[QuesnayJr]

In Arrow's version the inputs are continuous rather than discrete, so I don't know if NP-hard is the right criterion. There is a discrete version that is NP-hard, but I'm not sure you even have existence for that case. The continuous version of general equilibrium is as hard as solving an arbitrary continuous system of equations, which is probably pretty hard.

There are a bunch of criticisms of general equilibrium. Some of these were begun by Arrow himself. If you have prices that are out of equilibrium, can you adjust them to be in equilibrium? If you see the whole demand curve, then you could. But imagine you just know that there is unfulfilled demand for some goods, and excess supply for other goods. If you just make small adjustments in prices to lower excess demand or supply, will you eventually converge on market-clearing prices? Arrow showed that the answer is: it depends.