### Even Worse than Paul Krugman Imagines?

Reading Karl Smith’s comment on my previous entry, I started to think about the implications of rational expectations in the context of potential deflation. I’m thinking of a model like “Rational Expectations meets Calvo Pricing meets the Keynesian Multiplier meets the Mundell-Tobin Effect.” It goes something like this:

Start out imagining that prices are stable. Then introduce the expectation of an output gap (like the output gap that the CBO expects). An output gap implies that actual (sticky) prices are above equilibrium (flexible) prices. As more cohorts adjust their prices toward equilibrium levels, actual prices will fall. If you expect actual prices to fall, you have a disincentive from investing, because you have to pay today’s sticky prices for your capital goods, but you will only be able to sell your product at tomorrow’s (lower) flexible prices. So investment will be lower than it otherwise would be. And because of the multiplier effect, consumption will be lower than it otherwise would be.

So overall demand will be significantly lower than it otherwise would be. Therefore equilibrium prices will be even lower. Therefore we have to anticipate an even greater rate of deflation. Therefore we have to anticipate an even larger disincentive from investment, which implies an even lower level of investment, which implies an even lower level of consumption, which implies even less demand, which implies even lower equilibrium prices, which implies even faster deflation, which implies an even greater disincentive from investment, and so on. And all the “so on” is something that, if we have rational expectations, we will immediately anticipate.

Without actually writing down a model (which I’m not going to do), I can’t say for sure whether there will be an equilibrium, but if there is one, I’m pretty sure it is really, really, really ugly. My intuition says that, in an economy without a public sector or a foreign sector, there will normally be no equilibrium, and all production will simply cease.

If you throw in a government, then you can presumably have an equilibrium even without any private investment, so the economy won’t grind completely to a halt, but it will sure look pretty awful. Although I wonder: if the process of selling requires holding inventories, then it requires some investment. (Technically, it requires a level of investment that may not be positive but that can still be reduced if there are incentives to reduce it.) If the disincentive to investment rises without bound, then there will be no incentive to hold inventories, and production will still cease, even with public sector demand.

I would guess that someone has already done this sort of model more rigorously, and I don’t know what the conclusions were. But I would guess that they were quite unpleasant.

Start out imagining that prices are stable. Then introduce the expectation of an output gap (like the output gap that the CBO expects). An output gap implies that actual (sticky) prices are above equilibrium (flexible) prices. As more cohorts adjust their prices toward equilibrium levels, actual prices will fall. If you expect actual prices to fall, you have a disincentive from investing, because you have to pay today’s sticky prices for your capital goods, but you will only be able to sell your product at tomorrow’s (lower) flexible prices. So investment will be lower than it otherwise would be. And because of the multiplier effect, consumption will be lower than it otherwise would be.

So overall demand will be significantly lower than it otherwise would be. Therefore equilibrium prices will be even lower. Therefore we have to anticipate an even greater rate of deflation. Therefore we have to anticipate an even larger disincentive from investment, which implies an even lower level of investment, which implies an even lower level of consumption, which implies even less demand, which implies even lower equilibrium prices, which implies even faster deflation, which implies an even greater disincentive from investment, and so on. And all the “so on” is something that, if we have rational expectations, we will immediately anticipate.

Without actually writing down a model (which I’m not going to do), I can’t say for sure whether there will be an equilibrium, but if there is one, I’m pretty sure it is really, really, really ugly. My intuition says that, in an economy without a public sector or a foreign sector, there will normally be no equilibrium, and all production will simply cease.

If you throw in a government, then you can presumably have an equilibrium even without any private investment, so the economy won’t grind completely to a halt, but it will sure look pretty awful. Although I wonder: if the process of selling requires holding inventories, then it requires some investment. (Technically, it requires a level of investment that may not be positive but that can still be reduced if there are incentives to reduce it.) If the disincentive to investment rises without bound, then there will be no incentive to hold inventories, and production will still cease, even with public sector demand.

I would guess that someone has already done this sort of model more rigorously, and I don’t know what the conclusions were. But I would guess that they were quite unpleasant.