Kate's Diner offers one breakfast item, a breakfast special. The market price for this meal is $5. At her profit-maximizing level of output, Kate's average variable cost is $4 per meal. Her average total cost is $6 per meal. Since the market is perfectly competitive, Kate should .

keep producing in the short run but exit the industry or go out of business in the long run

Explanation:

A perfect competition is characterised by many buyers and sellers of homogeneous goods and services. Market prices are set by the forces of demand and supply. There are no barriers to entry or exit of firms into the industry.  

In the long run, firms earn zero economic profit.  If in the short run firms are earning economic profit, in the long run firms would enter into the industry. This would drive economic profit to zero.  

Also, if in the short run, firms are earning economic loss, in the long run, firms would exit the industry until economic profit falls to zero.  

A firm should shut down in the short run if price is less than average variable cost. But since the diner's price is greater than average variable cost, it should continue production.

A firm should exit the industry in the long run if price is less than average total cost. the diner's price is less than average total cost, so it should shut down in the long run

years agooo ahaha. but honestly they need to update ! : )