This question bugs for for a long period of time already and finally, I found a place to ask to native speakers.
Consider the following 2 situations:
There are 10 firms. Each of the 10 firms has 5 different products. (Say, product1, produt 2, ..., product 5) Each of the 10 firms sets price for each of the 5 products in each period.
There are 10 firms. Each of the 10 firms has exactly 1 product. (Say, firm 1 - product1, firm2 - produt 2, ..., firm 10 - product 1) Each of the 10 firms sets price for its own only product.
When you say the following sentence "10 firms set their prices in each period", which situation does this sentence describe, 1 or 2? By just reading this sentence, can you guess which situation the write refers to? In my opinion, this sentence includes both situations and just from it you can not deduce exactly which situation the write is referring to.
Would the following sentence be grammatically correct and at the same time precise for describing the first situation?
"10 firms set their price in each period".
Here, I used price in singular form to indicate that one firm sets only one price.
Basically, what I want to understand is when to use firms and prices at the same time and firms and price as the same time and what is difference between these two cases?