1. In the 1940s, Franco Modigliani showed that this kind of argument required infinite liquidity preference, not just very strong liquidity preference. This kind of discontinuity matters in most models with liquidity preference.
2. The model suggests that negative supply shocks don’t hurt the economy yet the Dust Bowl was bad for aggregate output. Arguably the AD curve should be kinked and vertical only after some inflection point. But then we are back to negative supply shocks mattering.
3. The model implies that labor unions won’t hurt output but the model does not show that labor unions won’t hurt employment and indeed the latter question was the original point of contention. A sufficiently high legally binding minimum wage will cause employers to lay off workers, vertical AD curve or not. Maybe capital substitutes for labor or Y stays put for some other reason but employment will go down.
4. I no longer understand Krugman’s overall story. He notes that the New Deal years saw a good bit of recovery (I agree), he notes that fiscal policy was not very expansionary (I agree), he believes there was a liquidity trap (I don’t agree), and he believes that positive supply shocks run up against a more or less vertical AD curve and thus don’t help output (I don’t agree). Given all of Krugman’s views, AS doesn’t much matter and AD didn’t much expand. So what exactly drove the (partial) recovery of the 1930s?
Maybe I am taking the model too literally but without the vertical AD curve there is not much else in the model to interpret.