Question

Explain with diagram, the determination of Income in a Two Sector Economy.

Hint:

The two approaches (AD=AS and S=I) are two sides of the same coin. The AD=AS approach focuses on total spending and total output, while the S=I approach focuses on leakages (Saving) and injections (Investment) from the circular flow of income. In equilibrium, planned leakages must equal planned injections.

Answer 1

Step 1: Understanding the Two-Sector Model
A two-sector economy is a simplified model of an economy that consists only of households and firms. There is no government sector (no taxes or government spending) and no foreign sector (no exports or imports). The equilibrium level of national income in this model can be determined by two equivalent approaches: the Aggregate Demand-Aggregate Supply (AD-AS) approach and the Saving-Investment (S-I) approach.

Step 2: Aggregate Demand-Aggregate Supply (AD-AS) Approach
\begin{itemize} \item Aggregate Supply (AS): This represents the total value of final goods and services planned to be produced in the economy. It is always equal to the national income (Y). So, \(AS = Y\). On a diagram, the AS curve is a 45-degree line from the origin, indicating that at any point on the line, total spending equals total income. \item Aggregate Demand (AD): This represents the total planned expenditure in the economy. In a two-sector model, it has two components: \begin{enumerate} \item Consumption Expenditure (C): Planned spending by households. It is a function of income, given by the consumption function \(C = \bar{C} + bY\), where \(\bar{C}\) is autonomous consumption (consumption at zero income) and \(b\) is the marginal propensity to consume (MPC). \item Investment Expenditure (I): Planned spending by firms on capital goods. In this simple model, we assume investment is autonomous, meaning it is a constant value (\(I = \bar{I}\)) and does not depend on the level of income. \end{enumerate} Therefore, the aggregate demand function is \(AD = C + I = (\bar{C} + \bar{I}) + bY\). \item Equilibrium Condition: The economy is in equilibrium when planned aggregate demand is equal to planned aggregate supply. \[ AD = AS \text{or} Y = C + I \] \end{itemize} Diagrammatic Representation (AD-AS Approach): \begin{center} \begin{tikzpicture} \begin{axis}[ axis lines=left, xlabel={National Income / Output (Y)}, ylabel={Aggregate Demand (AD)}, xmin=0, xmax=500, ymin=0, ymax=500, xtick={350}, xticklabels={$Y^*$}, ytick={350}, yticklabels={$AD^*$}, legend style={at={(0.05,0.95)},anchor=north west}, height=9cm, width=11cm ] % 45-degree line (AS) \addplot[thick, black, domain=0:500] {x} node[pos=0.9, above right] {AS = Y}; % Consumption function \addplot[smooth, thick, blue, domain=0:500] {50 + 0.6*x}; \addlegendentry{$C = \bar{C} + bY$} % AD function \addplot[smooth, thick, red, domain=0:500] {100 + 0.6*x}; \addlegendentry{$AD = C + I$} % Equilibrium point \node[circle, fill, inner sep=1.5pt, label=above right:E] at (axis cs:250,250) {}; % Corrected Equilibrium \node[circle, fill, inner sep=1.5pt, label=above right:E] at (axis cs:250,250) {}; \pgfmathsetmacro{\Yeq}{250} \pgfmathsetmacro{\ADeq}{250} \draw[dashed, gray] (axis cs:\Yeq,0) -- (axis cs:\Yeq,\ADeq); \draw[dashed, gray] (axis cs:0,\ADeq) -- (axis cs:\Yeq,\ADeq); \node[below] at (axis cs:\Yeq,0) {$Y^*$}; \node[left] at (axis cs:0,\ADeq) {$AD^*$}; % Autonomous components \node[left] at (axis cs:0,50) {$\bar{C}$}; \node[left] at (axis cs:0,100) {$\bar{C}+\bar{I}$}; \end{axis} \end{tikzpicture} \end{center} In the diagram, the equilibrium is at point E, where the AD curve intersects the 45-degree AS line. The corresponding level of income \(Y^*\) is the equilibrium level of income. At any income level below \(Y^*\), AD > AS, leading to an unplanned decrease in inventories and prompting firms to increase production. At any income level above \(Y^*\), AD \(<\) AS, leading to an unplanned increase in inventories and prompting firms to decrease production.

Step 3: Saving-Investment (S-I) Approach
This is an alternative expression of the same equilibrium condition. \begin{itemize} \item We know that Income (Y) is either consumed (C) or saved (S). So, \(Y = C + S\). \item The equilibrium condition is \(Y = AD = C + I\). \item Equating the two expressions for Y: \(C + S = C + I\). \item This simplifies to the equilibrium condition: \[ S = I \] This means the economy is in equilibrium when planned saving equals planned investment. \end{itemize}