Macroeconomics - Simple Keynesian System

Modern macroeconomic theory emerged from the catastrophic economic collapse known as the Great Depression (1929–1933). Originating with the Wall Street stock market crash of October 1929, the Depression engulfed the global capitalist economy. Across the United States and Western Europe, national income contracted by more than 30%, industrial output halved, commodity prices plummeted, and unemployment soared to unprecedented levels, exceeding 25% of the total labor force. Millions of willing and able workers queued for soup kitchens while factories, steel mills, and mines stood completely idle.

Prevailed at that time was the orthodox Classical Economic Paradigm, championed by luminaries such as Adam Smith, David Ricardo, Jean-Baptiste Say, and Arthur Cecil Pigou. Classical economists insisted that market economies possess an automatic self-equilibrating mechanism that guarantees full employment. They argued that prolonged mass unemployment was theoretically impossible under competitive conditions, asserting that the depression was merely a temporary aberration that would cure itself if wages and prices were permitted to fall freely. Yet, year after year, mass unemployment deepened, exposing the total inadequacy of classical doctrine to explain or resolve systemic economic failure.

In 1936, the British economist John Maynard Keynes (1883–1946) published his monumental treatise, The General Theory of Employment, Interest and Money. Keynes revolutionized economic science by dismantling classical orthodoxy, demonstrating that a capitalist economy can settle into a persistent underemployment equilibrium, and establishing that the overall level of economic activity and employment is determined not by productive capacity, but by the volume of Effective Demand.

The Classical macroeconomic framework rested upon four foundational pillars:

1. Say's Law of Markets ("Supply Creates Its Own Demand"):

   Formulated by French economist Jean-Baptiste Say, this postulate asserts that the very act of producing goods creates factor payments (wages, interest, rent, and profits) exactly equal to the market value of the output. These incomes are entirely spent by recipients to purchase the goods produced. Therefore, aggregate demand must always equal aggregate supply, ruling out any possibility of general overproduction or generalized involuntary unemployment.

2. Wage-Price Flexibility & The Labor Market:

   Classical economists treated the labor market like any commodity market. The demand for labor is a decreasing function of the real wage ($W/P$), while the supply of labor is an increasing function of the real wage. If unemployment arises (excess supply of labor), competitive bidding among workers drives money wages downward. As real wages fall, profit-maximizing firms hire more workers until the labor market clears at full employment. Thus, any persistent unemployment was dismissed as voluntary (workers refusing to accept lower wages) or frictional.

3. Saving-Investment Equilibrium via Flexible Interest Rates:

   Even if income earners do not spend all their earnings on consumer goods and choose to save ($S$), the classical school argued this does not create deficient demand. In the loanable funds market, the rate of interest is the equilibrating price. Saving represents the supply of loanable funds (positively related to interest rate), while investment ($I$) represents the demand for loanable funds (negatively related to interest rate). If saving exceeds investment ($S > I$), the interest rate falls freely, discouraging saving and stimulating capital investment until $S = I$ at the full employment level.

4. Neutrality of Money ("Money is a Veil"):

   Under the Classical Quantity Theory of Money ($MV = PY$), money serves exclusively as a medium of exchange (transaction motive). Changes in the money supply alter the general price level ($P$) proportionally, but exert zero effect on real output, real employment, or the real interest rate (Classical Dichotomy).

Keynes challenged each classical premise with devastating logical and empirical arguments:

• Rejection of Say's Law & The Principle of Effective Demand: Keynes pointed out that in a monetary economy, income recipients are under no compulsion to spend their entire income immediately on goods and services. When individuals save, they withdraw purchasing power from the circular flow. If planned investment fails to offset this leakage, aggregate demand falls short of aggregate supply, causing unsold inventories, production cutbacks, and mass unemployment. Hence, output is demand-constrained, not supply-determined.
• Wage Rigidity and the Fallacy of Wage Cuts: Keynes observed that in modern industrial economies, money wages are "sticky downwards" due to collective bargaining by trade unions, statutory minimum wage laws, long-term employment contracts, and worker psychology. More fundamentally, Keynes exposed a grave fallacy of composition in Pigou's wage-cut solution: while an individual firm can hire more workers by cutting its own employees' wages, an economy-wide cut in money wages slashes the aggregate purchasing power of the working class. Because workers have a high propensity to consume, this destroys aggregate demand, depressing sales and worsening unemployment rather than curing it!
• Saving Depends on Income, Not the Interest Rate: Keynes proved that aggregate saving is governed primarily by the level of national income ($S = f(Y)$), not the interest rate. When income is low, saving is zero or negative (dissaving), regardless of how high interest rates might be. The rate of interest is a purely monetary phenomenon determined by the supply of money and the public's liquidity preference.
• Possibility of Underemployment Equilibrium: Equilibrium in the goods market requires only that planned aggregate demand equals aggregate supply. There is no automatic mechanism ensuring that this equilibrium output coincides with full employment ($Y_F$). An economy can remain trapped indefinitely in an underemployment equilibrium unless active government intervention stimulates aggregate demand.

