consumption functions and theory

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economic consumption function and its theory





CONTENTS1.0 Consumption function and theory1.1 Keynesian Consumption function1.2 Relative Income hypothesis (RIH)1.3 Permanent Income hypothesis (PIH)1.4 Life Cycle hypothesis (LCH)1.5 Absolute Income hypothesis (AIH)2.0 Theory of Capital and Investment2.1 Meaning and types of Investment2.2 Marginal efficiency of capital2.3 The Present Value Concept2.4 The Interest rate2.5 Other factors that affect inducement to invest outside rate of interest.


1.1 KEYNESIAN CONSUMPTION FUNCTION:John Maynard Keynes (1936) was the first to evolve the concept of consumption function. According to him consumption function or propensity to consume refers to income consumption relationships. It is a functional relationship between two aggregates i.e total consumption and gross national income.Consumption demand depends on income and propensity to consume. Propensity to consume depends on various factors such as price level, interest rate, stock of wealth etc. constant in his theory of consumption. Thus with these factors being assumed constant in the short run, Keynesian consumption function considers consumption as a function of income. Thus we can represent the symbolical as C = F(Y)When C is consumption Y is income and F denotes functional relationship.Graphically we can represent this consumption function below:consumption


Fig 1.0C2



Figure 1 above shows a consumption function-denotary that consumption as a function of disposable income. Here consumption is a linear function based on the assumption that consumption changes by the same amount all through. The 45 line may be regarded as a zero saving line and shape and position of the C curve indicate the division of income between consumption and saving. It is important to note that the theory of consumption discussed here as propounded by J.M Keynes, according to him the main determinant of aggregate consumption expenditure is then aggregate level of income. This is often referred to as Absolute income Hypothesis. In a specific form, Keynesian function can be written asC = a + byWhere a and b are constant. While a is intercept term of the consumption otherwise known as Autonomous Consumption (Consumption of Zero level or no level of income), b stands for the slope of the consumption function and therefore represents marginal propensity to consume.We can illustrate the above expression graphically:Fig 2.0As = YC

C = a +by, = AEY > C

AS = Aggregation supplyAE = Aggregation expenditureEC


C >Y



From the diagram above the region denoted by a indicates autonomous consumption which is consumption at no level of income thus at this point such an economy is dissaving. When income is Zero output and hence aggregate expenditure is Zero. The higher the level of income the greater the national output and hence the greater the aggregate expenditure. All these stated above is represented by the 45 line. The point labelled E is the equilibrium level of income where AS = AEThere are some technical attributes of the consumption function there include:1. The Average Propensity to Consume:The Average propensity to consume may be defined as the ratio of consumption expenditure to any particular level of income. Algebraically, it is expressed as APC = C/Y Where APC = Average Propensity to Consume C = ConsumptionY = IncomeThe APC declines as income increases because the proportion of income spent on consumption decreases. Diagrammatically, the average propensity to consume is any one part the consumption curve as shown in the figure below.Consumption

Fig 3.0



Point E on the consumption curve above measure the Average propensity to consume. It pertinent to note that the APC declines as curve flattens to the right.2. The Marginal Propensity to Consume:The Marginal propensity to consume refers to the fraction of additional disposable income that is consumed. The concept is central to Keynesian economic analysis. The concept owes it origin to Keynes assertion that men are disposed as a rule and the average, to increase their consumption as their increases, but not by as much as the psychological law of consumption propounded by Keynes: according to which, as income increases consumption increases in income. Hence marginal propensity to consume is less than one.Summary we can say that the MPC is the ratio of the change in consumption to the change in income. It is expressed as MPC = C/ YRecall that marginal propensity to consume is less than one: thus1 > C/ Y > 0N:BThe MPC is constant at all level of income this is illustrated in the table below:INCOME YCONSUMPTION(C)APCC/YMPC C/ Y





Note: when income increases, the MPC falls but more than APC. On the other hand, When income falls, the MPC rises and the APC also rises but APC rises at a slower rate than MPC. This is possible during the cyclical fluctuations whereas in the short run there is no change in the MPC and MPC is less than APC. ( MPC < APC ). MPC is for short run analysis APC is for long run analysis

