Final answer:
Growth in labor productivity is dependent on the growth in total factor productivity (TFP) and the growth in the capital-labor ratio (K/L), formalized by the equation δ(Y/L)/(Y/L) ≈ δA/A + α×(δ(K/L)/(K/L)). This represents that any increase in output per worker is influenced by technological advancements and capital intensification.
Step-by-step explanation:
The growth in labor productivity can be understood by looking at the growth-accounting equation, which suggests that this growth depends on both growth in total factor productivity (TFP) and growth in the capital-labor ratio (K/L). According to this model, labor productivity (Y/L) increases when either TFP (A) or capital per worker (K/L) increases. Using the mathematical relationship that the growth rate of a product is approximately the sum of the growth rates of its factors, we can formalize this relationship as:
δ(Y/L)/(Y/L) ≈ δA/A + α×(δ(K/L)/(K/L))
This equation indicates that the percent change in productivity equals the percent change in TFP plus the contribution of percent change in capital intensity, which is represented by the parameter α (the output elasticity of capital).
Here, δ(Y/L) represents the change in labor productivity, δA symbolizes the change in TFP, and δ(K/L) denotes the change in the capital-labor ratio. The symbol α represents the share of output that is attributed to capital in the production process (α is typically less than one).
To summarize, the growth in labor productivity depends on improvements in efficiency and technology (TFP) as well as increases in capital relative to labor (capital deepening).