The sky cannot be both red and blue at the same time. It is, by the standards of physics, impossible. One could argue that both red and blue could be in the sky at the same time, but the second the two overlap, the color magenta takes both their places. Just as an item cannot be both a square and a circle, or water cannot be both frozen and liquid, an economy cannot be both socialist and capitalist at the same time. By the standards of capitalism, there is no government involvement, or rather, industry and trade are privately controlled. By the standards of socialism, the government owns and controls the means of production in all forms. While many proffer that socialism can also be a form of two private entities controlling the means of production, there is, inevitably, the government will still have control over said entity. Technically, socialism and capitalism do coexist. There are (few) countries that are undoubtedly capitalist and there are (many) countries that are socialist. But, seeing as I do not believe that is what the question pertains to (whether or not both are in existence, rather, if both can exist in one economy), I will undoubtedly disagree that an economy can both be socialist and capitalist. It is true, that an economy can borrow multiple aspects from each economic theory, but once combined, an entirely different monster is created from it. Furthermore, it is ill-advised to have capitalism and socialism existing in the same economy, as one will indefinitely dominate the other, causing the supporters of the dominated theory to use radical means of revolt. Socialism and Capitalism cannot exist in the same economy, if you want that economy to thrive.