Classical vs. Keynesian Demand, Multipliers & Fiscal Policy

Classical Quantity Theory, Money Demand & Cambridge Approach

• Quantity theory of money under classical economics involves

  • MV = PY (Fisher Equation) where

  • M = money supply.

  • V = velocity of money (assumed stable in short-run; determined by payments technology, frequency of wage payments, institutional factors).

  • P = aggregate price level.

  • Y = real output.

• Cambridge version (cash-balance approach):

  • Households desire to hold a fraction k of nominal income as money balances.

  • Money-demand equation: M^d = kPY.

  • Relationship between Fisher & Cambridge:

  • k = \dfrac{1}{V} \;\Rightarrow\; MV = PY \iff M = kPY.

  • Emphasis on the demand for money (why people hold cash) rather than on the transactions role alone.

• Classical aggregate-demand determination:

  • Given perfectly flexible prices/wages, output Y fixed at full-employment level \bar Y by supply side.

  • Nominal AD determined by M, V → decides price level P.

• Comparative statics inside classical model

  • Drop in M with fixed V ⇒ proportionate fall in P, output unchanged.

  • Exogenous rise in V (e.g., credit-card diffusion) ⇒ proportionate rise in P, no change in Y, N.

• Interest rate in classical theory

  • Determined by full-employment saving–investment equality; adjusts to equilibrate AD when components shift (crowding-out mechanism).

• Sample numerical exercise (Review Q-8)

  • M = 200,\; Y = 400,\; k0 = 0.5 → P0 = 1 because M = kPY ⇒ P_0 = \dfrac{M}{kY} = \dfrac{200}{0.5×400}=1.

  • If k falls to 0.25, P_1 = \dfrac{200}{0.25×400}=2.

  • Process: lower desire to hold money → excess money balances → higher spending → price bids up until real balances restored.

Keynesian System – Origins & Historical Motivation

• Developed amid Great Depression; unemployment in U.S. peaked at 25.2 % (1933), stayed >10 % through 1930s; real GNP −30 % 1929-33.

• U.K. suffered persistent >10 % unemployment since early 1920s.

• Classical prescriptions (balanced budgets, no activist fiscal policy) dominated:

  • Hoover’s 1932 tax increase; U.K. Treasury view: “state borrowing creates very little employment.”

• Keynes’s The General Theory (1936) fault line: Missing theory of aggregate demand.

  • High unemployment attributed to deficient AD, chiefly inadequate private investment.

  • Advocated fiscal activism (public works) & monetary/fiscal mix to regulate AD.

Simple Keynesian Model (Closed Economy, Fixed Prices)

• Equilibrium condition (three equivalent forms)

  1. Output = planned expenditure:
     Y = E = C + I + G.

  2. Leakages = injections:
     S + T = I + G.

  3. Desired = realised investment:
     I = I^r (no unintended inventory change).

• Accounting identities

  • Income disposition: Y \equiv C + S + T.

  • Product identity: Y \equiv C + I^r + G.

• Circular-flow intuition

  • Inner loop: firms → wages/dividends → households → consumption → firms.

  • Leakages: S, T out of households.

  • Injections: I (via financial markets), G (government purchases).

Consumption Function

• Keynesian linear form:
  C = a + bYD, \; a>0,\; 0D = Y - T.

• Marginal propensity to consume (MPC): b = \dfrac{\Delta C}{\Delta Y_D}.

• Corresponding saving function:
  S = -a + (1-b)Y_D, with MPS =1-b.

Investment Demand

• Short-run determinants:

  • Interest rate (negative relation, assumed exogenous here).

  • Business expectations (“animal spirits”): volatile, formed by extrapolation & convention; lead to unstable I.

Government Sector

• G, T treated as exogenous policy choices (can be altered discretionarily).

Graphical Representation (45°-Diagram)

• Plot E = C+I+G against Y.

• Intersection with 45° gives equilibrium Y.

• If YY → unintended inventory depletion → output rises.

• If Y>Y^* → E<Y → unintended inventory accumulation → output falls.

Algebraic Solution & Multipliers

• Substitute C into Y=E (with fixed T):
  Y = \dfrac{1}{1-b}\left[a - bT + I + G\right].

• Autonomous expenditure multiplier:
  k = \dfrac{1}{1-b} = \dfrac{1}{\text{MPS}}.

• Comparative-static effects

  • Investment: \Delta Y = k\,\Delta I.

