(a) Compare and contrast Marshallian and Walrasian approaches of the stability in equilibrium. (10 marks) (b) Using generalised…

(a) Marshallian and Walrasian stability. Marshallian stability is a partial-equilibrium, quantity-adjustment test: if the demand price exceeds the supply price at current output, firms expand output, otherwise they contract, dq/dt = λ[P_d(q) − P_s(q)]. Equilibrium is stable if (P_d − P_s) falls as q rises, i.e. demand cuts supply from above in the price–quantity diagram. Walrasian stability is a price-adjustment test: price rises where excess demand is positive and falls where it is negative, dp/dt = λZ(p); in one market it requires dZ/dp < 0, and in many markets, under tâtonnement, the Jacobian of Z must have eigenvalues with negative real parts (gross substitutability guarantees global stability). For downward-sloping demand and upward-sloping supply the two criteria agree. They diverge when supply is negatively sloped: a configuration that is Marshall-stable is then Walras-unstable, and vice versa.

(b) Generalised Lorenz dominance and welfare. The generalised Lorenz curve is GL(p) = μ·L(p), the average income per head of the bottom p share of the population, where L is the ordinary Lorenz curve and μ the mean. Shorrocks (1983) showed that if GL_A(p) ≥ GL_B(p) for every p, with strict inequality somewhere, then W_A > W_B for every social welfare function that is increasing in incomes, symmetric and Schur-concave (inequality-averse). For equal means, GL dominance reduces to Lorenz dominance, and A's Lorenz curve lies above B's exactly when A can be reached from B by Pigou–Dalton transfers from richer to poorer; each such transfer raises a concave welfare function. Equivalently, with the Atkinson index, W = μ(1 − I_ε), so for the same μ lower inequality means higher welfare. Hence lower inequality, with no loss of mean, is a higher welfare state; if Lorenz curves cross, no unambiguous ranking exists.

(c) Business cycle and autonomous expenditure. Autonomous expenditure (autonomous investment, government spending, exports) is independent of current income and fixes equilibrium output, Y* = A/(1 − c). A change in A shifts aggregate demand and output moves by ΔA/(1 − c), the multiplier effect. In the Samuelson–Hicks model, Yₜ = (c + v)Yₜ₋₁ − vYₜ₋₂ + A, so the accelerator v makes induced investment respond to the change in output, and the multiplier–accelerator interaction turns a one-time shift into a cycle. The roots of λ² − (c + v)λ + v = 0 are complex when (c + v)² < 4v, giving oscillation that is damped if v < 1 and explosive if v > 1; with real roots the path is non-cyclical. A rise in A drives the expansion, a fall drives contraction, and because autonomous investment is volatile (Keynes's "animal spirits"), repeated changes in A keep the cycle alive.

(d) Crowding out. No; crowding out is conditional. Deficit-financed spending shifts IS right; along an upward-sloping LM the interest rate rises and private investment falls. The degree depends on the slope of LM and the interest-sensitivity of investment: with a vertical LM, crowding out is complete; with a horizontal LM (liquidity trap) it is nil. With idle capacity and an accommodating central bank, the rate hardly moves, and public investment in infrastructure can even crowd in private investment by raising expected returns. Under Ricardian equivalence, households save the extra income to pay future taxes, so interest rates need not rise. In an open economy with floating rates, a higher interest rate appreciates the currency and crowds out net exports instead. Crowding out is thus strongest near full employment with tight liquidity, and weak in a slump.

(e) IS slope and taxes. False. The first half of the statement is wrong; the second half is right. Let C = a + c(Y − T0 − tY) and I = I0 − br. Then Y[1 − c(1 − t)] = a − cT0 + I0 + G − br, so the IS curve is r = (a − cT0 + I0 + G)/b − {[1 − c(1 − t)]/b}·Y, with slope dr/dY = −[1 − c(1 − t)]/b. A cut in the proportional rate t raises c(1 − t), lowers 1 − c(1 − t), and so the absolute slope falls: IS becomes flatter (the multiplier 1/[1 − c(1 − t)] rises), not steeper. A cut in the lump-sum tax T0 only raises the intercept, shifting IS rightwards in parallel and leaving the slope unchanged.