← 2. Aggregate Demand and Supply

Exercises

Problems to check your understanding of this chapter. The solutions are folded away — try them yourself first.

Medium

1Medium

The money supply stays at M=100M = 100, but the price level rises from P=1P = 1 to P=2P = 2.

How much does each of the wealth, interest-rate, and exchange-rate channels cut aggregate demand, and what does YY become?

Price level 22, money 100100 — the point where all three channels are negative.
Show solution

  1. Real balances are M/P=100/2=50M/P = 100 / 2 = 50, so the gap is Δ=−50\Delta = -50 below the baseline of 100100.

  2. The channels split by their weights: wealth 0.3×(−50)=−150.3 \times (-50) = -15, interest 0.5×(−50)=−250.5 \times (-50) = -25, exchange rate 0.2×(−50)=−100.2 \times (-50) = -10. The total is −50-50.

  3. So Y=1000−50=950Y = 1000 - 50 = 950. Higher prices made every wallet lighter, and that lightness trims spending through all three channels.

Hard

2Hard

A bigger supply shock lifts the short-run supply curve by 33 (shock size 3030).

Find the short-run equilibrium output and price level.

Then explain what happens to prices if the central bank expands aggregate demand to defend output, and what ultimately remains in the long run in this model.

Supply shock of size 3030 (the curve lifts by +3+3), year 00 — Y=90Y = 90, P=12P = 12.
Show solution

  1. Short-run supply is P=10+0.1 (Y−100)+3P = 10 + 0.1\,(Y - 100) + 3 and aggregate demand is Y=150−5PY = 150 - 5P. Solving the pair gives Y=90Y = 90, P=12P = 12 — output down 1010, prices up 22: stagflation.

  2. Expanding demand shifts the AD curve right and pulls output back toward its natural level, but the price level climbs even higher than 1212. Facing a supply shock means giving up one of the two: output or stable prices.

  3. The long run is calmer. This shock halves every year and expected prices settle back, so the economy ends at Y=100Y = 100, P=10P = 10 — a temporary supply shock leaves no long-run trace.