LESSON - 23 THE SAVING FUNCTOIN Learning outcomes After studying this unit, you should be able to: Define saving function Differentiate between saving function and consumption function Know propensity to save Know APS and MPS Identify determinants of saving function INTRODUCTION: Saving function tells us the relationship between income and savings. The relationship between income and consumption also tells us what kind of relationship exists between income and saving. So, the saving function may be derived with the aid of the consumption function. In our simple model with no government and no foreign trade sectors, income equals, by definition, consumption plus saving : Y = C + S But C is equal to a +by; after substitution Or Or Or Thus the saving function is S = -a+(1-b)y Y = a = a Y = S S = a Y = by S = a (1-b)Y S = -a + (1-b)Y [O<(1-b),1] Where a is the intercept and (1-b) is the slope. The saving function shows that saving changes. If the change in saving is denoted as S and the change in income as Y, the ratio of the change in saving to the change in income s/ y is 1-b, the slope of the saving function. This relationship is called the marginal propensity to save (MPS). Since b represents the MPC, the MPS is 1-MPC. It implies that the MPS is between 0 and 1, provided that the MPC is between 0 and 1.
Given a equal to Rs. 100 crores and b equal to 0.8, the saving function becomes S = -100 + (1-8)Y or S = -100 + 2Y Y Y=C C 1 B C 45º Y A Y 1 X Fig - 45 0 curve showing relationship between income and consumption The intercept is -100 and the slope, the marginal propensity to save, is 2. To plot the function, assume that income is zero, this means that saving is equal to 100. Negative saving or dissaving occurs if individual households consume more that their income. They may do so by spending part of their savings or by borrowing. Consequently, one point on the saving function is the point Y = 0, S = -100. To obtain another point, select another level of income, say Rs. 900 crores. At that level of income, saving equals 100 + 2 times, Rs. 900 crores or a total of Rs. 80 crores. Consequently, another point on the saving function is the point Y = Rs. 900 crores and S = Rs. 80 corores. Other points on the saving function could be obtained in the same manner. The saving function may be depicted graphically as well. To aid in this process, a 45 degree line is drawn from the origin. This line is illustrated separately in Fig. 5.5. The 45 degree line is a guideline which denotes that any point on the line in equidistant from the two axes. This means that the distance from the origin to some point on that horizontal axis will be the same as the vertical distance from that point on the horizontal axis to the 45
S = S 0. Select another level of income, say Y 1 where consumption function intersects the 45 0 degree line. In other words, when we graph the points that correspond to equal values on each axis, we obtain a line that exactly bisects 90 degree angle hence the name 45 degree line. In. Fig. 5.5, we measure income on the horizontal axis, and consumption expenditure is measured on the vertical axis. Notice that anywhere on the 45 degree line, income always equals consumption expenditure. For example, OY=OC at point A and OY 1 = OC 1 at point B. the level of income can, therefore, be measured either vertically to the 45 degree line or along the horizontal axis. This requires, of course, that same number scale be used on both axis of the diagram. Given the 45 degree line and the consumption function we can now derive the saving function graphically. Since income equals consumption plus saving, saving is the difference between income and consumption. Therefore, to find saving at each level of income, consumption is subtracted from income. Investment I 0 I-I 0 Rs. 80 crores Income Fig. Graphical Derivation of the Saving Function. Graphically, saving is the vertical distance between the 45 degree line and the consumption function, saving being positive (negative) when income is greater (less) than consumption. Consider income Y 0 in Fig. 5.6. At income Y 0, consumption equals C 0. S 0 is obtained by subtracting C 0 from Y 0. therefore, one point on the saving function is the point Y = Y 0, line. At that level of income, consumption equals C 1 which also equal Y 1. Therefore, at Y = Y 1, S 1 equals 0. Since S 1 equals Y 1 C 1 and C 1 equal Y 1, consequently, another point on the saving function is the point Y = Y 1, S = 0. Finally, suppose income is zero. At that level of income consumption equals a. hence saving equals a, obtained by subtracting C = a from Y = 0. Thus, a third point on the saving function is the point Y = 0, S = a. Other points on the saving function may be obtained by considering other levels of income. In Fig. 5.6, saving is positive at income levels greater than Y 1 since income exceeds consumption at those levels of income. Saving is negative at income less than Y 1 since income
exceeds consumption at those levels of income. Saving is negative at income les than Y 1 since consumption exceeds income. Determinants Propensity to Save Since saving is defined as that part of income which is not consumed, we have the following identity: Income Consumption + Saving (Y) (C) + (S) An income earner makes only one decision either regarding consumption or saving, the other component is only a residual. It follows then that determinants of aggregate consumption and aggregate saving are the same. Theories which explain total consumption also explain total saving. However, some of the important factors which affect propensity to save are discussed briefly below: (1) Saving and Income. In general, it is assumed that people have a strong preference for present consumption over future consumption. Therefore, a person will forgo present consumption only if he is paid premium equal to or greater than his marginal rate of time preference, i.e. an amount that will make the utility of a rupee received today equal to or smaller than the utility of the sum he will collect in a year if he lends the rupee. Presumably, a higher rate of interest will induce an individual to forgo some more present consumption in favour of future consumption. In other words, at higher rate of interest more will be the amount of saving and vice versa. The direct relation between interest and saving critically depends on the nature of individual s preferences. It is possible to have inverse relationship between saving and interest
