Chapter 3: Aggregate Expenditure and Equilibrium Study Notes

Approaches in Determining National Income Equilibrium

• Aggregate Demand=Aggregate Supply (AD=AS) Approach:

  • The real Gross Domestic Product (GDP) represents the total amount of final goods and services produced that individuals, businesses, governments, and foreigners plan to purchase.
  • Equilibrium occurs where the total amount produced equals the total amount planned to be bought.
  • Key formulas for the AD=AS approach based on the number of sectors include:
    • 2-Sector Economy: $Y = C + I$
    • 3-Sector Economy: $Y = C + I + G$
    • 4-Sector Economy: $Y = C + I + G + (X - M)$

• Leakage=Injection Approach:

  • Leakage (L): Represents a withdrawal from the income-expenditure stream. It consists of savings ($S$), taxes ($T$), and imports ($M$).
  • Injection (I): Represents additional spending into the income-expenditure stream. It consists of investments ($I$), government expenditure ($G$), and exports ($X$).
  • Equilibrium occurs when the total value of leakages equals the total value of injections ($L = I$):
    • 2-Sector Economy: $S = I$
    • 3-Sector Economy: $S + T = I + G$
    • 4-Sector Economy: $S + T + M = I + G + X$

Detailed Concepts of Aggregate Demand (AD) and Aggregate Supply (AS)

• Definition of Aggregate Demand (AD):

  • Aggregate demand is the sum of demands from various sectors for the current output of the economy. These sectors include households, businesses, governments, and foreign buyers of domestic products.
  • The AD curve is downward sloping, showing the relationship between the quantity of real GDP demanded and the price level.
  • Example: If the price level is $115$, the quantity of real GDP demanded is $12 \, \text{trillion}$.
  • A change in price level (ceteris paribus) results in a movement along the AD curve.

• Why the Aggregate Demand Curve Slopes Downward:

  1. Income Distribution Effect: Changes in price levels are crucial. A lower price level increases purchasing power. When people consume a larger proportion of their income, it contributes to the expansion of AD. Conversely, when the price level rises, AD tends to shrink.
  2. Real Balance Effect: People save a portion of their income in liquid assets (bank deposits, gold, unit trusts, bonds, equities). If prices rise, the real value of consumption falls and purchasing power decreases. Households then decide to spend less on goods/services and save more, causing AD to decrease. If prices fall, people increase consumption and reduce saving, causing AD to expand.

• Determinants of Aggregate Demand:

  1. Private Consumption (C): Derived from disposable income ($Y_d$). High savings reduce consumption. Tax reductions on personal income or commodities increase consumption.
  2. Private Investment (I): Spending on capital goods. Increases in private investment shift the AD curve to the right.
  3. Public Investment (G): Used to direct the economy toward national goals. Increases in public investment increase AD.
  4. Net Expenditure on Exports (X-M): An increase in foreign spending on domestic exports relative to import payments increases AD.

• Definition of Aggregate Supply (AS):

  • AS is the total real output that various sectors (business firms, government, foreign sellers/importers) are willing to produce at different price levels.
  • The AS curve shows a positive relationship between price and output level.

• Determinants of Aggregate Supply:

  1. Input Price: Wages and salaries are a high proportion of business costs. Higher production costs push prices up. A reduction in wages reduces per-unit costs, increasing production and shifting the supply curve downward to the right. Higher wage rates reduce output and shift the curve upward to the left.
  2. Price of Imported Resources: Modern economies import labor, capital, and materials. If the price of imported resources rises, aggregate output decreases, shifting the supply curve upward to the left.
  3. Productivity: A measure of efficiency in resource use. Obtaining maximum real output per unit using limited resources and advanced technology. Improvements through Research and Development (R&D), new machinery, better management, and job training reduce production costs and shift the AS curve downward to the right.

