Keynesian System I: Expenditure and Equilibrium in the Product Market

Keynesian System I: Expenditure and Equilibrium in the Product Market

John Maynard Keynes: Background and Influence

John Maynard Keynes (1883–1946) was a pivotal figure in the development of modern macroeconomics. His work, especially during and after the Great Depression, fundamentally changed economic policy and theory.

• The General Theory of Employment, Interest and Money (1936): Keynes' most influential work, introducing concepts that challenged classical economics.

• Key Contributions: Revolutionized macroeconomic theory, especially regarding government intervention and aggregate demand.

• Other Roles: Bursar of King’s College, British Treasury official, architect of the post-WWII international economic system.

• Philosophy: Viewed economic policy as a moral and ethical pursuit, not just about efficiency.

Keynes: Side Notes

• Minimal formal training in economics; background in mathematics and classics.

• Advocated for individual freedom and was critical of traditional capitalism’s moral shortcomings.

• Strong supporter of women’s rights and social progressivism.

Keynesian Model: Assumptions

• Short Run Analysis: Focuses on the short-term behavior of the economy.

• Fixed Prices: Assumes prices are sticky, so there is no distinction between nominal and real variables in the short run.

• Flexible Output: Output can adjust, and the economy does not necessarily operate at full employment.

Circular Flow Diagram

The circular flow diagram illustrates the movement of income and expenditure in the economy, emphasizing equilibrium conditions.

• Equilibrium Conditions:

  • Output = Expenditure ($Y = E$)

  • $Y = C + I + G + NX$

  • Leakages = Injections ($S + T + M = I + G + X$)

Consumption and Savings

Keynesian Consumption Function

• $C = a + bY_d$

• $Y_d = Y - T$ (Disposable income)

• $b = mpc = \frac{\Delta C}{\Delta Y}$ (Marginal Propensity to Consume, $0 < mpc < 1$)

• Autonomous Consumption ($a$): Consumption independent of income (wealth effect).

• Example: If $mpc = 0.8$, an increase in income of $100 increases consumption by $80; the remaining $20 is saved.

Keynesian Savings Function

• $S = -a + (1-b)Y_d$

• Marginal Propensity to Save ($mps = 1 - mpc$)

Investment

Investment in the Keynesian model is influenced by expectations, which are not always rational and are affected by 'animal spirits' (psychological factors).

• Investment Function: $I = f(i, \pi, Exp)$

• Note: $r = i - \pi$ (real interest rate)

• Expectations: Keynes likened investment decisions to a 'beauty contest,' where expectations are based on what others believe, not just fundamentals.

Government Spending

• Initially treated as exogenous (determined outside the model).

• In reality, government spending and taxes often respond to the business cycle (automatic stabilizers).

• Economists distinguish between structural and cyclical components of the deficit.

Net Exports

• Analysis focuses on a closed economy (ignoring net exports and international capital flows).

• Leakages = Injections: $M - X = I - S + (G - T)$

• Net exports function: $NX = f(Y, e, P^*, Y^*, P)$

Equilibrium Level of Income in the Product Market

• Equilibrium occurs where aggregate output equals aggregate expenditure ($Y = E$).

• Key equations:

  • $Y = C + I + G$

  • $Y = a + b(Y - T) + I + G$

  • $Y - bY = a - bT + I + G$

  • $Y = \frac{1}{1-b}(a - bT + I + G)$

• Multiplier: $\frac{1}{1-b}$

• Autonomous expenditure components: $a, -bT, I, G$

Graphical Representation

• Equilibrium is found where the 45-degree line ($Y = E$) intersects the aggregate expenditure line.

• The aggregate expenditure line is upward sloping due to the positive relationship between income and consumption.

Alternative Approach (Closed Economy)

• Leakages = Injections: $S + T = I + G$

• Algebraic manipulation leads to the same equilibrium income formula as above.

Effect of a Change in Autonomous Expenditure

• Multiplier Effect: A change in autonomous expenditure (e.g., investment) leads to a multiplied change in equilibrium income.

• Formula: $\Delta Y = \frac{1}{1-b} \Delta I$

• Example: If $mpc = 0.8$, a $200 drop in investment leads to$\Delta Y = 5 \times (-200) = -1000$

The Multiplier Process

The multiplier process shows how an initial change in spending leads to a series of income and consumption increases, diminishing over time.

Round 1	Round 2	Round 3
$100	$75	$25
$75	$56.25	$18.75
$56.25	$42.19	$14.06
$42.19	$31.64
$31.64	$23.73
$23.73	$17.80
Total = $400		Total = $100

Note: If $mpc = 0.75$, the multiplier is 4.

Other Important Expenditure Multipliers

• Investment Multiplier: $\Delta Y = \frac{1}{1-b} \Delta I$

• Autonomous Consumption Multiplier: $\Delta Y = \frac{1}{1-b} \Delta a$

• Government Spending Multiplier: $\Delta Y = \frac{1}{1-b} \Delta G$

• Tax Multiplier: $\Delta Y = -\frac{b}{1-b} \Delta T$

• Note: The tax multiplier is negative (tax cuts raise income) and smaller in magnitude than the spending multiplier.

Balanced Budget Multiplier

• The difference between the government spending multiplier and the tax multiplier is 1.

• For $mpc = 0.75$:

  • $\Delta Y = \frac{1}{1-0.75} \times 100 = 400$

  • $\Delta Y = -\frac{0.75}{1-0.75} \times 100 = -300$

  • Net $\Delta Y = 100$

• Keynesian theory allows for a balanced budget stimulus to increase income.

Crowding Out

• In the classical model, government spending financed by bonds is assumed to be ineffective due to higher interest rates reducing private investment.

• In the Keynesian model, deficit spending is 'self-financing' because increased income generates additional savings.

• Formulas:

  • $\Delta Y = \frac{1}{1-b} \Delta G$

  • $\Delta S = (1-b) \Delta Y$

  • $\Delta S = \Delta G$

Investment Volatility

• In the classical model, investment volatility is offset by interest rate changes.

• In the Keynesian model, volatility in investment expectations directly affects aggregate demand and output.

• Formulas:

  • $\Delta Y = \frac{1}{1-b} \Delta I$

  • $\Delta S = (1-b) \Delta Y$

  • $\Delta S = \Delta I$

Heresy of Keynes

• Equilibrium ($Y = E$ or Leakages = Injections) can occur at any level of income, not just full employment.

• The classical model finds equilibrium only at full employment.

• The Keynesian model allows for equilibrium with unemployment.

• Keynes argued that the 'invisible hand' does not always ensure socially or economically optimal outcomes.