Lucas Paradox, Declining Labor Share, Tendency of Rate of Profit to Fall of Karl Marx and Growth Theory of the Firm

Macroeconomic phenomena we observe are supposed to be analogous to conclusions derived from microeconomic models because macroeconomic phenomena are aggregation of data coming from microeconomic events. Since the firm plays the central role to produce output, I use growth theory of the firm to predict macroeconomic phenomena as below. First, the law of diminishing marginal product does not operate although marginal product derived from production function diminishes because the firm increases supply of output by scale growth without change in capital-labor ratio, not by change in capital-labor ratio under fixed scale. Thus, profit rate of rich (capital abundant) country is unnecessarily less than poor (labor abundant) country due to the law of diminishing marginal product so that capital does not outflow from rich country to poor country. Lucas’ paradox is solved. Second, labor share is equal to capital share in the long run if capital and labor can substitute each other perfectly because the optimal capital-labor ratio of the firm is equal to the ratio of wage rate to return rate on capital, K⁄N=w⁄γ. That is, labor is relatively more expensive (less productive) than capital if labor share is greater than 50 percent. Since labor share has been higher than 50 percent of GDP (i.e., there is room to substitute capital for labor) for centuries, growth theory of the firm explains the long term trend of declining labor share. Third, labor share is countercyclical and capital share is cyclical in the short run because the amplitude of investment and profit fluctuation is greater than employment and wage. Fourth, the production function that the firm uses to produce is increasing return to scale, which implies not only cyclical co-movement of investment, employment, productivity and factor prices domestically but also unbalanced trade and factor price differentiation internationally. Fifth, diminishing marginal revenue makes wage growth rate less than growth rate of labor productivity and growth rate of return rate on capital less than growth rate of capital productivity. Sixth, growth theory of the firm asserts principle of acceleration in macroeconomics. Seventh, profit rate rises when GDP grows. Thus, tendency of rate of profit to fall predicted by Karl Marx is wrong. In appendix, I propose to statistically approximate the true production function in real world by Taylor series because production functions economists have ever proposed (e.g., Cobb-Douglas) are not proved to be true by economists.