Productivity naturally has profit based impacts from an overall point of view.  Businesses that are producing a great deal are probably doing so because of the meeting of a demand in the marketplace.  This helps during competitive times because it reflects that the consumer is favoring said product and company. I think that productivity is vital during an economic slowdown because capitalism is a system predicated upon booms and busts.  The cyclical nature of capitalism invariably ensures that there will be trying times.  Businesses that do not produce during economic slowdowns will be ones whose engines will go off the tracks and shut down during these times. One cannot expect to survive in a capitalist setting if they do not envision the emergence of productivity during slow times.  This makes it imperative for businesses to produce in order to endure the trying times and eventually triumph over time.  The most valid and strong enterprises are the ones who can succeed in both the bear and the bull markets.

Productivity is always important for a firm.  But I suppose that you could say that it is especially important if the firm faces competition (as most firms do) and during an economic slowdown.

The reason for this is that productivity increases profit.  Whenever productivity rises, a firm's average total costs go down and profits go up.  Alternatively, when average total costs go down, a firm can lower their prices.  This second one, especially, is important in competition and economic slowdown.  In both cases, it is important to be able to lower prices without losing profit.