Consumption, Saving, and Investment Concepts

• Concept of Consumption:

  • Consumption ($C$) is the purchase of firm-produced goods and services by households.
  • Keynesian Consumption Function: $C = f(Y_d)$. Consumption depends on disposable income ($Y_d = Y - T$). In a 2-sector economy without tax, $Y_d = Y$.
  • Linear Consumption Equation: $C = a + bY_d$
    • $a$ = Autonomous consumption (consumption when income is zero).
    • $b$ = Marginal Propensity to Consume (MPC).

• Propensity to Consume:

  1. Average Propensity to Consume (APC): The ratio of total consumption to total income ($APC = \frac{C}{Y}$).
     • Example: If $Y = RM \, 1000$ and $C = RM \, 700$, then $APC = 700/1000 = 0.70$. This means households use $70\%$ of income for consumption.
  2. Marginal Propensity to Consume (MPC): The relationship between the change in total income and the change in total consumption ($MPC = \frac{C_1 - C_0}{Y_1 - Y_0} = \frac{\Delta C}{\Delta Y}$).
     • Example: $Y_0 = 1000, C_0 = 700$; $Y_1 = 1500, C_1 = 1000$. $MPC = \frac{1000 - 700}{1500 - 1000} = \frac{300}{500} = 0.6$.

• Concept of Saving:

  • Saving ($S$) is the portion of income not used for consumption ($S = Y - C$).
  • Autonomous Saving: Saving that does not depend on income level (linked to autonomous consumption).
  • Induced Saving: Saving that depends on the level of income. Higher income leads to higher savings.
  • Linear Saving Equation: $S = -a + (1 - b)Y_d$
    • $-a$ = Autonomous saving (negative value of autonomous consumption).
    • $(1 - b)$ = Marginal Propensity to Save (MPS).

• Propensity to Save:

  1. Average Propensity to Save (APS): The ratio of total savings to total income ($APS = \frac{S}{Y}$).
  2. Marginal Propensity to Save (MPS): The ratio of change in total saving to the change in total income ($MPS = \frac{\Delta S}{\Delta Y}$).

• Mathematical Relationships:

  • $APC + APS = 1$
  • $MPC + MPS = 1$

• Determinants of Consumption and Savings:

  1. Price and Wage Levels: Rising prices decrease the propensity to consume. Rising wage levels increase the propensity to consume.
  2. Taste and Fashion: Consumer preferences affect spending habits, though shifts are less significant in the short run.
  3. Expectations: Consumption and saving respond to anticipated future changes in the economy.
  4. Rate of Interest: Higher interest rates encourage more saving due to higher dividends/returns.

• Types of Investment:

  1. Autonomous Investment: Fixed and independent of national income. Influenced by interest rates, government spending, and technology levels.
  2. Induced Investment: Directly depends on national income. Increases as national income increases.

Sectoral Equilibrium Calculations

• Two-Sector Economy (Firms and Households):

  • Data: Autonomous consumption = $250$, $MPC = 0.6$, Autonomous Investment = $500$.
  • Function: $C = 250 + 0.6Y_d$.
  • AD=AS Methodsolve:
    • $Y = 250 + 0.6Y + 500$
    • $Y - 0.6Y = 750$
    • $0.4Y = 750$
    • $Y = 1875$
  • Leakage-Injection Method:
    • $S = I$
    • $-250 + 0.4Y = 500$
    • $0.4Y = 750$
    • $Y = 1875$

• Three-Sector Economy (Households, Firms, Government):

  • Scenario A: Fixed Tax ($MPC = 0.6$, $I = 500$, $G = 100$, $T = 100$, $C = 250 + 0.6Y_d$)
    • $Y = 250 + 0.6(Y - 100) + 500 + 100$
    • $Y = 850 + 0.6Y - 60$
    • $0.4Y = 790$
    • $Y = 1975$
  • Scenario B: Induced Tax ($T = 0.2Y$)
    • $Y = 250 + 0.6(Y - 0.2Y) + 500 + 100$
    • $Y = 850 + 0.6(0.8Y)$
    • $Y = 850 + 0.48Y$
    • $0.52Y = 850$
    • $Y = 1634.6$

• Four-Sector Economy (Households, Firms, Government, Foreign Sector):

