DETERMINATION OF EQUILIBRIUM INCOME

                         

             DETERMINATION OF EQUILIBRIUM INCOME:                                        THREE  SECTOR MODEL

  Aggregate demand in the three sector model of closed economy (neglecting  foreign trade) consists of three  components namely, household consumption(C), desired business investment demand(I) and the government sector’s demand for goods and services(G). Thus in equilibrium, we have

Since there is no foreign sector, GDP and national income are equal. As prices are

                                           Y = C+ I + G                     (2.13)

   assumed to be fixed, all variables are real variables and all changes are in real terms. To help interpret these        

   conditions, we turn to the flowchart below. Each of the variables in the model is a flow variable

Circular Flow in a Three Sector Economy

  The functioning of the two sectors namely household and the business sector has been discussed by us in the    two sector model. The three-sector, three-market circular flow model which accounts for government intervention highlights the role played by the government sector. From the above flow chart, we can find that the government sector adds the following key flows to the model:

         i.   Taxes on households and business sector to fund government purchases

       ii.   Transfer payments to household sector and subsidy payments to the business sector

     iii.   Government purchases goods and services from business sector and factors of production from household sector, and

     iv.   Government borrowing in financial markets to finance the deficits occurring when taxes fall short of government purchases.

However, unlike in the two sector model, the whole of national income does not return directly to the firms as demand for output. There are two flows out of the household sector in addition to consumption expenditure namely, saving flow and the flow of tax payments to the government. These are actually  leakages. The saving leakage flows into financial markets, which means that the part of that is saved is held in the form of some financial asset (currency, bank deposits, bonds, equities, etc.). The tax flow goes to to the government sector. The leakages which occur in household sector do not necessarily mean that the total demand must fall short of output. There are additional demands for output on the part of the  business sector itself for investment and from the government sector. In terms of  the circular flow, these are injections. The investment injection is shown as a flow from financial markets to the business sector. The purchasers of the investment goods, typically financed by borrowing, are actually the firms in the business sector themselves. Thus, the amount of investment in terms of money represents an equivalent flow of funds lent to the business sector.

The three-sector Keynesian model is commonly constructed assuming that government purchases are autonomous. This is not a realistic assumption, but it   will simplify our analysis. Determination of income can be explained with the help   of figure 1.2.7

  Determination of Equilibrium Income: Three Sector Model

 The variables measured on the vertical axis are C, I and G. The autonomous expenditure components namely, investment and government spending do not directly depend on income and are exogenous variables determined by factors outside the model. You may observe that in panel B of the figure 1.2.7,  the lines  that plot these autonomous expenditure components are horizontal as their level does not depend on Y. Therefore, C + I + G schedule lies above the consumption function by a constant amount.

The line S + T in the graph plots the value of savings plus taxes. This schedule   slopes upwards because saving varies positively with income. Just as government spending, level of tax receipts (T) is decided by policy makers.

The equilibrium level of income is shown at the point E 1 where the (C + l + G) schedule crosses the 45° line, and aggregate demand is therefore equal to income (Y). In equilibrium, it is also true that the (S + T) schedule intersects the (I + G) horizontal schedule.

We shall now see why other points on the graph are not points of equilibrium. Consider a level of income below Y. We find that it generates consumption as  shown along the consumption function. When this level of consumption  is added  to the autonomous expenditures (I + G), aggregate demand exceeds income; the    (C + I + G) schedule is above the 45° line. Equivalently at this point I + G is greater than S + T, as can be seen in panel B of the figure 1.2.7. With demand outstripping production, desired investments will exceed actual investment and there will be an unintended inventory shortfall and therefore a tendency for output to rise. Conversely, at levels of income above Y1, output will exceed  demand; people are  not willing to buy all that is produced. Excess inventories will accumulate, leading businesses to reduce their future production. Employment  will  subsequently decline. Output will fall back to the equilibrium level. It is only at Y that output is equal to aggregate demand; there is no unintended inventory shortfall or accumulation and, consequently, no tendency for output to change. An important thing to note is that the change in total spending, followed by changes in output and employment, is what will restore equilibrium in the Keynesian model, not changes in prices.