rate. To some extent this may be due to the fact that some individuals save towards a lumpsum of wealth in future. An increase in the rate of interest will enable the individuals to put aside a smaller sum every year and still reach the desired goal of saving a fixed sum. Similarly, while an increase in the rate of interest will induce the individual to substitutes future consumption, the high rate of interest also improves his future income prospects so that he may tend to save less today. (3) Saving and Taxation Policy. Taxes reduce the disposable income of the people and they have also to cut down their consumption expenditure. As a result, the level of compulsory saving increase in an economy. (4) Saving and Social Insurance and Life Insurance. Deductions towards provident fund, insurance premium, etc., from the money income also raise the level of saving. (5) Saving and the Price Level. The nature of relationship between saving and the price level is rather uncertain in economic theory. On the one hand, real balance effect suggests a positive relation between saving and the price level. At high price the value of real balances falls which reduce consumption and increases saving. On the other hand, it is a argued that high prices are associated with lower interest rates in the course of cheap money policy. When the authorities attempt to peg interest rates at low levels, saving is discouraged. However, a positive change in the price level is found to have favourable effect on saving. It is possible that people expect prices to rise if there is a price rise in the preceding period. This may increase consumption of durables like housing etc. which is recorded as saving. (6) Saving and Distribution of Income. Aggregate saving in an economy may depend, among other things, on the distribution of income. Since the marginal propensity to save of the rich persons is high, therefore, disparities of income will raise the level of saving in an economy. Equitable distribution of income on the other hand, lowers the propensity to save. SIGNIFICANCE OF CONSUMPTION FUNCTION AND SAVING FUNCTION The relationship between consumption and income (or alternatively saving and income) is the foundation stone of Keynesian revolution. The functions in relation to investment function help to explain underemployment equilibrium and provide a challenge to the classical thinking, particularly the Say s Law. The saving function and consumption function are fundamental bases of the Keynesian theory of income determination and multiplier analysis. THE INVESTIMENT FUNCTION Like consumption, investment depends on many variables. For simplifying our analysis we assume that investment is given independently of the level of income. Thus, investment is a consultant I 0. the determinants of investment are examined in detail in Chapter 8. Since investment is assumed to be constant at the I 0 level the investment function is I = I 0 (I 0 >0)
where I 0 represent a given positive level of investment. Suppose I 0 equal s Rs. 8 crores. With investment on the vertical axis and income on the horizontal axis, the investment function is plotted as a straight line parallel to the horizontal axis. POINTS FOR QUICK REVISION 1. Keynes consumption function or the propensity to consume relates current consumption expenditure to current income. In the linear version, C = a + by, the constant a can be incorporated in the term for autonomous expenditure while the include component of consumption is by 2. APC is the ratio of the total consumption to total income. APS is the ratio of total saving to total income. 3. the concept of margin is important in economics. It measures the response of one variable to a small change in another variable. MPS is the ratio of the change in saving to change in income. 4. Two important results of Keynes theory are APC + APS = 1 MPC + MPS = 1 5. Major determinants of consumption function or the propensity to consume, other than income, are the distribution of income, availability of consumer credit, the existing stock of consumer durables, wealth and liquid assets. 6. Major determinants of saving function or the propensity to save, other than income, are the interest rate, price level and distribution of income. 7. Like consumption, investment depends on many variables. But here we confine our study to autonomous investment. It is assumed to be fixed for all levels of income.
POINTS TO PONDER: Saving function Saving function tells us the relationship between income and savings The saving function may be derived with the aid of the consumption function. Determinants Propensity to Save Following are the main determinants of saving function: Saving and Income Saving and Taxation Policy Saving and Social Insurance and Life Insurance Saving and the Price Level Average propensity to save Average Propensity to Save is the ratio of total saving to total income.
Marginal propensity to save Marginal Propensity to Save is the ratio of the change in saving to change in income. Results of Keynes theory Two important results of Keynes theory are APC + APS = 1 MPC + MPS = 1 FOR REFERENCE 1. J. Liudaure : Macro Economics, Ch.3 2. Norman F. Keiser : Macro Economics, Ch.4,6, and 7. 3. Gardner Ackley : Macro Economics Theory, Ch.10-12. 4. F. S. Brooman : Macro Economics, Ch.5 5. Edward Shapiro : Macro Economics, Ch.8 and 10.
QUESTIONS FOR SELF ASSESSMENT 1. State and explain Keynes Psychological Law of Consumption. 2. What are the MPC and the APC and how do they differ? 3. Compare linear and non-linear Consumption functions. 4. Explain the determinants of propensity to consume and propensity to save. 5. Given the following consumption functions C 1 = Rs. 10 crores + 0.6 Y C 2 = 0.6Y Derive the corresponding saving functions and compute the value of saving when Y+Rs. 800 crores. 6. Complete the Table assuming the following consumption function C = Rs. 100 croes + 0.6Y Income (in crores Rs.) 200 500 800 Consumption (in crores Rs.) Table MPC 7. What do you mean by consumption function? What are the factor on which depends? 8. Write a short note on : 9. (i) Mareginal and average Propensity to Consume (ii) Marginal and Average Propensity to save