Income Determination
 By Keynesian Model: The most important measurement of economic activity is GDP in the closed economy. GDP = C+I+G In the classical model the level of economic activity is measured. AD = AS In the simple Keynesian model the short run is the period of two or three years, where the price is stable and no of inflation, so all variables are real variable. We assumed that for simplicity, AD = Y + C+I Where G=o, NX=O (Here is no role of govt is foreign trade). So here is only the private sector. The consumption behavior is influenced by the household sectors, however the income level is a most important determinant. Consumption Function: Many different factors, including taste and preference income is interest rate determine the consumption for example, if the income of one household is greater than the income of another the farmer in likely to consume more. C = F(Y) Keynes postulated that consumption is increasing function consumption is assumed to be increasing as income increases, it means that income and consumption are correlated positively, but Keynes didn’t specify the mathematical function. Consumption function is a linear function. The shape of consumption function is, C = a+bY C = Consumption. A = Consumption intercept. B = Slope of the consumption function. Y = income. Where “c” is the dependent variables and “Y” is explanatory variable. Consumption depends on income because when the Y = o then c = a. In this function “a” is positive and “b” lies o S = -a + y – by. As we have consumption function. C = a + by. Putting the values of C in the equation (1) Y = a + by + S => S = Y – by – a => S = -a + (1-b) y -A = this saving, when the income level is zero. (1-b) = MPs. Which is defined as a change MPs = or (1-b) is also called the slope of the saving function. Saving function plotted above. Saving is increasing function in other words saving increasing as income increases. Prepared by : Zia Ur Rahman Marwat(goldmadlist) M.Phill Student Gomal University D.I.Khan Investment & Equilibrium Level of Income (Investment Multiplier) According to keynes model, AD = AS Income is equal to spend (AD) at a particular level of income, not at all levels of income, this implies that income & spending are functionally related not identically. It is the aggregate demand of Keynesian analysis that represent the major point of departure from the classical point of view by stating that income & spending are equal at a every point , keynes denied the validity of the of the, say’s law, the say’s law stated. AD = AS They are identically equal to each other not functionally related. (Total income = money volume of output) This means that all output will purchase regardless level of the income. AD = AS It is the classical view that there is no unemployment, it means that they are equal at all points and firm are able to sell their entire output. Keynes offered the innovation that, AD = AS It is an equal at particular points. But in 1930 there was a great depression unemployment the classical view failed at this position. Keynes offered decision of two types (i) Spending decision (ii) output decision. They are made by different economic units and different motive. If AD = AS, then why there was unemployment? It is not necessary that they will always equal motives. In 1930 the 25% labor force was unemployed. The Govt start a new program for the solution of the problem and this called “New deal”. Its means that Govt must stepping towards the economy. ↑AD ↑C + I + G↑ When the increase in govt expenditure then the consumption and AD also increase, this is the multiplier effect. Multiplier: With the change in investment we find that a change in the income occurs. A relationship between ‘ can be obtained this relationship is called investment multiplier. Yo = C + Io Where Io = Io is a exogenous its means that it is independent of the level of the income. How the change in AD? In the short run the consumption function is more or less stable, now we have left only investment. How ? This investment is made by the private sector / Public sector. Yo – bYo = a + Io Yo – (1-b)o = a + Io Yo = a + bYo + Io Yo – (1-b)o = a + Io Yo = Yo = + ------- (2) Y1 = C + I1 = a bY1 + I1 Y1 – (1-b)o = a + I1 Y1 = . Y1 = + ----------- (3) Subtract equation (2) from equation (3) Y1 – Yo = + - Y1 – Yo = - => Y = Where K = = = . k is the reciprocal to MPs. K = = 4 = K = 4 If ↑I by $1 ↑Y by $4 = K investment multipier Investment Functions: Investment depends on numbers of factors including interest rates. We assume for the time being income deter mention that investment is exogenous variable, a variable whose value is determined outside the model. Thus I is exogenous it means I doesn’t depend on income. It is dependent the level of income. Change in investment will certainly lead to changes in income, but the change in income will not leads to change in investment. Because investment is exogenous, we can write. I = I0 , (investment is constant). Since the investment function is I = Io (Io > 0). Where II represents real investment and Io represent a given positive level of investment. Suppose Io equal $50 billion, with investment on vertical axis and income on the