This dissertation revisits the long-standing debate on the Marxian falling-rate-of-profit hypothesis---rising organic composition of capital leads to lower profitability. On the theoretical front, I construct a Marxian input-output model that considers the turnover of capital, which has long been neglected by the input-output literature. Within this framework, I generalize the Fundamental Marxian Theorem, the Okishio Theorem, and some other well-known propositions in the literature. However, the falling-rate-of-profit hypothesis is found to be theoretically indeterminate; in particular, the determinate result as obtained by Laibman (1982) is overturned. On the empirical front, I first apply the structural vector autoregression method on annual time series data of the United States for the period 1929--2019. I find no significant long-run effect of the organic composition of capital on profitability, regardless of how the rate of profit and organic composition of capital are measured. I then apply the difference and system generalized method of moments on a large cross-country industry-level panel dataset derived from the World Input-Output Database for the period 2001--2014. The finding is mixed: If the organic composition of capital is measured in nominal terms, it is found to have significant long-run negative effect on the rate of profit; if it is measured in real terms, the effect is instead significantly positive.