To isolate the fundamental mechanics of income determination, Keynes formulated the baseline "Simple Keynesian Model" anchored on five essential assumptions:

1. Short-Run Analysis: The macroeconomic time horizon is strictly short-run. The capital stock, industrial technology, labor skills, and institutional arrangements are held constant. Output can change solely through changes in employment of labor.
2. Closed Economy: The model abstracts initially from foreign trade (exports $X = 0$, imports $M = 0$). We examine a two-sector economy (Households and Firms) and subsequently introduce the Government sector (Three-Sector Model).
3. Excess Capacity and Perfectly Elastic Aggregate Supply: The economy operates with pervasive idle capacity and involuntary unemployment. Producers are willing to supply whatever quantity of final goods is demanded at the existing price level.
4. Fixed General Price Level ($P$ is Constant): Because widespread excess capacity exists, increases in aggregate demand lead entirely to increases in real physical output and employment, without causing upward pressure on prices or inflation.
5. Autonomous Investment: In the baseline model, private business investment expenditure is treated as an autonomous variable ($ar{I}$), determined by long-term business confidence and animal spirits rather than current national income.

In macroeconomic theory, Aggregate Demand (AD) refers to the total planned, intended, or ex-ante expenditure that all sectors of the economy are willing to spend on final goods and services produced within the domestic boundary during an accounting year at a given price level.

In a simplified two-sector economy consisting exclusively of households and business firms (without government taxation or foreign trade), Aggregate Demand consists of two components:

• C (Consumption Expenditure): Total planned spending by households on durable goods, non-durable goods, and consumer services.
• I (Investment Expenditure): Total planned spending by business firms on capital formation, machinery, structures, and intended changes in inventory.

The Consumption Function (or Propensity to Consume) expresses the functional relationship between total planned consumption expenditure ($C$) and the level of national income ($Y$):

In the Simple Keynesian Model, the consumption function is typically represented as a linear relationship:

Here, the parameters represent:

• $ar{C}$ (Autonomous Consumption): The baseline consumption expenditure that takes place even when national income is zero ($Y = 0$). Human survival requires basic food, shelter, and medical care, which must be financed by drawing down past savings (dissaving) or borrowing. Thus, $ar{C} > 0$.
• $b$ (Marginal Propensity to Consume, MPC): The slope of the consumption function ($\Delta C / \Delta Y$). It measures the change in consumption expenditure resulting from a one-unit change in national income ($0 < b < 1$).
• $bY$ (Induced Consumption): The portion of consumption expenditure that varies directly with the level of national income.

Macroeconomists evaluate two distinct measures of consumer propensity:

1. Average Propensity to Consume (APC):

   The ratio of total consumption expenditure to total national income at a given income level:

   APC = C / Y = (ar{C} / Y) + b

   Behavioral Characteristics of APC:

   • APC > 1: At very low income levels, consumption exceeds income ($C > Y$), resulting in dissaving.
   • APC = 1: At the Break-even Point, consumption exactly equals income ($C = Y$), and saving is zero.
   • APC < 1: Beyond the break-even point, consumption is less than income ($C < Y$), resulting in positive saving.
   • APC declines steadily: As income rises, $ar{C}/Y$ approaches zero, causing APC to fall progressively.
2. Marginal Propensity to Consume (MPC):

   The ratio of the change in consumption expenditure to the change in national income:

   MPC = \Delta C / \Delta Y = b

   In a linear consumption function, MPC is constant and equals the slope $b$. In reality, $0 < ext{MPC} < 1$. Because people neither save all their additional income ($ ext{MPC} e 0$) nor spend all of it ($ ext{MPC} e 1$), MPC is strictly a positive fraction.

National income is either consumed or saved ($Y \equiv C + S$). Therefore, planned saving is the residue of income after consumption:

Substituting the linear consumption function $C = ar{C} + bY$ into the saving identity yields:

Here:

• $-ar{C}$ (Autonomous Dissaving): When income is zero, households must dissave by an amount equal to autonomous consumption ($S = -ar{C}$).
• $1 - b = ext{MPS}$ (Marginal Propensity to Save): The slope of the saving function ($\Delta S / \Delta Y$).

