(a) "Under rational expectation hypothesis, systematic monetary policy is ineffective." Explain the above statement using a…

Part (a) Rational expectations, associated with Muth and Lucas, assume agents forecast using their information sets and the true model, so forecast errors are random and cannot be predicted by any systematic rule. In a simple New Classical model with log variables, aggregate demand is yₜ=mₜ-pₜ. The Lucas supply curve is yₜ=yₙ+α(pₜ-Eₜ₋₁pₜ), where yₙ is the natural rate and α>0. Combining gives (1+α)pₜ=mₜ+αEₜ₋₁pₜ. Subtracting Eₜ₋₁pₜ yields (1+α)(pₜ-Eₜ₋₁pₜ)=mₜ-Eₜ₋₁mₜ, so yₜ-yₙ=[α/(1+α)](mₜ-Eₜ₋₁mₜ). If monetary policy is systematic, mₜ is a known function of past variables, so Eₜ₋₁mₜ=mₜ; the surprise term is zero and output remains at yₙ, with only price-level effects. Only unanticipated money surprises can temporarily move output away from the natural rate. This is the policy ineffectiveness proposition: anticipated, rule-based policy is neutral for real variables because markets clear and agents adjust prices and expectations. The Lucas critique is distinct: it warns that structural parameters may change when policy rules change, while the proposition follows from rational expectations and market clearing. Empirically, RBI inflation targeting and forward guidance are expected to anchor prices rather than produce persistent output gains; only surprise liquidity shocks may have short-run real effects.

Part (b) In IS-LM, investment is I=I₀-br, where b is the interest elasticity of investment. With C=c(Y-T) and G, the IS curve is Y=A-br, so dr/dY=-1/b: low b makes IS steep, high b flat. The LM curve from M/P=kY-hr is r=(kY-M/P)/h. Substituting gives Y(1+bk/h)=A+(b/h)(M/P). The fiscal multiplier is dY/dG=1/(1+bk/h); the monetary multiplier is dY/d(M/P)=(b/h)/(1+bk/h). As b rises, the fiscal multiplier falls because expansion raises interest rates more strongly and crowds out private investment; the monetary multiplier rises because a given rate cut induces more investment. Diagrammatically, with steep IS (low b), fiscal expansion shifts IS right; the rise in r crowds out little investment so fiscal policy is effective; monetary expansion shifts LM right but produces little extra investment so it is weak. With flat IS (high b), fiscal expansion raises r and crowds out a large amount of investment, while monetary expansion lowers r and strongly stimulates investment, making it effective. In India, rate-sensitive private investment makes RBI repo-rate cuts potent, while capacity, policy, or credit constraints make fiscal capex more effective.

Part (c) Keynes divided money demand into transactions demand L1(Y), rising with income, and speculative demand L2(r), falling with the interest rate. The liquidity preference schedule L1(Y)+L2(r) intersects M/P to determine r; LM slope depends on h=-dL2/dr. Speculative demand is important because it transmits money-supply changes into interest-rate changes and hence into investment and aggregate demand. If L2 is relatively inelastic, a small increase in money supply lowers r appreciably, raising investment and output, so monetary policy can help remove unemployment. If L2 becomes highly elastic at low r—the liquidity trap—LM is horizontal, additional money is held rather than spent, r cannot fall, and monetary policy becomes ineffective. In that case an unemployment equilibrium can persist despite abundant liquidity, making fiscal activism, such as public works or direct demand support, more relevant. However, speculative demand is not the only source of underemployment equilibrium. Keynesian unemployment can also arise from deficient effective demand, a low marginal efficiency of capital, or investment that is interest-inelastic, even when L2 is finite and LM is not horizontal. Thus speculative demand is a crucial channel and a limiting case for monetary policy, but not a necessary condition for unemployment equilibrium. In India, weak credit demand after the 2020 rate cuts shows low rates alone may not eliminate unemployment if investment and consumption remain weak. Overall, the consensus has shifted from Keynesian demand management to New Classical caution about systematic policy, while retaining Keynesian channels for unanticipated shocks and liquidity traps.