Question

If Country A produces a product that is consumed domestically and that is also exported to another country, free trade will result in the price of that product being the same in both the exporting and the importing countries.

Answer 1

Yes it will.

If trade is free, that means there is no transaction costs or any barriers like tariffs, quotas and so on. Hence, goods can be transferred costlessly.

In this case, if the prices of a good is higher in some country, people will start importing more of the good from the foreign country, where the price is less. And they will then sell it at a higher price in their home country. In this process, they will get a riskless profit which is called arbitrage.

Arbitrage basically means "buy cheap and sell dear"

When goods are in high supply in the country where the prices are high, it will drive down the prices. The country having the lower price will experience excess demand and the prices will rise there. In the end, prices will setlle down somewhere in the middle and it will be equal across countries.