The dual propensities to save are defined as:

• Average Propensity to Save (APS): $ ext{APS} = S / Y = -ar{C}/Y + (1 - b)$. Can be negative (at income below break-even), zero (at break-even where $S = 0$), or positive (at income above break-even). APS increases continuously as income expands.
• Marginal Propensity to Save (MPS): $ ext{MPS} = \Delta S / \Delta Y = 1 - b$. Represents the proportion of additional income that is saved ($0 < ext{MPS} < 1$).

Examiners frequently evaluate the algebraic proof of two fundamental identities:

In everyday language, an individual who purchases existing equity shares on the stock exchange, government bonds, or mutual fund units is said to "invest". However, in macroeconomic theory, such transactions are classified strictly as Financial Investment. They represent a mere transfer of title to existing financial assets from one individual to another, creating zero addition to the physical productive capacity of the nation.

In contrast, Real Investment (Capital Formation) refers to net additions to the physical capital stock of the economy during an accounting period. It includes:

• Fixed Business Investment: Expenditure by firms on newly produced physical assets—such as industrial machinery, assembly plant equipment, computers, transport vehicles, and factory buildings.
• Residential Construction: Spending on constructing new houses, apartment complexes, and residential townships.
• Inventory Investment: The net change in the stocks of raw materials, semi-finished goods (goods-in-process), and finished unsold goods held by business enterprises over the year.

Macroeconomic theory distinguishes between two fundamentally different types of investment expenditure:

In the basic WBCHSE Simple Keynesian Model, all investment is treated as autonomous: $I = ar{I}$. This critical analytical simplification is adopted for three vital reasons:

1. Short-Run Stability of Capital Decisions: Major capital expenditure plans (building steel mills, power projects, automotive factories) require years of advance planning and financing. In the short run, actual investment disbursements are governed by long-past commitments and long-term expectations rather than volatile month-to-month fluctuations in current GDP.
2. Focus on the Multiplier Mechanism: Keynes wished to demonstrate how an initial, exogenous shift in investment spending triggers iterative rounds of consumption and income expansion. Treating investment as an autonomous exogenous parameter ($ar{I}$) allows us to calculate the pure Investment Multiplier without the confounding feedback loop of induced accelerator effects.
3. Role of Public Investment in Economic Stabilization: During a deep depression, private induced investment collapses to near zero because private firms face massive excess capacity and pessimism. The only viable investment that can revive the economy is autonomous public expenditure injected by the state, which is strictly policy-determined and independent of current market profits.

According to Keynes, when private firms evaluate a potential capital investment project, their decision is governed by the comparison of two factors:

1. Marginal Efficiency of Capital (MEC): The expected rate of return (or internal rate of return) over the asset's operating life. MEC depends on the prospective yield (expected net annual revenue generated by the machine) and the supply price (replacement cost of the capital asset).
2. Market Rate of Interest ($r$): The cost of borrowing capital (or the opportunity cost of investing internal retained earnings).

In macroeconomic theory, national income and employment reach short-run equilibrium at that level of real output where the total quantity of goods and services that producers plan to produce exactly balances the total quantity of goods and services that buyers plan to purchase. In a two-sector closed economy without government, this equilibrium can be demonstrated through two mathematically equivalent approaches:

1. The Aggregate Demand – Aggregate Supply Approach (AD = AS or Keynesian Cross):

   Aggregate Supply (AS): Represents the total monetary value of final goods and services planned to be produced in the economy. Since factor incomes generated in production identically equal the value of final output, Aggregate Supply is identically equal to National Income ($Y$):

   AS = Y = C + S

   Diagrammatically, the AS curve is drawn as a 45-degree line originating from the zero origin. Every point on this line represents equal values of planned expenditure and realized national income.

   Aggregate Demand (AD): Represents total planned expenditure by households on consumption and by business firms on capital investment:

   AD = C + I = (ar{C} + bY) + ar{I} = (ar{C} + ar{I}) + bY = ar{A} + bY

   where $ar{A} = ar{C} + ar{I}$ is total autonomous expenditure, and $b = ext{MPC}$ is the upward slope of the AD schedule.

