Unit 3: Determination of Income and Employment

---

The aggregate demand and aggregate supply (at constant price)

This unit focuses on the Keynesian Model (or "Keynesian Cross"), which assumes that the price level is constant (fixed). This is a short-run model where the economy is assumed to have spare capacity (unemployment), so firms can increase output without raising prices.

Aggregate Supply (AS)

In this constant-price model, the Aggregate Supply (AS) curve is a 45-degree line starting from the origin.
Why? Because the total value of output produced (AS) must, by definition, be equal to the total income (Y) generated from producing it (wages, rent, profit). The 45-degree line represents all points where AS = Y (or where total spending = total income).

Aggregate Demand (AD) or Aggregate Expenditure (AE)

Aggregate Demand (AD) or Aggregate Expenditure (AE) is the total planned spending in the economy. In a simple two-sector model (households and firms), it has two components:

AE = C + I

• C (Consumption): Spending by households.
• I (Investment): Planned spending by firms.

The AE curve is e="font-weight:bold;">upward-sloping because consumption (C) increases as income (Y) increases.

---

Simple Keynesian Model

The Simple Keynesian Model is the framework that uses the AS and AE curves (from Topic 1) to find the equilibrium level of national income (Y).

Its central idea, which was a revolution against classical thought, is that:

"Demand creates its own supply."

This means the equilibrium level of output and employment is determined by the level of aggregate demand (AE), not by aggregate supply. If AE is low, the economy will settle at a low-output, high-unemployment equilibrium.

---

Consumption Function, Saving and Investment Functions

The Consumption Function (C)

This describes the relationship between consumption spending and disposable income.

C = a + b(Y)

• C = Total Consumption Spending.
• a = Autonomous Consumption. This is the minimum level of consumption that occurs even at zero income (e.g., by using savings). It is the vertical intercept of the C-function.
• b = Marginal Propensity to Consume (MPC). This is the fraction of an *additional* dollar of income that is spent on consumption. It is the slope of the C-function.
  MPC = (Change in C) / (Change in Y)
  (Assumed to be: 0 < MPC < 1)
• Y = Disposable Income.

Average Propensity to Consume (APC): The fraction of *total* income that is consumed.
APC = Total Consumption (C) / Total Income (Y)

The Saving Function (S)

Saving is the part of income that is *not* consumed (S = Y - C).

S = -a + (1-b)Y

• -a = Autonomous Saving (or Dissaving). If you spend 'a' at zero income, your saving must be '-a'.
• (1-b) = Marginal Propensity to Save (MPS). This is the fraction of an *additional* dollar of income that is saved.
  MPS = (Change in S) / (Change in Y)

The Investment Function (I)

In the simple Keynesian model, planned investment (I) is assumed to be Autonomous Investment. This means it is fixed at a certain level (e.g., I = I₀) and does *not* depend on the level of income (Y).
Graphically, the Investment Function is a horizontal line.

---

Determination of Equilibrium output

Equilibrium National Income (Y*) is the level of output where the economy is "at rest" and there is no tendency to change. This occurs where total production equals total planned spending.

There are two equivalent ways to find this:

1. Aggregate Supply-Aggregate Expenditure (AS = AE) Approach

Equilibrium is where the AS curve (45-degree line) intersects the AE curve.

• Equilibrium Condition: Y = AE
• In a two-sector economy: Y = C + I
• Derivation:
  1. Y = (a + bY) + I₀ (Substitute the C and I functions)
  2. Y - bY = a + I₀ (Collect Y terms)
  3. Y(1 - b) = a + I₀ (Factor out Y)
  4. Y* = (a + I₀) / (1 - b) (This is the equilibrium income formula)
  5. Or, since (1-b) = MPS: Y* = (Autonomous Spending) / MPS

[]

2. Leakage-Injection (S = I) Approach

Equilibrium is where planned leakages (withdrawals) from the circular flow equal planned injections (additions).

