Suppose in a purely competitive market that American firms consider labor costs to be mostly variable while Japanese firms consider labor costs to be mostly fixed

What implication would this have for the viability of firms in each country if they compete with one another in the short run? What about the long run?

In the short run this might give the Japanese firms an advantage in that if prices fall below their average total costs but still remain above their average variable cost that they may be able to continue to enjoy an operating profit. However, if this price is below the average variable cost of the American firms it will likely lead them to shut down in the short run. However, in the long run the difference in the composition of variable and fixed costs of firms is not going to make any difference so long as the average total cost of production are the same.