   Equilibrium Condition: Equating Aggregate Demand to Aggregate Supply:

   Y = AD ⇒ Y = ar{C} + bY + ar{I} ⇒ Y(1 - b) = ar{C} + ar{I} ⇒ Y^* = (ar{C} + ar{I}) / (1 - b)
2. The Saving – Investment Approach (S = I):

   In the circular flow of income, saving ($S$) represents a leakage (withdrawal) of purchasing power from the spending stream, while investment ($I$) represents an injection of new spending into the stream.

   Equilibrium requires that planned leakages equal planned injections: $S = I$.

   Substituting the saving function $S = -ar{C} + (1 - b)Y$ and autonomous investment $I = ar{I}$:

   -ar{C} + (1 - b)Y = ar{I} ⇒ (1 - b)Y = ar{C} + ar{I} ⇒ Y^* = (ar{C} + ar{I}) / (1 - b)

How does an economy automatically move toward equilibrium if it starts in disequilibrium? The Keynesian adjustment mechanism operates through unintended (unplanned) changes in business inventories:

A pivotal conceptual distinction in macroeconomics is that between planned (ex-ante) and realized (ex-post) magnitudes:

The concept of the multiplier was originally developed by British economist R.F. Kahn in 1931 as an "Employment Multiplier". John Maynard Keynes adapted and generalized Kahn's concept into the Investment Multiplier in his 1936 General Theory.

Definition: The Investment Multiplier ($k$) is defined as the ratio of the resulting change in equilibrium national income ($\Delta Y$) to an initial autonomous change in investment expenditure ($\Delta I$):

The central insight of the multiplier is that an initial capital expenditure (such as building a bridge costing ₹100 crores) does not merely add ₹100 crores to national income; it triggers a chain reaction of successive rounds of consumer spending that expands total national income by a multiple of that initial investment.

The multiplier formula can be derived algebraically through two equivalent methods:

The multiplier works through an iterative expenditure sequence. Consider an initial injection of autonomous investment $\Delta I = ext{₹1,000 crores}$ in an economy where the Marginal Propensity to Consume is $ ext{MPC} = 0.8$ (and $ ext{MPS} = 0.2$):

The total change in income is the sum of an infinite geometric progression with common ratio $c = ext{MPC} = 0.8$:

• Range of the Multiplier: Since $0 \le ext{MPC} \le 1$:
  • When $ ext{MPC} = 0$: $k = 1 / (1 - 0) = 1$ (minimum bound: income increases solely by the initial investment).
  • When $ ext{MPC} = 1$: $k = 1 / (1 - 1) = \infty$ (maximum theoretical bound: income expansion is boundless).
  • Thus, the value of the multiplier lies strictly in the range: $1 \le k \le \infty$.
• Forward vs. Reverse (Backward) Multiplier: The multiplier is a double-edged sword. A Forward Multiplier occurs when an initial increase in investment ($\Delta I > 0$) triggers a multiple expansion in national income. A Reverse (Backward) Multiplier occurs when a decrease in investment ($\Delta I < 0$) triggers a multiple contraction in national income. During the Great Depression, a collapse in private investment generated a devastating reverse multiplier contraction.
• Leakages from the Multiplier Process: Leakages are diversions of income away from domestic consumer spending that dampen the multiplier: (1) Saving (primary leakage); (2) Debt repayment; (3) Spending on imports; (4) Cash hoarding; (5) Direct and indirect taxes.

The Paradox of Thrift (সঞ্চয়ের আপাতবৈপরীত্য / बचत का विरोधाभास) is one of Keynes' most famous conceptual discoveries. It demonstrates that:

"An attempt by all individuals in a society to save a higher fraction of their income (an increase in MPS) may fail to increase total aggregate savings, and will instead cause national income, output, and employment to contract!"

The Mechanism of the Paradox:

1. Suppose households become pessimistic about the future and decide to save more at every income level. This causes an upward shift in the Saving function (and a downward shift in the Consumption function).
2. Because people spend less on consumer goods, Aggregate Demand ($C + ar{I}$) shifts downward.
3. Producers experience unintended accumulation of unsold inventories and respond by cutting output and employment.
4. National income contracts via the reverse multiplier until a new, lower equilibrium income is reached. At this lower national income, total realized saving ($S = s imes Y$) returns exactly to the original level of autonomous investment ($ar{I}$). Total savings do not rise at all—society ends up poorer, with lower income and higher unemployment!

This phenomenon is a classic Fallacy of Composition: What is a virtue for a single household (personal thrift) becomes an economic vice for the macro-economy if adopted collectively without a matching increase in investment.

