Maybe not double but certainly increase sharply. It doesn't matter if a price is high if your wage rises with it. Money doesn't have any other value than what men put on it. With internal trade, prices will not rise beyond the prevailing wage. The market forces will keep the two in line. Job abundance and relative worker scarcity will keep the wages in line with prices.
We don't have to wonder about this process. It has already worked. What's the point of changing it? 
So, sneakers double in price and my salary will increase sharply? Why? Does my employer have to boost my salary to stay competitive with sneaker makers?
With internal trade, prices will not rise beyond the prevailing wage.
Why? How much will these American shoe makers pull down in salary? $6 an hour? $20 an hour?
Job abundance and relative worker scarcity will keep the wages in line with prices.
So, salaries double, prices double, how is that not 100% inflation? How does that not destroy 50% of our savings?