• In a two-sector economy:
  • The only Leakage is Saving (S).
  • The only Injection is Investment (I).
• Equilibrium Condition: S = I
• Derivation:
  1. -a + (1-b)Y = I₀ (Substitute the S and I functions)
  2. (1-b)Y = a + I₀ (Rearrange)
  3. Y* = (a + I₀) / (1 - b) (Same result)

[]

---

The concept of Multiplier

The Investment Multiplier (k) is the concept that an initial change in autonomous spending (like Investment) leads to a much larger final change in equilibrium national income.

Multiplier (k) = (Change in Income, ΔY) / (Initial Change in Spending, e.g., ΔI)

Why does this happen?

The multiplier works because "one person's spending is another person's income."
Example:

1. Government spends $100 on a new road (ΔI = $100).
2. This $100 becomes income for a worker.
3. Assume MPC = 0.8. The worker saves $20 (MPS=0.2) and spends $80.
4. This $80 becomes income for a shopkeeper.
5. The shopkeeper saves $16 (0.2 * 80) and spends $64.
6. This $64 becomes income for someone else... and so on.

The total change in income is: $100 + $80 + $64 + ...
This is a geometric series that sums to: ΔY = $100 × [ 1 / (1 - 0.8) ] = $100 × [ 1 / 0.2 ] = $100 × 5 = $500.

Multiplier Formulas (MUST KNOW):

k = 1 / (1 - MPC) k = 1 / MPS

---

Classical Theory of Employment

The Classical Theory (predating Keynes) held that a market economy has a natural tendency to move D full employment automatically, without government intervention. This theory is based on flexible wages, prices, and interest rates.

They argued that full employment was maintained by three markets:

1. Labor Market: They believed wages are perfectly flexible. If there is unemployment (Supply of Labor > Demand for Labor), wages will *fall* until all workers willing to work are hired.
2. Goods Market: Governed by Say's Law (see next topic). Flexible prices ensure that whatever is supplied is sold.
3. Money/Capital Market: They believed savings are always channeled into investment. If Savings > Investment, the *interest rate* will fall, making borrowing cheaper and investment more attractive until S = I.

Conclusion: In the classical view, any unemployment is temporary and voluntary (frictional).

---

Say's law of market

This is the central pillar of the Classical Theory, attributed to Jean-Baptiste Say.

"Supply creates its own demand."

Meaning:

The act of producing goods (supply) necessarily generates an equivalent amount of factor income (wages, rent, interest, profit). This income is then used to purchase the very goods that were produced (demand).

Implications:

• General overproduction is impossible: Since supply *creates* its own demand, there can never be a situation where (in aggregate) goods are produced but cannot be sold.
*
• No deficiency of demand: The economy cannot get "stuck" in a recession due to a lack of spending.
• Savings are not a problem: The classical school argued that any income that is saved (a leakage) is automatically channeled into investment (an injection) by flexible interest rates. Thus, saving is just another form of spending (on capital goods).

Keynes famously attacked this law, arguing that savings and investment are done by different people for different reasons, and there is no guarantee that S will equal I, leading to a deficiency of demand.

---

Classical dichotomy

The Classical Dichotomy is the theoretical separation of the economy into two distinct parts:

1. The "Real" Sector: This includes real variables like output (Y), employment (L), and the real interest rate (r). In the classical model, these are determined by real factors: the production function, the supply of labor, and saving/investment preferences.
2. The "Nominal" (or Monetary) Sector: This includes nominal variables like the general price level (P), the inflation rate, and the nominal interest rate (i).

The "dichotomy" (separation) is the idea that the nominal sector does not influence the real sector. Changes in the money supply (M) will, according to the Quantity Theory of Money (MV=PT), only change the price level (P). It will not change real output or employment.

This concept is also known as "The Neutrality of Money."

Keynes rejected this, arguing that in the short run, changes in money (nominal) can and do affect real output and employment (e.g., by changing interest rates, which changes Investment).