The Delhi School problems

1. Write each market’s equilibrium in letters, then substitute. Solve LM for r and put it into IS, as in Lesson 4; the multipliers fall out.
2. For “which way” questions, differentiate and sign. Most options differ only in a sign or in which parameter is in the denominator.
3. Check the extremes. Let a parameter go to zero or infinity and see which option gives the textbook answer (a vertical LM, a liquidity trap). Wrong options usually fail one of these checks.

Other questions in this part turn on one slope. In DSE 2011’s model, a more interest-sensitive money demand (m₂ more negative) means a flatter LM and a smaller rise in r when G rises, and with c₁ near 1 (a flat IS) more money barely lowers r. An endogenous money supply that rises with the interest rate flattens LM and strengthens fiscal policy (DSE 2008, 2013). With the central bank targeting the interest rate, a higher target lowers output (DSE 2020), and AD becomes vertical (DSE 2018).

The Delhi School likes to build the AS curve from a labour market and ask how it changes shape. The set from 2004, repeated in 2017, is the classic. Without a floor, the market clears at w = ½ whatever P is, so employment is ½ and AS is vertical at f(½). With a floor W₀ on the money wage:

So AS slopes up at low price levels and turns vertical at P = 2W₀. With IS–LM demand, a monetary expansion raises P and does not lower output (it raises it while the floor binds), and a fiscal contraction lowers P and does not raise output. A higher floor shifts AS left (DSE 2017).

DSE 2010 used a linear technology, Y = αK + βL, with a fixed money wage. Then labour demand is all-or-nothing at W/P = β: firms hire nobody if P < W/β and as many as will work if P > W/β, when employment is labour supply −γ + δW/P, which falls as P rises. The short-run AS is vertical at low P, downward sloping in the middle, and vertical again at high P, where labour supply falls to zero.

The questions on this part now sit in Lesson 12 of the inflation module, with a workbench for the four wage-setting rules. The summary below stays here because it belongs to the AD–AS story.

The natural rate is where expectations are met, π = π^e: (1 + μ)F(u_n, A) = 1. A higher mark-up needs a lower F, so a higher u_n; so does higher productivity, in this set-up, since F rises with A. With F = A/u − 1, the NAIRU is u = A(1 + μ)/(2 + μ), and if A grows at γ, unemployment must grow at γ to keep inflation steady.

In the linear forms (DSE 2019, 2020) productivity drops out when it scales both relations equally, so it has no effect on the natural rate. If wage-setting is W/Pᵉ = A^α(1 − u)^1−α while price-setting gives A/(1 + μ), a rise in A lowers unemployment (DSE 2020): only part of productivity feeds into wage claims. And with π_t − π_t−1 = 0.1 − 3u_t, holding u at 3% adds a point of inflation every year (DSE 2021), Lesson 7’s lab.

The Mundell–Fleming questions are Lesson 9’s results in letters. With a floating rate and perfect mobility, a rise in lump-sum taxes leaves GDP and the interest rate unchanged and depreciates the currency (DSE 2007); a rise in foreign income leaves output unchanged (DSE 2006); and higher government spending on imported goods changes neither output nor the interest rate (DSE 2021). In DSE 2009’s model, IS slopes down and LM is vertical in (Y, e); a higher world rate shifts IS left and LM right; and a higher price level lowers Y and raises e.

DSE 2012 built a model from pieces over four questions: the goods market as a schedule in output and the real exchange rate, whose slope depends on the Marshall–Lerner condition; an asset-market and interest-parity schedule; and how G and M move their crossing.