If there are two countries that produces two goods, X & Y, and for both countries Y is more capital intensive and X is more labor intensive, and one of the countries decides to export Y and import X without completely specializing, is there any way we can determine which country has a higher autarky price ratio without any numbers?

My thought process is initially no. Without any numbers, even telling us what one country does when it trades, doesn't matter because we're trying to determine autarky price ratio. However, I also think it may be possible somehow. Like there could be a possibility that the country we're given information about, maybe they don't completely specialize since the amount of X the other country produces is not enough? If thats the case, can't we automatically assume that the given country produces more than the other country in both X and Y, so therefore their price ratio is... I don't exactly know but thats what I'm thinking. Let me know if I'm on the right track or not please! Thanks.