According to Keynes, there are two factors that determine and influence the consumption function. They can be classified as either objective or subjective factors. The subjective factors are Endogenous (internal) to the economic system they include Psychological characteristics of human natures, social practices and institutions and social arrangements.The objective factors on the other hand are exogenous: external to the economy itself. They may therefore undergo rapid changes and may cause marked shifts in the consumption function: they include: the level of income, income distribution, price level, availability of credit, fiscal policy etc.1.2 RELATIVE INCOME HYPOTHESIS (RIH): in 1949 An American economist James .S. Duesenberry put forward the theory of consumer behaviour which lay stress on relative income of an individual rather than his absolute income as a determinant of his consumption. According to Duesenberry, the consumption of a person does not depend on his current income level. This theory was based on ideals that were not considered in earlier economic analysis. These are1. That consumption behaviour of individual was influence by consumption behaviour of other individuals and2. That the consumption behaviour of individuals exhibits a ratchet effect deriving from the fact that consumption behaviour tends to be habitual: the habitual nature connecting that people try to maintain the standard of living they have become used to, the fact that they may have experienced a decline in income notwithstanding.Duesenberry posited that an individuals consumption and saving decision are influence by his social environment. Thus, given a level of income, an individuals is likely to consume more of that income if he lives in environment dominated by the well-to-do in society than if he lives in less affluent neighbourhood. Moreover efforts by the individual to maintain a certain economic status in his neighbourhood means that he spend more out of his income to maintain that status. Thus, his consumption, rather than being related to his absolute income level would be related to his relative income within his neighbourhood. This makes for a constant average propensity to consume given a relatively constant income distribution. Hence it makes for a proportional relationship between aggregate consumption and aggregate disposable income.Demonstration Effect: By emphasising relative income as a determinant of consumption, the relative income hypothesis suggests that individuals or households try to imitate or copy the consumption levels of their neighbours or other families in a particular community. This is called demonstration effect or Duesenberry effect. Two things fellows from this, First, the average propensity to consume does not fall. This is because of incomes of all families increase in the same proportion, distribution of relative income would remain unchanged and therefore the proportion of consumption expenditure to income which depends on relative income will remain constant.Secondly, a family with a given income would devote more of his income to consumption if it is living in a community in which that income is regarded as relatively low because of the working of demonstration effect. On the other hand, a family will spend a lower proportion of its income if it is living in a community in which that income is considered as relatively high because of demonstration effect will not be present in the case. For example, family with a given income say N500,000 per month spend a larger proportion of their income on consumption if they live in urban areas. The higher proportion to consume of families living in urban areas is due to the working of demonstration effect where families with relatively higher income reside whose higher consumption standards tempt others in lower income brackets to consume more.Duesenberry explains the social character of consumption pattern to mean the tendency in human beings not only to keep up with the Jenses but also to surpass the Jenses.Ratchet effect: in this regard, Duesenberry argued that people having become used to standard of living find it difficult to lower some even in the face of declining income. The second part of Duesenberry theory in the past part peak of income hypothesis while explains the short-run fluctuation in the consumption function and refutes the Keynesian assumption that consumption function relative are reversible. Here, once people reach a particular peak income level and become accustomed to this standard of living. They are not prepared to reduce their consumption pattern during a recession. Duesenberrys hypothesis are combined together into this formCt / Yt = a - b Yt/Yo

Where C and Y are consumption and income respectively.(t) Refers to current period(o) Refers to the previous peak(a) Is a constant relating to the positive autonomous consumption at#(b) Is the consumption function.In the above equation, the consumption function ratio in the current period ( Ct/Yt ) is regarded a function of ( Yt/Yo ) or the ratio of current income to the previous peak in income.GRAPHICAL ILLUSTRATION.The graph below illustrates Duesenberrys explanation of proportional / non-proportional relationship of consumption and disposable income.











