Please keep in mind that there is no such thing as perfect competition in the real world. However, I would say that the closest thing to the situation you describe would occur in the market for various kinds of farm products.
The factor market for these products includes such things as farm labor and fertilizers and seeds. All of these things are commodities that are relatively competitive. They are not all perfectly competitive, but at least the labor market is quite close.
The product market for agricultural goods is about as close any market ever comes to perfect competition.
There are no perfectly competitive markets either for any factor of production or for finished product in any country of the world. But there can be markets that are close to perfect competition.
In factors of production,the market for manpower, particularly the unskilled or semiskilled is nearly competitive in almost all countries of the world. So with unskilled manpower and semiskilled manpower as two factors of production you can name as many countries as you like to get twice the number of examples.
Another example of factor of production with competitive market will be will be the farming land in countries like India and Bangladesh, where average farm land holding is quite low. I believe even in countries like USA with big farms, the number of farms is large enough to consider the market for land as competitive.
In consumer products category most of the commodity products like rice, wheat, sugar, have competitive market in all developing and undeveloped countries (like, say, India, China, Pakistan, and Bangladesh), where there is no branding of such products. If you need more examples, you can easily add many other agricultural products to the small list of three give here.
can you please give two examples of the products and countries?? :)