(a) Derive short-run aggregate supply curve following Lucas, when expectations are not realised, assuming that labour market clears. What will be its shape when expectations are fulfilled ? (10+5 marks)
(b) Describe high powered theory of money suppl

Question

(a) Derive short-run aggregate supply curve following Lucas, when expectations are not realised, assuming that labour market clears. What will be its shape when expectations are fulfilled ? (10+5 marks)
(b) Describe high powered theory of money supply in brief. State the assumptions made in its construction. (8+7 marks)
(c) Do you think that increase in Government spending through borrowing from public accompanied by fall in required reserve ratio generates recession in the economy ? Illustrate your answer:
(i) in a closed economy with fixed exchange rate.
(ii) in an open economy with fixed exchange rate and without any capital mobility. (20 marks)

UPSC Answer Check · Accepted Answer

(a) Lucas misperception model with clearing labour market. Let Y = F(L), F′ > 0, F″ < 0. Firms set W/P = F′(L). Workers supply labour on expected real wage: W/Pᵉ = ψ(L), ψ′ > 0. Labour-market clearing gives:
P F′(L) = Pᵉ ψ(L).
Log-linearise around full-information equilibrium P = Pᵉ, L = L*, Y = Y*. Let λ = −L*F″(L*)/F′(L*) > 0 and δ = L*ψ′(L*)/ψ(L*) > 0. Then:
ln F′(L) ≈ ln F′(L*) − λ(ln L − ln L*),
ln ψ(L) ≈ ln ψ(L*) + δ(ln L − ln L*).
Since F′(L*) = ψ(L*), subtracting gives:
ln P − ln Pᵉ = ln ψ(L) − ln F′(L) = (λ + δ)(ln L − ln L*).
Hence:
ln L = ln L* + [1/(λ + δ)](ln P − ln Pᵉ).
Using ln Y = ln Y* + ε_L(ln L − ln L*), where ε_L = L*F′(L*)/Y* > 0, the Lucas short-run aggregate supply curve is:
ln Y = ln Y* + α(ln P − ln Pᵉ), α = ε_L/(λ + δ) > 0,
or equivalently:
Y = Y*(P/Pᵉ)^α.
It is upward sloping: when P > Pᵉ, workers mistake the price rise for a higher real wage and supply more labour, while firms demand more labour. When expectations are fulfilled, P = Pᵉ, so ln Y = ln Y*. Thus SAS is vertical at natural output Y*.

(b) High-powered money theory: Let H = C + R, M = C + D, c = C/D. If total reserve ratio is r = R/D, then:
M/H = (C + D)/(C + R) = (1 + c)/(c + r),
so M = mH, where m = (1 + c)/(c + r) is the money multiplier. If required reserve ratio is r_r and excess reserve ratio is e, then r = r_r + e and m = (1 + c)/(c + r_r + e). The central bank controls H; the public determines c; banks determine r_r and e. Hence M = mH, and the central bank can influence M by changing H, provided m is stable.

Assumptions: (i) central bank exogenously controls H; (ii) currency-deposit ratio c is stable and determined by public habits; (iii) required reserve ratio r_r is stable or policy-determined; (iv) excess reserve ratio e is stable or negligible; (v) money multiplier m is stable and predictable; (vi) interest rates do not significantly alter c, r_r and e; (vii) no foreign-exchange or other leakages disturb H.

(c) Bond-financed G↑ shifts IS right. Fall in required reserve ratio rr↓ raises m, so M = mH rises and LM shifts right.

(i) In a closed economy, there is no foreign sector, so the fixed exchange-rate clause is inoperative. Use IS-LM. G↑ shifts IS right; rr↓ shifts LM right. At initial interest, both raise Y. Equilibrium output and employment rise. Interest may rise or fall depending on relative shifts. Crowding-out from G is offset or reversed by the monetary expansion. Thus no recession is generated.

(ii) Use Mundell-Fleming. Open economy, fixed exchange rate E, no capital mobility. The BP condition is NX(Y,E) + K(r) = 0 with K = 0, so NX(Y,E) = 0, i.e. Y = Y_T, giving a vertical BP curve. G↑ shifts IS right; rr↓ shifts LM right. Both tend to raise Y above Y_T. Then imports exceed exports, causing a BoP deficit. To defend the fixed exchange rate, the central bank sells foreign exchange and buys domestic currency, so H falls. LM shifts left. With no capital mobility, interest cannot attract capital, so adjustment occurs through reserve loss. Final equilibrium restores Y = Y_T. The increase in G raises interest and crowds out investment or consumption, while the fall in rr merely raises the multiplier and forces a larger reserve loss. Output is unchanged relative to the initial trade-balance level, not reduced below it. Hence the policy mix does not generate recession in the standard equilibrium; it mainly causes foreign-reserve depletion and higher interest.

(a) Derive short-run aggregate supply curve following Lucas, when expectations are not realised, assuming that labour market…

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