Response of Optimal Labor to the Wage
Finding how a price-taking firm's profit-maximising labor changes with the wage, for a Cobb-Douglas or a Leontief technology.
Amara runs an online course provider that records video lessons. Its weekly output, in lessons, is Q = pfunc, where L is the number of hours of instructor labor and K the number of hours of filming-studio time used per week. Amara sells each lesson for $price, pays a wage of $w per hour of instructor labor and $rent per hour of filming-studio time, and chooses both inputs freely to maximize profit; all markets are competitive. How does the profit-maximizing amount of instructor labor respond to the wage? Writing L*(w) for her profit-maximizing hours of instructor labor per week at a wage of $w per hour, which expression gives dL*/dw?
Use it
from datasets import load_dataset
ds = load_dataset("narunraman/steer_me", "input_price_response")curl "https://steer-benchmark.cs.ubc.ca/api/sample?element_name=input_price_response&n=5&seed=42"
See the Reference for the parameters.