Doing A means B says that if you do A then B happens. So If I walk to the shop, I will be at the shop. But, I cannot say that if I am at the shop, I must have walked there. So Doing A means B & Doing B means A say different things, in general. As an example, I could discount the cost of goods, so that would make the second sentence questionable, while the first sentence remains correct.

Yes, but the second sentence should start like this, "They realized that to increase purchasing power, wages and salaries must be raised."