Determination of Income in Two-sector Model

• A two-sector economy consists only of households and firms (government and foreign sectors are ignored).
• Ex-ante Aggregate Demand (AD) is the sum of planned consumption expenditure and planned investment expenditure.
• Equilibrium is achieved when planned output equals planned aggregate demand.

AD = C + I

Where:

• AD = Ex-ante Aggregate Demand
• C = Ex-ante Consumption Expenditure
• I = Ex-ante Investment Expenditure

\[Y=\overline{C}+\overline{I}+cY\]

Where:

• Y = Planned (Ex-ante) Output
• \[\bar C\] = Autonomous Consumption
• \[\bar I\] = Autonomous Investment
• c = Marginal Propensity to Consume (MPC)

• Autonomous expenditure is expenditure that is independent of income.
• It consists of:
  • Autonomous Consumption (\[\bar C\])
  • Autonomous Investment (\[\bar I\])
• Autonomous consumption is relatively stable.
• Autonomous investment fluctuates over time.

\[\overline{A}=\overline{CD}+\overline{I}\]

\[Y=\overline{A}+cY\]

Where:

• \[\bar A\] = Total Autonomous Expenditure

• In the equilibrium equation, Y on the LHS represents planned (Ex-ante) output, while the RHS represents planned aggregate demand.
• They are equal only at equilibrium.
• This differs from the National Income Accounting identity, where Actual Output (Ex-post) = actual consumption + Actual Investment.

• Inventories are goods produced but not sold.
• Change in inventories is called Inventory Investment.
• Inventory investment may be:
  • Planned
  • Unplanned
• It is:
  • Positive when inventories increase.
  • Negative when inventories decrease.
• If planned demand is less than planned output, unsold goods accumulate as unplanned inventories.

• Government affects aggregate demand through:
  • Government Expenditure (G)
  • Taxes (T)
• Taxes reduce disposable income.

\[Y_d\] ​= Y − T

Where:

• \[Y_d\] = Disposable Income
• Y = National Income
• T = Taxes

\[Y=\overline{C}+\overline{I}+G+c(Y-T)\]

Where:

• G = Government Expenditure
• T = Taxes

G − cT becomes part of autonomous expenditure and does not change the basic analysis. For simplicity, the chapter continues with the two-sector model.

• In the absence of indirect taxes and subsidies, GDP = National Income.
• Hence, throughout the chapter, Y is used interchangeably for GDP and National Income.

• In a two-sector economy, AD = C + I.
• Equilibrium occurs when planned output equals planned aggregate demand.
• Autonomous expenditure = Autonomous Consumption + Autonomous investment.
• Inventory investment arises due to differences between planned and actual sales.
• Disposable Income = Y − T.
• Without indirect taxes and subsidies, GDP = National Income.