Quantitative analysis on L.-K. Hua's input-output model

In his celebrating input-output model, Loo-Keng Hua's revealed a profound and original economic phenomena, which indicated that eventually there existed at least one product used up. This was called the 'collapse' theorem. Mu-Fa Chen gave a Markov chain proof for the 'collapse' theorem. In this paper, we found a new and equivalent quantity description of the collapse, from which we gave the quantity estimate for the upper bound of the collapse time. The method was to use the strong ergodicity for the Markov chain. The absorbing Markov chain was introduced to describe the input-output model with consumption, and the continuous-time evolution equation was also presented to settle the real production process.