In perfect competition, the firm is a price taker. It must charge the same price as everyone else in the market. This means that it can make no economic profit. It also means that the price for its products does not change with the quantity that is produced. In other market structures, prices change with quantity produced. This is how you can tell that this firm is in perfect competition. You can see that its marginal revenue is the same for every extra 100 kg that it produces. This means that it is charging the same price at every level of output.
In this table, then, you can see that the price is always $.48 per kg and the marginal revenue is always $.48 per kg. This shows that the firm is in perfect competition.