If we aggregate MCF curves of different firms there will be a smooth S-shaped MCF 1 curve, as in Figure 9. This curve shifts upward from MCF 1 to MCF 2 when the cost of funds (interest rate) rises from R 1 to R 2 and shifts downward from MCF 2 to MCF 1 with the fall in the cost of funds from R 2 to R 1. The amount of investment funds is determined by the intersection of ME1 and MCF curves.
The main determinants of the MEI curve are the rate of investment, output (income), level of capital stock and its age and rate of technical change. The determinants of MCF are retained earnings (profits minus dividends), depreciation, debt position of firms and market interest rate. It is the shifts of the MEI and MFC curves that determine the level of investment funds. Suppose the MEI and MCF curves interest at point E in Figure 10 which determines OI investment at the interest rate (the cost of funds) OR. If the MCF curve shifts to the right to MCF 1 with the increase in retained earnings (profits) of the firm, the MEI curve will cut the MCF 1 curve at E 1. The cost of funds will fall from OR to OR 1 but investment funds will rise to OI 1 from OI.
On the other hand, if the MEI curve shifts to the right to MEI 1 with the increase in income and capital stock, it will cut the MCF 1 curve at point E 2. There will be increase in both the cost of funds to OR 2 and in the investment funds to OI 2. The above explanation is related to the short-run behaviour of MEI and MCF curves. But the same factors that determine the position and shifts of these curves have different effects over the business cycle. Since the MEI curve depends primarily on output, it shifts backward to the left to MEI 1 when output (income) decreases in a recession, as shown in Figure 11. Both MEI and MEI 1 curves intersect the MCF curve in its perfectly elastic region.
In a recession, retained profits decline but depreciation allowances remain with firms. So the elastic portion of the MCF curve becomes shorter. Meyer and Kuh found that firms generally spend more of their retained earnings in recessions and a low interest rate does not have any effect on investment. But when recovery starts, the MEI 1 curve shifts outward to the right to MEI. As a result, there is an increase in investment spending of the firm out of its retained earnings in the perfectly elastic portion of the MCF curve.
Thus during a recession, monetary policy or the market rate of interest plays no role in determining the cost of capital of a firm. On the other hand, during a boom when output increases, the MEI curve shifts outward to the right to MEI 1 and intersects the MCF curve in its elastic rising region, as shown in Figure 12. In the upswing leading to boom, firms borrow funds on interest for investment spending. Thus monetary policy or interest rate is an important determinant of investment only in boom years.
Its Criticisms: The financial theory of investment has been criticised on the following grounds: 1. The results of studies by Meyer and Kuh on investment behaviour of firms show that when demand is expanding rapidly, capacity expansion is the most important determinant of business investment during boom periods. In terms of our Figure 8, the MEI curve intersects the MCF curve in region B. In recessions and early years of recovery, the MEI curve shifts back to region A, and the level of retained earnings provides the best explanation of investment spending. Meyer and Kuh found that firms take a longer view while making investment spending, whereas Duesenberry explains a short-run model of investment. Their results indicate that firms primarily invest in capacity expansion during a boom period and their overall level of investment will not fall as much as indicated by Duesenberry’s short-run model when the interest rate rises.
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On the other hand, firms generally spend most of their retained earnings on technological improvements to reduce costs and on advertisement to increase their market share. Empirical evidence in the theory of investment by Kuh and Meyer shows that monetary policy is the least effective of all the macroeconomic policy instruments. In the analysis represented in Figure 10, we have seen that the market rate of interest plays only a small role in the financial theory of investment.
Critics point out that the main effect of rising interest rates would be to increase the steepness (or reduce the elasticity) of region B of the MCF curve. This would stop investment when retained earnings of firms had been exhausted. On the other hand, declining interest rates would flatten (increase the elasticity) region B of the MCF curve. This would have no effect in a recession if firms finance their investment spending from retained earnings. Thus monetary policy would be more effective in controlling a boom than in stimulating investment in recession. This theory neglects the role of fiscal policy in investment which is more effective than monetary policy. A reduction in corporate taxes in a recession can increase investment by firms.
