One Shock, Three Schools

In micro, prices moved the moment they were out of line. In macro, how fast prices move is exactly what splits the schools.

A sudden drop in demand leaves output below where it should be. That shortfall is called a gap. Classical economists say prices fall at once and close it. Keynes said prices freeze, so the gap just stays. New Keynesians say prices crawl, so the gap shrinks little by little. The only difference is the speed in the formula below.

For example, say a 🏪 snack bar raises its prices and 🧑 customers vanish overnight. One owner cuts prices again the very next day. Another cannot be bothered reprinting the menu and leaves them for months. A third lowers them a little each week. Customers come back at a different speed for each owner.

gt+1=(1−λ)gtg_{t+1} = (1 - \lambda) g_t
gt=g0(1−λ)tg_t = g_0 (1 - \lambda)^t

Part of these learning paths

Examples & Exercises

A demand shock opens an output gap of −6%-6\%.

In the classical world, where are the gap and the price level (starting at 100100) one period later?

Shock 66, classical (λ=1\lambda = 1).
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  1. The classical school lets prices move instantly (λ=1\lambda = 1). The gap is g1=g0(1−λ)=−6⋅0=0g_1 = g_0 (1 - \lambda) = -6 \cdot 0 = 0 — gone in a single period.

  2. Falling prices filled the whole hole: the price level drops to 100−6=94100 - 6 = 94 and stays there. Prices, not output, absorbed the entire adjustment.

The shock is bigger now, 10%10\%.

In the New Keynesian world, what are the output gap and the price level after two periods?

Shock 1010, New Keynesian (λ=0.4\lambda = 0.4).
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  1. Prices fill 40%40\% of the remaining gap each period, so the gap keeps 0.60.6 of itself: g2=−10⋅0.62=−3.6%g_2 = -10 \cdot 0.6^2 = -3.6\%. Halving the gap takes about 1.41.4 periods.

  2. Prices have fallen by 10⋅(1−0.36)=6.410 \cdot (1 - 0.36) = 6.4 so far, putting the price level at 100−6.4=93.6100 - 6.4 = 93.6. The gap left over, 3.63.6, plus what prices absorbed, 6.46.4, adds back up to exactly the shock, 1010.

1. The Macro Lens