Automation, Tasks, and Labor Share

This study distinguishes between traditional and automated capital in a task-basedTask-based framework and examines the effects of automation on economic growth and labor shareLabor share. The threshold for automationThreshold for automation is determined endogenously and depends positively on automated capital per labor. Labor share is determined not only by the threshold for automation but also by the elasticity of output with respect to labor. In the derived aggregate production function, total factor productivityTotal Factor Productivity (TFP) (TFP) and the elasticity of aggregate output with respect to production factors depend on the threshold for automationThreshold for automation, and therefore the automated capital per labor. The CES production functionCES production function is obtained using the productivity specifications. The non-arbitrageNon-arbitrage condition between the two types of capital results in the aggregate Cobb–Douglas production functionCobb-Douglas production function. The growth rate and labor share along the balanced growth path (BGP) are derived. When traditional capitalTraditional capital is twice as large as automated capital along the BGP and the traditional capital share is 0.4, the effect of the ratio of traditional capital to automated capital on the growth rate is positive when the elasticity of substitution between automated capital and laborElasticity of substitution between automated capital and labor is greater than 1.6. Then, the labor shareLabor share along the BGP is computed as 0.3.