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

(a) Ineffectiveness of systematic monetary policy under rational expectations

The rational expectations hypothesis (Muth, Lucas) holds that people use all available information and the correct model of the economy, so their forecast errors are random and cannot be predicted by any policy rule. The New Classical model (Lucas, Sargent and Wallace) draws the implication.

Model, in logarithms:

• Aggregate demand: yₜ = mₜ − pₜ.
• Lucas supply: yₜ = yₙ + α(pₜ − Eₜ₋₁pₜ), with α > 0. Output departs from its natural level yₙ only when the price level differs from what was expected.
• Policy rule: mₜ = g + θyₜ₋₁ + εₜ, where the authority reacts systematically to past output, and εₜ is an unpredictable shock.

Substituting, (1 + α)(pₜ − Eₜ₋₁pₜ) = mₜ − Eₜ₋₁mₜ, so yₜ − yₙ = [α/(1 + α)](mₜ − Eₜ₋₁mₜ) = [α/(1 + α)]εₜ.

The systematic part (g + θyₜ₋₁) is known to the public in advance, so it is fully built into expectations and into wages and prices; it changes only the price level, not output. Only the unpredictable shock εₜ can move output, and then only temporarily. Hence a rule-based monetary policy cannot stabilise output or reduce unemployment below the natural rate; it can only affect inflation. Lucas's critique adds that estimated relationships change when the rule changes.

Evaluation: the result depends on market clearing, full information about the rule and flexible prices. New Keynesians (Fischer, Taylor) show that with long-term contracts and sticky prices, even anticipated policy has real effects. Evidence that money has short-run real effects, and that credible rules such as inflation targeting anchor expectations, supports a qualified version: policy cannot systematically fool rational agents, but can stabilise when prices are sticky.

(b) Effectiveness of monetary and fiscal policy and the interest elasticity of investment

Let investment be I = I₀ − br, consumption C = c(Y − T), money demand L = kY − hr. IS: (1 − c)Y = A − br, where A is autonomous spending (including G). LM: M/P = kY − hr. Solving gives Y = [A + (b/h)(M/P)] / [(1 − c) + bk/h].

Fiscal multiplier: ∂Y/∂G = 1 / [(1 − c) + bk/h]. Monetary multiplier: ∂Y/∂(M/P) = (b/h) / [(1 − c) + bk/h].

As b (interest elasticity of investment) rises, the fiscal multiplier falls and the monetary multiplier rises.

• Low b (steep IS): a fiscal expansion raises income a good deal, because the rise in interest rate crowds out little investment, so fiscal policy is effective. A monetary expansion lowers r, but investment barely responds, so monetary policy is weak.
• High b (flat IS): a fiscal expansion raises r, which crowds out much investment, so it is weak. A monetary expansion lowers r and investment responds strongly, so it is powerful.

The extreme cases are a vertical IS (b = 0), where only fiscal policy works, and a horizontal IS, where only monetary policy works. The slope of LM (h) works similarly. The choice of policy in practice therefore depends on how rate-sensitive private investment is.

(c) Speculative demand for money and unemployment equilibrium

In Keynes's theory, money demand has a transactions and precautionary component L₁(Y) and a speculative component L₂(r), which falls as the interest rate rises, because at a low rate people expect it to rise, bond prices to fall, and so hold cash.

Its importance is that it makes the interest rate, not just income, the variable that equilibrates the money market, and it makes the effect of money on spending indirect. A rise in the money supply lowers the interest rate only as far as speculative demand absorbs it; the fall in r raises investment and hence income.

It gives two results. First, when L₂ is very elastic at a low interest rate (the liquidity trap), extra money is simply held, r cannot fall, investment does not rise, and monetary policy cannot restore full employment, so equilibrium with unemployment persists and fiscal policy is needed. Second, speculative demand weakens the quantity-theory link between money and prices.

But it is not the only reason for unemployment equilibrium. Unemployment can also persist because investment is interest-inelastic, because the marginal efficiency of capital is low, or because money wages are rigid and effective demand is deficient, even if L₂ is finite. The Pigou effect also shows that flexible prices could restore full employment in theory.

Thus speculative demand is an important, but not necessary, condition for unemployment equilibrium; it explains the limit of monetary policy in a slump.