Horizontal axis the investment function is plotted as the horizontal line in diagram, indicating the investment doesn’t change with level of income. Restating the model the investment and consumption function are, These equations are behavioral equations, because the purport to explain the behavior consumption’s and investments. To complete the model, we specify a equilibrium condition, that is a condition necessary for a particular level of income to be an equal level. The equilibrium condition may be specific as, AD = AS Thus for income or output to be an equilibrium level, as must equal AD. The equilibrium condition may specified as I = S. Thus for income to be an equilibrium level aggregate demand approach supply and aggregate demand approach. The equilibrium condition may also be specified as, I = S This income to be an equilibrium level investment must equal saving. This approach is investment saving approach. Equilibrium Income Aggregate Supply, Aggregate Demand Approach: With the help of aggregate Supply, aggregate demand approach we can demand the equilibrium level of income. Aggregate supply = nation’s output of goods and services Aggregate demand = Society’s demand for those goods and services which are supplied by the suppliers. The essence of aggregate supply – aggregate demand, approach is that, the nation’s output of goods and services must equal to the demand for those goods and services for income to be at its equilibrium level. If the nation’s output equals the demand for those goods and services firm will be able to sell their entire output. Consequently, no incentive exists for them to alter their production and income remains at equilibrium level. If the nation’s output exceeds the demand for goods and services, firm are unable to sell their entire output and experience a blind up in their inventories. An incentive exists for the firms reduce the production. As a result, output falls until it equals the demand for goods and services. Similarly if the nation’s output is less than the demand for goods and services, firms sell more than they are producing experience a depletion ( ) of their inventories. An incentive exists, therefore for them to increase the production. As a result, output rise unites its equals the demand for goods and services. According to this diagram the aggregate supply is depicted by line with the same scale. On both axis 45o means any point lies on 45o line is equidance from both axis with the same scale on both axis output on vertical axis equals output on horizontal axis for a point on 45o line. But this is unrealistic assuming. The 45o line is not an aggregate supply curve because it indicates that any amount form “O” to may be produced, but this is not possible production is limited by an economy. Nevertheless, in the development of the model it is to think of the 45o line as an aggregate supply curve. Aggregate demand represents society’s demand for goods and services with govt and foreign trade sectors. It consists of the demand for the consumer and services and the demand for investment goods. The consumption function represents the demand for consumer goods and services. Since it shows the level of consumption for each level of income. Similarly investment function represent the demand for investment goods together the two function represent the aggregate demand for goods and services. Consequently aggregate demand is equal to “c” which by substitution equals. a + by + Io Graphically the aggregate demand is vertical summation of “c” and “Y” lines or to put it differently it is the c + constant Io The “c + Io” line is depicted in the figure with the 45o line representing AS and the “c+I” line representing AD the equal level of income “Yo”. Income level “Yo”must be equilibrium level since it the only for which AS = AD. At income level > “Yo” AS (representing by 45o line) is > then AD (representing by c+I) and income has a tendency to fall. At income level less then “Yo” AS is less then AD and income has a tendency to rise. Equilibrium Income The income _Saving Approach: We can use investment saving approach to determine equilibrium level of income. Y = C +S S = Y – C Y = C + I I = Y - C The former implies that saving is the difference between income and consumption the latte implies that investment is the difference between income and consumption. Since both investment and spending equal to difference between income and consumption by definition investment equals saving by definition. How I = S can serve an equilibrium condition for a level of income to be an equilibrium level when the condition holds at every level of income? We can distinguish between realized investment and intended investment. Realized Investment: Realized investment equals saving at every level of income. Intended Investment: Intended investment equals saving at only on the equilibrium level of income consequent for I=S to be an equilibrium condition investment must be interpreted as intended investment. Intended or ex-anti investment is the amount of investment which firms intended or planned to investment. Its magnitude is indicated by the investment function I=Io Unintended Investment: Unintended