Can a small country influence prices in the international market? Why? Can a large country influence prices in the international market? Why?

In International Economics, we define a small country as a country whose exports and imports are price taker. What does this mean? It means that the share country's exports and imports have over the total global production of the goods is small, that small that the country cannot influence in any way international prices.

Instead, a large country is not price taker. Indeed, a large country has share on imports and exports that big that can influence prices in the international market.

Of course, here It's key to note that a country may be quite small in what regards total population or total GDP. However, it may be a large country in what respects one specific good.