  • Gov’t spending: \Delta Y = k\,\Delta G.

  • Taxes: \Delta Y = -\dfrac{b}{1-b}\,\Delta T.

  • Balanced-budget change ((\Delta G = \Delta T)): Net impact =1\times\Delta G.

Multiplier Process Logic (ripple effect)

• Initial autonomous rise (say \Delta I =100).

• First-round income +100 → C rises by b\times100.

• Second-round income +(100b) → C rises by b(100b) =100b^2, etc.

• Infinite geometric series sum ⇒ k = 1+ b + b^2 + \dots = \dfrac{1}{1-b}.

Fiscal Stabilisation Policy

• Objective: offset autonomous AD shocks (esp. investment).

• Example (Figure 5-8 logic):

  • I drops ((-\Delta I)) ⇒ E shifts down, equilibrium to YLP.

  • Discretionary policy: raise G or cut T such that \Delta G = -\Delta I (scaled by multipliers) ⇒ restores Y_P.

• Historical illustrations

  • 1964 Kennedy-Johnson tax cut: used expansionary fiscal policy to combat recession.

  • Late-1960s Vietnam War spending surge produced excess AD, proving fiscal actions can be destabilising.

  • 2009 ARRA (~$800 bn): mixture of spending & tax cuts; CBO estimated +1.1 to +3.5 % to GDP and +1.8–3.5 m jobs (Q4-2010).

Open-Economy Extension (Imports & Exports)

• Equilibrium with trade:
  Y = C + I + G + X - Z.

• Behavioural equations

  • Consumption: C = a + bY (taxes omitted for brevity).

  • Imports: Z = u + vY where

  • u autonomous imports.

  • v marginal propensity to import (MPI).

  • Exports X exogenous (foreign income driven).

• Solving for Y:
  Y = \dfrac{1}{1-b+v}\left[a + I + G + X - u\right].

• Implications

  • Multiplier is smaller: k_{open}=\dfrac{1}{1-b+v}<\dfrac{1}{1-b} because import leakage v>0.

  • Shocks:

  • \Delta Y = k_{open}\,\Delta X (export boom is expansionary).

  • \Delta Y = -k_{open}\,\Delta u (autonomous import surge is contractionary).

  • The higher the openness (larger v), the more muted the domestic income response to any autonomous spending change.

Key Concept Recap (Glossary)

• Quantity theory variables: M, V, P, Y; Cambridge k =1/V.

• Velocity of money: average frequency money changes hands; assumed stable classically.

• Consumption Function: C=a+bY_D.

• MPC (b): fraction of extra Y_D consumed.

• MPS (1-b): fraction of extra Y_D saved.

• Autonomous expenditures: a - bT + I + G + X - u (items not triggered by current Y).

• Autonomous expenditure multiplier k = 1/(1-b) (closed) or 1/(1-b+v) (open).

• Balanced-budget multiplier = 1.

• Leakages (S, T, Z) vs injections (I, G, X).

• Unintended inventory change links output to demand (I = I^r equilibrium).

Review Questions (Guided Study Prompts)

• Explain unemployment origins of Keynesian revolution and contrast with classical remedies.

• Demonstrate equivalence of Y=E, S+T=I+G, and I=I^r.

• Derive saving function, show how \Delta Y_D affects S.

• Analyse expectation-driven instability of investment & policy implications.

• Interpret Table 5-1: why consumption share rises in recessions despite stable MPC.

• Trace tax-increase impact on Y via partial leakage into saving (why only b\Delta T hits AD).

• Justify sign/size differences between spending and tax multipliers.

• Solve labour-supply curve shift when marginal tax rate t_y=0.20 (refer to Fig 3-3b).

• Classical model exercises: effects of raised t_y on Y, N, P$$ under varying bond-sale vs money-finance scenarios.

Ethical & Practical Insights

• Stabilisation is not purely technical; political resistance to deficits (1930s, 1960s) shapes policy choices.

• Misuse of fiscal tools (e.g., war finance) can over-stimulate, validating Keynesian warnings about discretion.

• Open-economy leakages highlight interdependence; unilateral demand management less potent in globalised world.

Connections to Later Topics

• Interest-rate determination & monetary policy (to be integrated in IS-LM framework, Ch 6).

• Price level flexibility and inflation dynamics (aggregate-supply analysis forthcoming, Ch 7-8).

• Modern extensions: permanent-income & life-cycle consumption, rational expectations, and policy ineffectiveness critiques (Part III).