  • Data: $C = 250 + 0.6(Y-T)$, $I = 500$, $G = 100$, $T = 100$, $X = 100$, $M = 50$.
  • AD=AS Method:
    • $Y = 250 + 0.6(Y - 100) + 500 + 100 + (100 - 50)$
    • $Y = 900 + 0.6Y - 60$
    • $0.4Y = 840$
    • $Y = 2100$
  • Leakage-Injection Method:
    • $I + G + X = S + T + M$
    • $500 + 100 + 100 = -250 + 0.4(Y - 100) + 100 + 50$
    • $700 = -140 + 0.4Y$
    • $0.4Y = 840$
    • $Y = 2100$

Multiplier Concepts

• General Multiplier (K): The ratio of the change in income to the change in aggregate demand (AD). It shows how many times an initial change in AD is multiplied to cause a change in aggregate income.

  • The size of the multiplier depends on the MPC: $K = \frac{1}{1 - MPC} = \frac{1}{MPS}$.

• Specific Multipliers:

  1. Investment Multiplier ($K_i$): Ratio of change in equilibrium income to a change in investment. $K_i = \Delta Y / \Delta I$.
  2. Government Expenditure Multiplier ($K_g$): Ratio of change in equilibrium income to a change in government expenditure. $K_g = \Delta Y / \Delta G$.
     • Example: $C = 300 + 0.8Y$, $T = 100$, $G = 80$, $I = 150$. If investment increases by $50 \, \text{million}$:
     • $K_i = 1 / 0.2 = 5$
     • $\Delta Y = 5 \times 50 = 250 \, \text{million}$
     • $New \, Y = 2250 + 250 = 2500$.
  3. Tax Multiplier ($K_t$): Ratio of reduction in national income to a tax increase. Tax increases have a negative impact on aggregate income.
     • Formula: $K_t = \frac{-MPC}{1 - MPC} = \frac{-MPC}{MPS}$.
     • Example: If $MPC = 0.8$, $K_t = -0.8 / 0.2 = -4$. If tax increases by $100 \, \text{million}$, income changes by $-400 \, \text{million}$.
  4. Balanced-Budget Multiplier ($K_b$): Occurs when government expenditure and taxes are increased by the same amount.
     • Formula: $K_b = K_g + K_t$. Usually, the balanced-budget multiplier equals 1.
     • Example: If $G$ and $T$ both increase by $50 \, \text{million}$: $\Delta Y = (5 \times 50) + (-4 \times 50) = 250 - 200 = 50 \, \text{million}$.

Economic Gaps and Policy Implementation

• Inflationary Gap:

  • Occurs when national income (real GDP) exceeds the full employment (potential GDP) level ($Y > Y_{fe}$).
  • Measured as the excess of aggregate expenditure over full employment aggregate supply.
  • Results in an increase in the general price level.
  • Remedy: Contractionary fiscal policy (reducing government expenditure and raising taxes) or increasing withdrawals while decreasing injections.

• Deflationary Gap:

  • Occurs when national income is below the full employment level ($Y < Y_{fe}$).
  • Indicates that resources are not being fully utilized.
  • Measured as the difference between aggregate expenditure and full employment aggregate supply.
  • Remedy: Expansionary fiscal policy (increasing government expenditure and cutting taxes) or increasing injections while reducing withdrawals.

Questions & Discussion

• Calculating Propensities: The transcript provides a consumption schedule to find APC and MPC and a saving schedule to find APS and MPS.
  • Consumption Schedule Task: At $Y_d = 200$ and $C = 200$, find APC and MPC.
    • $APC = 200/200 = 1$.
    • $MPC$ (from $100$ to $200$ income): $\Delta C / \Delta Y = (200 - 150) / (200 - 100) = 50 / 100 = 0.5$.
  • Saving Schedule Task: At $Y_d = 300$, $C = 250$, $S = 50$.
    • $APS = 50/300 = 0.1667$.
    • $MPS = \Delta S / \Delta Y = (50 - 0) / (300 - 200) = 50 / 100 = 0.5$.