investment is the change in business inventories due to a discrepancy between AS and AD. If AS exceeds AD the due to increased production business inventories increase. The increase in inventories is treated as an investment in the national income accounts. Geometrically unintended investment is represented by the vertical distance between the 45o line (AS) and the C+I line (AD). Realized or Exposit Investment: It is the sum of intended and unintended investment. The relationship between AS and AD investment saving approach is illustrated in the diagram.According to this diagram, we can illustrate the relationship between AS and AD and also investment saving approach can be illustrated. If intended investment equals saving aggregate supply and AD are equal and income is at its equilibrium level. If saving exceeds intended investment, however AS exceeds AD and income is at an equilibrium level with AS greater the AD investment accumulated and the income tends to falls. Similarly, if intended investment exceeds saving AD exceeds AS with AD greater then AS investment are depleted and income tend to rise. Thus, when saving exceeds intending investment income tends to fall and when intend investment exceeds saving income tends to rise. Under these circumstance incomes will eventually gravitate to the equilibrium level were intended investment equal saving. Govt Purchase Multiplier: An increase in govt purchase increases income whereas tax increase the opposite effect. To estimate the change in income resulting from the change in one of these variable we can drive multiplier for them to derive the govt purchase multiplier we use the following procedure. In three sector economy, AD = C + I + G. Govt sector is also very important in LDCS govt play a very important role through its various policies notable fiscal policy. The govt represented the govt spending and govt taxes. Govt spends a numbers of ways. (1) Transfer payment. (2) Purchase of goods and services (this is an expenditure side of the govt) Taxes are concerned with resource or revenue generation. Taxes take numbers of types but we talk about net taxes. Net taxes = govt expenditure – govt taxes. This is Keynesian aggregate demand analysis. In Keynesian system govt and public policy does matter.The Govt policy effect the aggregate demand (AD) in keynes system. Govt purchases Multiplier: There are two conditions, 1) Taxes are exogenous Now consumption will take the form. C = a+byd Yd = disposable income = Y-T Its means actual income – taxes. G = Go , I = Io , T = To All these three are exogenous variable. Exogenesis: They are exogenesis of the level of the income. As income change will no change the any macroeconomic variables Now we derive when taxes are exogenesis. Y = C+I+G Where C = a+by d Y = a+byd +Io+Go Yd = (y-To) Y = A+b(Y-To) + Io+Go  a+by – bTo +Io+Go Y-by = a-bTo+Io+Go  y(1-b) = a-bTo+Io+Go Y = (1) Yo is initial equilibrium level of income, G is govt spending. In Keynesian model all variables are real there is price stability and no inflation. Suppose Govt increase spending about the fiscal policy what influence on the economy. Now level of income. Y1 = (2) Now subtract the equation (2) from (1). Y1-Yo = ( ) – ( ) Y1-Yo = = dy = = Kg . dG Kg = govt purchases multiplier when taxes are exogenesis. Kg = 4 If the increase in Kg 4 and the govt expenditure with $20. dy = 4 x $20bin = $80bin Increase in govt expenditure will lead to higher increase in -----------------------------------. There is no crowding out. According to keynes that there is a partial crowding when govt spend. Case 2: When the taxes are endogenous. Endogenous: Endogenous are the dependent variables on the level of income. If will lead to (change in any macro variable) In case of Endogenous: Y = AD = C+I+G C = a+byd Yd = Y – T T = Ty I = Io G = Go Again equip condition. Ad = AS Y = a+b(y-T) +Io+Go At initial equip. Yo = a+b(Yo-TYo) + Io+Go (1) Y1 = a+b(Y1-ty1) + Io+Go (2) Subtract equation (2) from (1) Y1-Yo = b(1-t) + [1-b (1-t)] = = Kg = ---------------- endogenous (taxes) Kg = ------------------------ endogenous (taxes) Taxes Multiplier: Case no1: Taxes are exogenous. Y = C+I+G C = a+byd Y = y-t C = a+b(y-t) G = Go I = Io Y = a+b(Y-t)+Io+Go Yo = a+b(Yo-to)+Io+Go When T = to (taxes are exogenous) Y1=a+b(Y1-T1)+Io+Go Subtract equation (3) from (2) Y1-Yo = a +b(y-t1) + Io+Go-a-b(yo-to) – Io - Go = b(y1-t1) – b(yo-to) = by1 – bt1 – byo + bto = b(y1-yo) – b(T1-To) Y1-Yo-b(y1-yo) = -b - b( = -b Y (1-b) = -b Y = (Exogeneous) = = MPs Taxes Multiplier (Endogenous) When taxes are endogenous Y = C+I+G (1) Where C = a+byd Yd = y-T T = To-Ty C = a+b(y-To-Ty)  a+by-bTo-bty I = Io , G = Go a-bTo +b(1-t) y (2) Y = a-bTo+b(1-t)y+Io+Go (3) For initial equilibrium Yo = a-bTo+b(1-t)Yo+Io+Go (4) Y1 = a-bT1+b(1-t)Y1+Io+Go (5) Subtract equation (5) from (4) Y1-Yo = a-bT1+b(1-t)Y1 +Io+Go-a+bTo+btyo-I-Go = -bT1+bTo+b(1-b)Y1-b(1-t)Yo = -b(T1-To) +b(1-t) (Y1-Yo) Y1-Yo-b(1-t)(Y1-Yo) = -b Y –b(1-t)(Y1-Yo) = -b = Balance Budget Multiplier Govt Purchase multiplier Taxes multiplier (exogenous) = = kT . = kg . (1) Since (some amount of govt spending and taxes) kg. kT . (kg+kT) Putting the values of KT and kg = kT = = [ + ] [ ] 1 . = 1