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Рік заснування видання - 2014

INVESTMENT FUNCTION ANALYSIS

22.08.2020 16:39

[Section 5. Mathematical methods, models and information technologies in economy]

Author: Hu Sen, Master Student, Sumy National Agrarian University


Investment function refers to the functional relationship between investment expenditure and factors affecting investment, which reflects what determines investment. There is a close relationship between investment and economic growth, and the reasonable degree of investment scale affects the stability of economic operation.

Investment is a function of interest rates. One of the important factors affecting economic growth is interest rate, and the change of interest rate affects the change of investment demand to a great extent. In the case that the expected future investment profit does not change, the investment demand of enterprises is determined by the real interest rate due to the characteristics of time value of funds. If the investor invests by borrowing funds, the interest borne by the investor is the cost of borrowing funds. If an investor invests with his own capital, the interest on the capital borne by the investor is the opportunity cost for him to use his own capital for the investment rather than for other aspects. Under normal circumstances, the level of interest rate is an indicator to measure the opportunity cost. The investment function can be expressed as a function of interest rate, and its formula is: I＝I0－bi, where I represents investment demand, I0 represents autonomous investment, and b represents the sensitivity coefficient of investment demand to interest rate. When the sensitivity coefficient of investment demand to interest rate b is large, investment demand is greatly affected by interest rate. When the sensitivity coefficient b of investment demand to interest rate is small, investment demand is less affected by interest rate.

The marginal efficiency of capital (r) is the discount rate at which the present value of the expected earnings of each period, over the life of a capital good, is equal to the supply price of the capital good. Expressed by the formula as follows:

k=R1/(1＋r)＋R2/(1＋r)2 ＋⋯＋Rn/(1＋r)n .

Where, K is the supply price of capital goods, R1, R1, ... Rn are the expected returns of different years. If the income of each future period remains unchanged, the marginal efficiency of capital will decrease as the price of capital goods rises. If the price of the supply of capital goods remains constant, the marginal efficiency of capital will decrease with the decline of the income in each future period. According to Keynes's theory, with the continuous increase of investment demand, the supply price of capital goods will rise, and the future returns will decline, which will lead to the diminishing marginal efficiency of capital, which means that manufacturers' expected returns will fall, and investment demand will decline.

Investment is a function of profit. If π is profit, I0 is autonomous investment, and t is the sensitivity coefficient of investment demand to profit, the investment function can be expressed as the formula I＝I0＋tπ. Through the relationship between investment and profits, it can be concluded that with the continuous increase of profits obtained by investors, GDP will continue to grow, the national income will surely grow, the investment environment will continue to improve, and the investment demand will also show a trend of rapid growth.

The principle of investment acceleration. The acceleration principle formula is expressed as It＝Kt－Kt－1＝V(Yt－Yt－1).Where, It represents the net investment in period t, Kt－Kt－1 represents the change of capital stock, V represents the capital-output ratio, which is the acceleration number of investment, and Yt－Yt－1 represents the change of national income. The above formula shows that changes in national income affect changes in net investment, and the magnitude of the changes depends on the acceleration number. The "acceleration principle" suggests that even if income changes little, investment will change a lot.

Literature:

1. Hayashi F, Tobin's Marginalq and Averageq: A Neoclassical Interpretation. Econometrica 50:213–224. https://www.jstor.org/stable/1912538

2. Hempenius, A.L. On the specification of an investment function. De Economist 120, 52–73. https://doi.org/10.1007/BF01461251

________________

Scientific supervisor: Svitlana Lukash, PhD of Economic, Associate Professor, Sumy National Agrarian University

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