The line LRCF is the long run consumption function, passing through the origin and therefore without an intercept guarantees the equality of MPC and APC. But the SRCFs are down to reflect the short run cyclical fluctuations which account for the drifts in the short run consumption functions. Thus given an while level of income Y0 consumption will initially be on the LRCF at point Y. This coincides with point Co on the vertical axis. A rise in income to Y1 will make an increase in consumption. But the movement will be along the short-run consumption function to point b. if the increase in income for Y0 to Y1 is persistent, the ratchet effect will hold and consumption will move up to point Z along the LRCF. This means an increase in consumption from C1 to C2 on the vertical axis. However, if consumers were to experience a decline in income to Y2, consumption would rather decline along the LRCF to point e fall along the SRCF, to point C. this is because consumption is still influence by his previous peak. The RIH suggest the following behavioural relationship between the APC and MPC depending on the direction of the change in income.a) If income is growing at a constant rate, APC would be constant with MPC equalling APC.b) If current income falls below a previous income level, the APC would be greater than the MPC.c) If income is rising but lags behind a previous income level the APC would be declining while the MPC would be rising but would nevertheless be less than the APC.d) If income is rising and it is above a previous level, the APC would be constant but would ensure the equality between MPC and APC.DEFECTS OF THE RIH A major defect of the RIH was its emphasis on the habitual behaviour and the demonstration effect arguments as the factors underlying consumption with the utility maximization assumption of the consumer as well as the rational behavioural assumption of consumers.1.3.THE PERMANENT INCOME HYPOTHESIS. (PIH)The permanent income hypothesis is found in Milton Friedmans famous study titled A theory of the consumption function published in 1957. According to Friedmans, permanent income is the amount a consumer unit could consume (or believes that it could) while maintaining wealth intact. While permanent consumption is the value of the services that it is planned to consume during the period in question.The permanent income hypothesis states that the ratio of the permanent consumption to permanent income is constant regardless of the level of permanent income.To friedman, the average propensities to consume may depend upon such factors as the ratio of interest, the ratio of non-human wealth to permanent income, the ages of members and the number of members in the consumers unit, the extent of income variability, etc. Notwithstanding the influence which these factors may exert on the individual consumer units consumption, the value of the consumption-income ratio is independent of the level of permanent income. The permanent income hypothesis can be set forth in terms of the following equations.CP=( i, w, u ) YpY=Yp+YiC= Cp+Yib ( Yp, YT ) = Ob ( Cp, CT ) = Ob ( YT, CT ) = O Where:Y = measured or observed disposable incomeC = measured or observed consumptionYp= permanent incomeYT= transitory incomeCP= permanent consumptionCT= transitory consumptionK = proportionality constant between permanent consumption and permanent incomeI = rate of interestW = ratio of non-human wealth to permanent incomeU = propensity of the consumer unit to add to consumption rather than to wealth. The most important factors which determine the value of U are the number ages of family members in the consumer unit and consumption i.e the extent of income variability and b = the correlation coefficient term.

Given the above assertion, Friedman gives a series assumptions concerning the relationships between permanent of transitory component of income and consumption.1. There is no correlation between transitory and permanent incomes2. There is no correlation between permanent and transitory consumption.3. There is no correlation between transitory consumption and transitory income.4. Only difference in permanent income affects consumption systematically.

DEFECTS OF PIH A major defect of the PIH is the elusive nature of the key variables in the hypothesis. These variables are permanent income and consumption. Being elusive these key concepts are difficult to isolate and utilize for statistical testing of the hypothesis. Past experiences and expectations determine a households permanent income. Yet experience and expectations changes overtime, such changes equally bringing about changes in permanent income. This it is difficult to obtain a measure of permanent income. It is needed this, the unobservability of the permanent income variable that stands put as the sore thumb in the PIH.

1.4LIFE CYCLE HYPOTHESIS LCH:The life cycle hypothesis was formulated by Ando and Modigliani. According to this theory, consumption is a function of lifetime expected income of the consumer. The consumption of the individual consumer depends on the resources available to him, the rate of return on capital, the spending plan, and the age at which the plan is made. The LCH posits that individuals wish to spread lifetime income such that they would enjoy a pattern of consumption that is optimal over their lifetime. This behaviour is consistent with the behaviour of individual income over their life cycle which in the early years is usually low and largely obtainable from labour services in the later years. Labour income is usually higher with this higher labour income being augmented by some return on wealth. However, labour income drops to zero on retirement and any consumption after retirement will be financed from accumulated wealth. To Modigliani and Ando, age is a crucial variable in determining the relationship of consumption and wealth over their life time, individuals experiences low income in the initial earning years, rising income in the middle of his career and again low at retirement.Ando and Modigliani specification of the LCH took the following mathematical form:C1 = ao ylt a2 yet a3 w tWhere C1 is consumption in year t,Yt l= is labour income at time t,Yte= is expected labour income at time t,Wt= is wealth at time t.The coefficients are the respective marginal propensities.The graph below can be used to explain the life cycle hypothesis.