When we extend the Simple Keynesian Model to incorporate the Government Sector, we arrive at the Three-Sector Closed Economy. The government participates in the macroeconomic circular flow through two fundamental fiscal instruments:

• Government Purchases ($ar{G}$): Autonomous public expenditure on goods and services (defense, roads, schools, public administration). This represents a direct injection into Aggregate Demand.
• Lump-Sum Taxes ($ar{T}$): Taxes levied on households that reduce their disposable income. This represents a leakage from the income stream.

In this three-sector framework, planned Aggregate Demand is:

Households make consumption decisions based not on total national income ($Y$), but on Disposable Income ($Y_d$)—the income remaining after paying government taxes:

Substituting $Y_d$ into the linear consumption function:

Now applying the goods market equilibrium condition ($Y = ext{AD}$):

From the equilibrium national income equation, we derive three distinct fiscal policy multipliers:

1. The Government Expenditure Multiplier ($k_G$):

   Measures the change in equilibrium national income per unit change in autonomous government spending:

   k_G = \Delta Y / \Delta G = 1 / (1 - b) = 1 / (1 - ext{MPC})

   Because government spending represents a direct addition to Aggregate Demand, $k_G$ is strictly positive and operates identically to the investment multiplier.

2. The Lump-Sum Tax Multiplier ($k_T$):

   Measures the change in equilibrium national income per unit change in autonomous lump-sum taxation:

   k_T = \Delta Y / \Delta T = -b / (1 - b) = - ext{MPC} / (1 - ext{MPC})

   Crucial Properties of $k_T$:

   • $k_T$ is negative: Higher taxes reduce disposable income, depressing consumption and shrinking national output.
   • $|k_T| < k_G$: The absolute magnitude of the tax multiplier is strictly smaller than the government expenditure multiplier ($|k_T| = b \cdot k_G$). This occurs because households do not cut spending by the full tax amount; they absorb part of the tax by reducing savings (by $(1 - b) \Delta T$).
3. The Balanced Budget Multiplier ($k_B$ / Haavelmo's Theorem):

   What happens if the government increases its spending and taxes by the exact same amount ($\Delta G = \Delta T$), maintaining a completely balanced fiscal budget?

   \Delta Y = k_G \cdot \Delta G + k_T \cdot \Delta T = [1 / (1 - b)] \Delta G + [-b / (1 - b)] \Delta T
   ext{Since } \Delta G = \Delta T ⇒ \Delta Y = [(1 - b) / (1 - b)] \Delta G = 1 imes \Delta G
   k_B = \Delta Y / \Delta G = 1

   The Balanced Budget Multiplier is ALWAYS equal to 1! Even if public spending is 100% tax-financed, national income expands by exactly the amount of the expenditure increase ($\Delta Y = \Delta G$).

A foundational contribution of Keynes was demonstrating that the equilibrium level of national income ($Y^*$) determined by effective demand does not necessarily coincide with the Full Employment National Income ($Y_F$). Full employment income represents the maximum potential output an economy can produce when all available labor and capital resources are fully and efficiently utilized. Three macroeconomic states are possible:

• $Y^* = Y_F$ (Full Employment Equilibrium): Planned aggregate demand exactly matches aggregate supply at full capacity. Ideal macroeconomic stability.
• $Y^* < Y_F$ (Underemployment Equilibrium / Deficient Demand): Aggregate demand falls short of full capacity output, resulting in involuntary unemployment and deflationary pressures.
• $Y^* > Y_F$ (Over-Full Employment Equilibrium / Excess Demand): Aggregate demand exceeds the physical productive capacity of the economy, resulting in demand-pull inflation.

Deficient Demand occurs when planned aggregate demand is less than the aggregate supply required to maintain full employment output ($ ext{AD} < ext{AS}$ at $Y_F$).

"The Deflationary Gap is the vertical distance by which actual aggregate demand falls short of aggregate supply at the full employment level of national income."

Excess Demand occurs when planned aggregate demand exceeds the aggregate supply corresponding to full employment ($ ext{AD} > ext{AS}$ at $Y_F$).

"The Inflationary Gap is the vertical distance by which actual aggregate demand exceeds aggregate supply at the full employment level of national income."

Economic Consequences of Excess Demand: Because the economy is already at full employment ($Y_F$), real physical output cannot expand in the short run. Instead, the excess purchasing power bids up the prices of fixed goods and services, generating pure Demand-Pull Inflation and wage-price spirals without any gain in real national output.

To steer the economy back to full employment stability, the central bank and the government execute coordinated stabilization policies: