Entrepreneurs are always arbitraging to take advantage of differences in prices. If prices were lower in states without sales taxes, then entrepreneurs would shift supply toward the higher priced state. The costs of production are not higher in the sales tax state because the sales tax is imputed backward to lower the prices of factors of production. Since it may be that entrepreneurs cannot pay less for materials, then wages would be lower.
These theoretical proposition are difficult to verify with superficial empirical evidence because the “other things equal” condition of the theory is rarely met in the world. Consider the following case, with which I’m familiar. Pennsylvania has no sales tax on clothing. Grove City, Pa. has a large Prime Outlet mall with many name-brand clothing stores. The prices for clothes in these stores are lower than normal retail. But, the reason is not that Rothbard’s analysis is wrong and the lack of sales tax permits lower costs of production and thus, lower prices. It’s because the clothes sold at Grove City Prime Outlets are “seconds,” i.e., clothes returned to other stores and repaired to be resold.
You would have a similar difficulty in empirical investigation of prices at restaurants in the two different states. If prices are lower in Portland, it might be because Vancouver is a more desirable location than Portland and not because Vancouver has a sales tax and Portland does not.