DETERMINATION OF EQUILIBRIUM INCOME:    FOUR SECTOR MODEL

The four sector model includes all four macroeconomic sectors, the household sector, the business sector, the government sector, and the foreign sector. The foreign sector includes households, businesses, and governments that reside in other countries. The following flowchart shows the circular flow in a four sector economy Figure 1.2.8

Circular Flow in a Four Sector Economy

In the four sector model, there are three additional flows namely: exports, imports and net capital inflow which is the difference between capital outflow and capital inflow. The C+I+G+(X-M) line indicates the total planned expenditures of

consumers, investors, governments, and foreigners (net exports) at each income level. In equilibrium, we have

                          Y =  C + I + G + (X – M)             (2.14)

                     

The domestic economy trades goods with the foreign sector through exports and imports. Exports are the injections in the national income, while imports act as leakages or outflows of national income. Exports represent foreign demand for domestic output and therefore, are part of aggregate demand. Since imports are  not demands for domestic goods, we must subtract them from aggregate demand. The demand for imports has an autonomous component and is assumed to depend on income. Imports depend upon marginal propensity to import which is the increase in import demand per unit increase in GDP. The demand for exports depends on foreign income and is therefore exogenously determined. Imports are subtracted from exports to derive net exports, which is the foreign sector's contribution to aggregate expenditures. With the help of figure 1.2.9, we shall explain income determination in the four sector model.

Figure 1.2.9

Determination of Equilibrium Income: Four Sector

 

Equilibrium is identified as the intersection between the C + I + G + (X - M)  line  and the 45-degree line. The equilibrium income is Y. From panel B, we find that the leakages(S+T+M) are equal to injections (I+G+X) only at equilibrium level of income.

We have seen above that only net exports(X-M) are incorporated into the  four sector model of income determination. We know that injections increase the level  of income and leakages decrease it. Therefore, if net exports are positive (X > M), there is net injection and national income  increases. Conversely,  if X<M, there is  net withdrawal and national income decreases. The figure 1.2.10 depicts a case of X<M.

We find that when the foreign sector is included in the model (assuming M  > X),  the aggregate demand schedule C+I+G shifts downward with equilibrium point shifting from F to E. The inclusion of foreign sector (with M > X) causes a reduction in national income from Y0 to Y1. Nevertheless, when X > M, the aggregate demand schedule C+I+G shifts upward causing an increase in national income. Learners may infer diagrammatic expressions for possible changes in equilibrium income for X>M and X = M.

Figure 1.2.10

Effects on Income When Imports are

  We have seen in section 2.5 above that equilibrium income is expressed as  a product of two terms: ∆ Y = k ∆I; i.e the level of autonomous investment expenditure and the investment multiplier. The autonomous expenditure multiplier in a four model  includes  the  effects  of foreign transactions and  is stated as and ¹(1−𝑏𝑏+𝑣𝑣)                                                

                       where v is the propensity to import which is greater

 than zero. You may recall that the multiplier in a closed economy is (1−𝑏𝑏)

The greater the value of v, the lower will be the autonomous expenditure multiplier. The more open an economy is to foreign trade, (the higher v is) the smaller will be the response of income to aggregate demand shocks, such as changes in government spending or autonomous changes in investment demand. A change in autonomous expenditures— for example, a change in investment spending,—will have a direct effect on income and an induced effect on consumption with a further effect on income. The higher the value of v, larger the proportion of this induced effect on demand for foreign, not domestic, consumer goods. Consequently, the induced effect on demand for domestic goods and, hence on domestic income will be smaller. The increase in imports per unit of income constitutes an additional leakage from the circular flow of (domestic) income at each round of the multiplier process and reduces the value of the autonomous expenditure multiplier.

An increase in demand for exports of a country is an increase in aggregate demand for domestically produced output and will increase equilibrium income just as an increase in government spending or an autonomous increase in investment. In summary, an increase in the demand for a country’s exports has an expansionary effect on equilibrium income, whereas an autonomous increase in imports has a contractionary effect on equilibrium income. However, this should not be interpreted to mean that exports are good and imports harmful in their economic effects. Countries import goods that can be more efficiently produced abroad, and trade increases the overall efficiency of the worldwide allocation of resources. This forms the rationale for attempts to stimulate the domestic economy by promoting exports and restricting imports.

CONCLUSION

According to the Keynesian theory of income and employment, national income depends upon the aggregate effective demand. If the aggregate effective demand falls short of that output at which all those who are both able and willing to work  are employed, it will result in unemployment in the economy. Consequently, there will be a gap between the economy's actual and optimum potential output. On the contrary, if the aggregate effective demand exceeds the economy's full  employment output (production capacity), it will result in inflation. Nominal output will increase, but it simply reflects  higher  prices, rather than additional real output. It is not necessary that the equilibrium aggregate output will also be the full employment aggregate output. It is undesirable and a cause of great concern for  the society and government if large number of people remains unemployed. In the absence of government policies to stabilize the economy, incomes will be unstable because of the instability of investment.

 By making appropriate changes in government spending (G) and taxes, the government can counteract the effects of shifts in investment. Appropriate changes in fiscal policy by adjusting  in  government expenditure and taxes could keep the autonomous expenditure constant even in the face of undesirable changes in the investment.