On the other hand, an increase in corporate taxes can reduce investment and shift the MCF curve to the left. Changes in depreciation allowances can also help in manipulating investment in recessions and booms. Investment spending is also influenced by the level and changes in aggregate demand. Besides taxes, expenditure policy and other government measures also affect aggregate demand and the MEI curve which in turn influence the level of investment. Jorgensons’ Neoclassical Theory of Investment: Jorgenson has developed a neoclassical theory of investment. His theory of investment behaviour is based on the determination of the optimal capital stock.
His investment equation has been derived from the profit maximisation theory of the firm. It’s Assumptions: Jorgenson’s theory is based on the following assumptions: 1. The firm operates under perfect competition. There is no uncertainty. There are no adjustment costs. There is full employment in the economy where prices of labour and capital are perfectly flexible. There is a perfect financial market which means the firm can borrow or lend at a given rate of interest.
The production function relates output to the input of labour and capital. Labour and capital are homogeneous inputs producing a homogeneous output. Inputs are employed upto a point at which their MPPs are equal to their real unit costs. There are diminishing returns to scale. There is the existence of “putty-putty” capital which means that even after investment is made, it is instantly adapted without any costs to a different technology.
The capital stock is fully utilised. Changes in current prices always produce ceteris paribus proportional changes in future prices. The price of capital goods equals the discounted value of the rental charges. The firm maximises the present value of its current and future profits with perfect foresight in relation to all future values. The Model: Jorgenson develops his theory of investment on the assumption that the firm maximises its present value. In order to explain the present value of the firm, he takes a production process with a single output (Q), a single variable input labour (L), and a single capital input (I-investment in durable goods), and p, w, and q representing their corresponding prices.
The flow of net receipts (R) at time t is given by R (t) =p (t) Q (t) – w (t) L (t) – q(t) I(t).(1) Where Q is output and p is its price; L is the flow of labour services and w the wage rate; I is investment and q is the price of capital goods. The present value is defined as the integral of discounted net receipts which is represented as W= ∫ o ∞ e -r t R (t)dt (2) Where W is the present value (net worth); e is the exponential used for continuous discounting; and r is the constant rate of interest. The present value is maximised subject to two constraints. First, the rate of change of the flow of capital services is proportional to the flow of net investment. The constant of proportionality may be interpreted as the time rate of utilisation of capital stock that is the number of units of capital service per unit of capital stock.
Net investment is equal to total investment less replacement investment where replacement investment is proportional to capital stock. This constraint takes the form: K (t) = I (t)-δ K(t).(3) Where K (t) is the time rate of change of the flow of capital services at time (t) while δ is the rate of depreciation attached to capital stock. This constraint holds at each point of time so that K, K and I are functions of time. To simplify the analysis, Duesenberry uses K in place of K (t), I in place of I(t), and so on. Second, the levels of output and the levels of labour and capital services are constrained by a production function: F (Q, L, K) = 0.(4) The marginal productivity of labour is equal to the real wage: ∂Q/∂L = w/p. (5) Similarly, the marginal productivity of capital is equal to its real user cost: ∂K/∂L = w/p.
(6) Where c = q(r + δ)-q (7) In the above equation, q is the average price of capital assets, r is the rate of discount, δ is the rate of depreciation of capital goods and q is the rate of appreciation of capital assets or time derivative of q. Therefore, the crucial determinant of the optimal capital stock is c, the user cost of capital. Since most firms own rather than rent their capital assets, therefore c is basically an implicit or shadow price constructed in order to permit parallel analytical treatment of capital and labour inputs.