Graph of the life cycle Hypothesis.Y = income curve

C, Y




LifetimeRetirementT3T2Middle ageYoung0T1DissavingfYo

In the diagram above, the consumption level of the individual throughout his lifetime is somewhat or slightly increasing, as shown by the CC curve.The Yo Y Y1 curve shows the individual consumers income stream during his lifetime T. during the early period of his life, represented by T, he borrows C Yo B amount of money to keep his consumption level CB. Which is almost constant in the middle of the years of his life represented by T1 T2, he saves BSY amount to repay his dept and for the future. In the last years of his life represented by T2 T3 he dissaves S C1 Y1 amount.DEFECTS OF THE LCH:Like the PIH, the LCH cannot be subjected to rigors of empirical testing because of the unobservable nature of one of its key explanatory variables viz. the expected labour income in this regard; John Muellbaeur for example has argued that the inability to observed life cycle income has protected the hypothesis from serious testing and possibility of rejection.

1.5ABSOLUTE INCOME HYPOTHESISThe absolute income hypothesis was propounded by John Maynard Keynes and it states that when income increases, consumption also increases but by less than the increase in income and vice versa. This means that income consumption relationship is non-proportional. This hypothesis was tested by James Tobin and Arthur Smithies in separate studies and came to the conclusion that the short-run relationship between consumption and income is non-proportional, but the time series data show the long-run relationship to be proportional. Their explanation is based on the following factors.1. Consequent upon an increase in their accumulated wealth, households have tended to spend a larger fraction of their income on consumption causing an upload shift in the aggregate consumption function.2. A charge in age composition in favour of the old people in the population.3. The unit reduction of new consumer grods regarded as essentials by the typical household also causes an upward shift in the consumption function.The absolute income hypothesis can be expressed diagrammatically below: Y



Cons umptionB





In the fig above, Ci is the long-run consumption function which shows the proportional relationship between end income as we move along the long-run curve. For instant, the APC and the MPC are equal at point A and B on this curve. CS1 and CS2 are short-run consumption functions. However, due to the factors mentioned above, they tend to drift upward from point A to point B along the long-run consumption function CL.The great advantage of this hypothesis is that if lays tress on factors other than income which affect the consumers behaviour.However as pointed out by Shapiro more and more economists now feel that the basic consumption function is proportional, which amounts to a rejection of the major tenet of the absolute income hypothesis.

2.0 THEORY OF CAPITAL AND INVESTMENT.2.1 MEANING:Investment in ordinary usage refers to buying of shares, stocks, bonds and securities which already exist in the stock market. This is however financial investments it involves the transfer of existing assets and does not affect aggregate spending.When referring to Keynes assertion, investment means real investment which adds capital equipment. It includes building of roads, construction of dams, buildings etc. To Joan Robinson By investment is meant an addition to capital, such occurs when a new house is built or a new factory is built. Investment means making an addition to capital. Capital in the other hand refers to real assets like factories, plants, equipment and inventories of finished and semi-finished goods. In more precise term INVESTMENT is the production or acquisition of real capital assets during any period of time. Capital and investment are therefore related to each other through net investment. Due to depreciation and obsolescence, some capital stock to wear out. When this is deducted from gross investment, it forms net investment. If gross investment equals depreciation net investment is zero investment.

TYPES OF INVESTMEMTAfter Keynes two types of investment have been established,I. Induced investmentII. Autonomous investment1. Induced investmentThis is investment that is profit or income motivated. Factors like prices, wages and interest charges which affect profits, influence induced investment. Similarly demand also influences it.

The relationship between investment and income can be expressed functionally as; I = f(Y). it is income elastic: this means as income increases investment also increases. INDUCED INVESTMENT11

F.g 7.013




The diagram above shows induced investment, the vertical and horizontal axis measure investment and income respectively. At OY1 level of income, investment is O. when income rises to Oy3, investment also increases to I3 Y3. A drop in income level from OY3 to OY2 causes a drop in investment level from I3Y3 to I2 Y2. Induced investment may be further divided into i. Average propensity to invest and ii. Marginal propensity b invest.I. Average propensity to invest:This is the ratio of influence to income. It can be expressed symbolically as 1/Y, where 1 is investment and Y is income with reference to fig 7.0 above, average propensity to invest at OY3 income level for instant is I3 Y3/ OY3.

