Factor Shares in Equilibrium
Computing labor's or capital's share of total factor payments when each input is paid the value of its marginal product.
Arjun runs a recycling plant that turns plastic waste into pellets. The recycling plant has a linear technology: its weekly output, in tonnes of pellets, is Q = pfunc, where L is the number of hours of sorter labor and K the number of hours of shredder time used per week. Arjun sells each tonne of pellets for $price and uses labor hours of sorter labor and capital hours of shredder time a week. The input markets are competitive, and each input is paid the value of its marginal product: the wage w per hour of sorter labor equals the price times the marginal product of labor, and the rental rate r per hour of shredder time equals the price times the marginal product of capital. What share of the total payments to the two inputs, wL + rK, goes to shredder time? Give the percentage, rounded to two decimals.
Use it
from datasets import load_dataset
ds = load_dataset("narunraman/steer_me", "factor_shares_equilibrium")curl "https://steer-benchmark.cs.ubc.ca/api/sample?element_name=factor_shares_equilibrium&n=5&seed=42"
See the Reference for the parameters.