Income and output determination in a two-sector model
Income Determination in a Two-Sector Economy
In the two-sector model of income and output determination, there are two main sectors of the economy: consumption and investment. The model states that consumption and investment are the main drivers of economic growth and that changes in these two components will affect the level of income and output in the economy.
Two sector economy is a hypothetical economy that does not exist in reality. But this provides a simple and very convenient starting point in understanding income and output determination.
Income determination in two sector economy can be explained with the help of two approaches.
AD-AS Approach
Saving and Investment Approaches
AD-AS Approach
The Aggregate Demand and Aggregate Supply approach views the economy as the sum total of demand and supply of goods and services. Aggregate Demand, also known as total expenditure, is the sum of all the demands for goods and services in an economy. It consists of four components, including consumption, investment, government sector, and foreign sector (net exports). On the other hand, Aggregate Supply, also known as total output, represents the total quantity of goods and services produced within a given period in an economy. Equilibrium is reached when the Aggregate Demand is equal to the Aggregate Supply.
AD = C + I
AD = a + bY + I
AS = Y
For equilibrium, aggregate demand must be equal to aggregate supply.
Now, AD = AS
a + bY + I = Y
a + I = Y ( 1 - b)
Y = a + I / (1 - b)
Saving and Investment Approaches ( Leakage-Injection Approach)
The Leakage-Injection approach views the economy in terms of withdrawals and additions to the income-expenditure stream. Leakages refer to withdrawals from the stream and include savings, taxes, and imports. On the other hand, injections refer to additions to the stream and consist of investments, government expenditures, and exports. Equilibrium is achieved when the sum of leakages is equal to the sum of injections.
AD = C + I
AS = C + S
For equilibrium, aggregate demand must be equal to aggregate supply.
AD = AS
C + S = C + I
S = I
But S = Y - C
S = Y - a - bY
then Y - a - bY = I
Y ( 1 - b) = a + I
Y = (a + I)/(1 - b)
Y = (a + I )/ (1 - MPC), where b = MPC.
Graphically, 
The upper panel shows the AD-AS approach and the lower panel shows the saving-investment approach. The equilibrium is shown in the diagram at E, where the investment and savings curves intersect. I = S at this point.
The anticipated inventory would drop below the required level if S is greater than I. The producers increase their output in order to restore the Inventory to the required level. Greater output equals more earnings. Growth in output leads to growth in I, while growth in income leads to growth in S. Both keep climbing until they reach E, S=I.
The anticipated inventory exceeds the desired amount when S is smaller than I. Businesses intend to reduce output until S equals I in order to reduce the undesirable growth in inventory.
As a result, equilibrium only exists at point E when S=I.