(a) Show that differences in underlying expectation lead to differences in Keynesian and classical aggregate supply curve. (15…

(a) Expectations and the aggregate supply curve. Suppose the nominal wage is set to clear the labour market at the expected price level, W = W(P^e), while firms hire until W/P equals the marginal product of labour. Output then behaves as Y = Y* + α(P − P^e). In the classical view, expectations are correct (P^e = P, perfect foresight), so nominal wages move one-for-one with prices, the real wage W/P stays at its market-clearing level, employment and output remain at the natural level Y*, and AS is vertical. In the Keynesian view, the expected price level, and with it the money wage, is fixed in the short run by contracts and wage rigidity. A rise in P above P^e lowers the real wage, so firms hire more and output rises: AS slopes upward, being nearly flat when unemployment is heavy and steepening as capacity is approached. The same labour-market logic thus gives different AS curves only because of different expectations: P^e = P in the classical case, P^e fixed in the Keynesian.

(b) Liquidity preference and the interest rate. Money is demanded for transactions, precautionary and speculative motives, so real money demand is L(Y, r), rising with Y and falling with r. The money supply M/P is fixed by the central bank, a vertical line in the (M, r) diagram. If M rises, then at the initial rate r₀ people hold more money than they wish; they use the excess to buy bonds, which raises bond prices and lowers yields. The rate falls until money demand has risen to equal the new supply; the lower opportunity cost of holding money makes people willing to hold it. In India, an RBI open-market purchase of government securities works through this channel. The explanation assumes that the price level is fixed (or sticky) in the short run, so that a higher nominal M means higher real balances M/P. If prices rose in proportion, M/P and the rate would be unchanged. In a liquidity trap, at a very low rate, demand for money is infinitely elastic and extra money does not lower the rate.

(c) Regressive expectations and Keynes's speculative demand. Keynes treated money as a store of value held for speculation. An investor compares the current rate r with the "normal" rate r̄ to which he expects it to return; this is a regressive expectation, r^e = r + θ(r̄ − r) with 0 < θ ≤ 1. For a perpetuity, the expected capital gain is g = r/r^e − 1, which equals (r − r̄)/r̄ if θ = 1. Bonds are held only if r + g > 0, that is, if r exceeds the critical rate r_c = r̄/(1 + r̄); below it, all wealth is held as money. The model exposes several weaknesses. First, the choice is all-or-nothing: an individual holds either only money or only bonds, never a mix, so individual demand is a step function and contradicts the fact that people hold both. Second, a smooth aggregate demand curve arises only if investors differ in their r̄, not from individual behaviour. Third, the expected gain is treated as certain, so risk is ignored; Tobin (1958) showed that risk-averse investors diversify, giving a smooth, downward-sloping L(r) from the risk–return trade-off. Fourth, r̄ is exogenous and fixed; if actual rates stay away from it, r̄ itself shifts, so the demand function is unstable.