Equations (5) and (6) are called “myopic decision criteria” because the firm is engaged in a dynamic optimisation process and simply equates the MP of labour with the ratio of its price and MP of capital with the ratio of user cost of capital. There are two reasons for the myopic decision in the case of capital assets. First, it is due to the assumption of no adjustment costs so that the firm does not gain by delaying the acquisition of capital. Second, it is the result of the assumption that capital is homogeneous and it can be bought and sold or rented in a perfectly competitive market. The myopic decision is illustrated in Figure 13 where in the upper portion the two alternative time paths of output prices, P 1 and P 2, are shown and in the lower portion are shown the optimal capital stocks, in Panel (A), the output prices are identical up to time t 0, and then their time paths diverge when P 1 is always lower than P 2.
With the myopic decision, the optimal capital stock is identical up to t 0 for both time path of output prices. But after that, for the time path of P 1 price, the optimal capital stock K 1 moves at a constant rate, while for P 2 time path of output price, the optimal capital stock K 2 increases as the former rises. Thus in the Jorgenson model, there are no inter-temporal trade-offs. Assuming that there are no adjustment costs, no uncertainty and perfect competition exists, as Jorgenson does, the firm will always be adjusted to the optimal capital stock so that K=K. Therefore, the question of adjustment to a discrete change in the interest rate does not rise. Instead, Jorgenson treats this problem as one of comparing two optimal paths of capital accumulation under two different interest rates. For this, he takes the demand for investment goods as given by the following equation: I = K + δ (8) Where I stands for gross demand for investment goods, K the rate of change in capital stock, 8 the rate of depreciation and K the fixed level of capital assets which is expressed as K =f (w, c, p).
(9) The condition of equation (9) implies that with w and p fixed, c must remain unchanged. From the expression for c in equation (7), this, in turn, implies that holding the price of investment goods constant, the rate of change of price of investment goods must vary as the interest rate varies so as to leave c unchanged.
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Formally, this condition can be represented by ∂c/∂r = 0 Where r is the interest rate. This condition implies that the own-interest rate on investment goods (r-q/q) must be left unchanged by variations in the interest rate. Jorgenson assumes that all changes in the interest rate are exactly compensated by changes in the price of investment goods so as to leave the own-interest rate on investment goods unchanged.
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This condition implies that ∂ 2q/∂t ∂r = q He further assumes that changes in the time path of interest rate leave the time path of forward or discounted prices of capital goods unchanged. This condition implies that ∂ 2q/∂t ∂r = c Combining these two conditions, we obtain ∂I/∂r = ∂k/∂c x c 1) or less than 1 (q 1, the market value of the firm’s shares in the stock market is more than the replacement cost of its real capital, machinery etc. The firm can buy more capital and issue additional shares in the stock market. In this way, by selling new shares, the firm can earn profit and finance new investment. Conversely, if q.
Accelerator Theory of Investment. 1. Autonomous Investment Induced Investment. National Income Investment I`I National Income Investment I` I. C = R1/1+r + R2/(1+r)2 + R3/(1+r)3 +. + Rn/(1+r)n C = SUPPLY COST OR THE REPLACEMENT COST R= ANNUAL PROSPECTIVE YEILDS FROM THE CAPITAL ASSET r = MEC. Period Output Income Required Stock of Capital Capital Replacement Net Investment Gross Investment t -1 500 1500 300 0 300 t 510 1530 300 30 330 t + 1 525 1575 306 45 351 t +2 550 1650 315 75 390 t +3 575 1725 330 75 405 t + 4 575 1725 345 0 345 t +5 560 1680 345 -45 300.
Kt = Stock of Capital for time t Net Investment = Kt – Kt -1 Gross Investment = Capital Replacement + Net Investment V = Constant Here, we take the Value of V as 3 ASSUMPTIONS: - 1. CAPITAL OUTPUT RATIO WILL ALWAYS BE CONSTANT. DEPRECIATION THAT TAKES PLACE IN THE STOCK OF CAPITAL WILL BE 1/5 TH OF THE STOCK EXSISTING IN THE PREVIOUS YEAR, THUS, 1/5 TH OF THE STOCK OF THE CAPITAL SHOULD BE REPLACED EVERY YEAR.
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