II. The marginal propensity to invest: This is the ratio of change in investment to the change in income, i.e 1/ Y of the figure 7.0 above is considered; Y

=13 a/Y2 Y31/

2. Autonomous investment; Autonomous investment is independent of the level of income and is thus income inelastic. Other factors known as exogenous factors such as innovations, inventions, growth of population, researches, etc influence this level of investment. It is however not influence by changes in the level of demand. Rather it influences demand. Diagrammatically it is shown belowFig 8.0




The diagram above explains the fact that investment is income inelastic. It is represented by a line parallel to the horizontally axis. It indicates that all level of income, investment remains constant. an upward shift of the investment curve to 1 indicates an increased steady flow of investment at a constant rate O12 at all levels of income for purposes of income determine, the autonomous investment curve is superimposed on the C curve in a 45o line diagram.

Determinant of investment:While making investment decisions certain factor are taken into consideration. These include: the cost of capital, the expected rate of return from it during its influence, and the market rate of interest. Keynes sums up these factors in his concept of marginal efficiency of capital (MEC).2.2 Marginal efficiency of capital:This is the highest rate of return expected from an additional unit of a capital asset over its cost. To Kurihara, it is the ratio between the prospective yield of additional capital-goods and their supply prices. The prospective yield in the aggregate net return from an asset during its life time, while the supply price is the cost of producing this asset. Keynes relates the prospective yield of a capital asset to its supply price ad defines the MEC an equal to the rate of discount which would make the present value of the series of annuities given by the returns expected from the capital asset during its life just equal to its supply price. Symbolically, this can be expressedSP = R1/(1=i) + R2/(1+i)2 +.. Rn/(1+i)nWhere; SP is the supply price or cost of the capital asset, R1, R2. And Rn are the prospective yields or the series of expected annual returns from the capital asset in the years 1, 2.. and n.i is the rate of discount which makes the capital asset exactly equal to the present value of the expected yield from it.Thus i is the MEC or the rate of discount which equates the two sides of the equation.2.3THE PRESENT VALUE CONCEPT:The net present value (NPV) method is one the discount cash flow (DCF) technique that explicitly take into account both the time value of money and also the total profitability over a projects life. Its underlying premise is that cash flow arising at diferrent periods differ in value and are comparable only when their equivalent present value is found. The method aims at investment proposal using any acceptable hurdle rate. The cost of capital is usually used as the appropriate discount rate. NPV is concerned with liquidity. The discount formula to calculate the future value of a future sum of money at the end of n time period is PV = FV ( 1/(1+i)n)PV = period valueFV = future valuei = interest rate or discount rate n = number of years The decision rule of the NPV method is given as i. For independent project;If NPV > 0 : Accept project, butIf NPV < 0 : Reject the project

2.4 THE INTEREST RATE:The interest rate play a major role in influencing investment decision rate is seen as the cost of borrowing.The argument is that since interest rate is the cost of borrowing, the higher the interest rate, the more costly it is to borrow, and as borrowing becomes more costly, businessmen are likely to reduce borrowing. It is assumed that borrowing makes funds available for investment. Therefore as borrowing reduces, due to the high interest rates, investment will fall. In a similar manner, the lower the interest rate the cheaper it is to borrow, and this will lead to more investment spending assuming that other factors are held constant.FACTORS OTHER THAN THE RATE OF INTEREST AFFECTING INDUCEMENT TO INVEST.There are number of factors other than the rate of interest which affect the inducement to interest. They are the following:1. Element of uncertainty:To Keynes, the MEC is more volatile than the rate of interest. This is because business expectations affect the prospective yield of capital assets. The yield of capital may change quickly and drastically in response to the general mood of the business community, rumors, technical developments etc. Due to uncertainty, investment projects usually have a short-pay-off period. Capital assets become obsolete earlier than their expected life due to rapid technological developments.2. Level of income:If the level of income rises in the economy through rise money wage rates and other factor prices, the demand for goods will rise which one in turn, raise the inducement to invest contrastically the inducement to invest will fall the lowering of income levels.3. Existing stock of capital goods:If the existing stock of capital goods is large, it would discourage potential investors from entering into the making of goods. Again, the induced investment will take place if there is excess or idle capacity in the existing stock of capital assets. In a situation the existing stock of machines is working to its full capacity, there would be an increase in the demand for goods manufactured.


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