Abstract
From the perspective of the economics，labour productivity growth has many theoretical research results, however , by mathematical models to analyse conditions of labour productivity growth , both of theoretical assumptions and preconditions are more crude． In this paper by the research of mathematical models of the Chinese labour population growth, the establishment of the Chinese version of the production function Cobb-Douglas and the using of Solow model, we obtain mathematical terms of labor productivity growth． We introduce the impact of the GDP and investment to the growth in labour productivity． It has been concluded that mathematical terms of labor productivity growth, and we use to artificially control labor productivity to grow． When labor productivity appears grown or negative grown, by increasing investment , we make it continue growing． But the growth period depends on incremental investment． Moreover , in the end of the paper we make Matlab achieve in graphics, and vividly describe the impact of investment on labour productivity．
From the existing labour productivity growth conditions, the paper concludes that adjusting of investment can change productivity． This conclusion is compared with the one that the relative growth rate of labour productivity greater than the rate of the initial investment increased the labour productivity． By controlling the investment it makes labour productivity increase, which is more workable and also more meaningful．
Keywords: Productivity，Mode of economic growth, Labor, Invest
