Shephard's Lemma
Finding a firm's cost-minimising labor or capital as the derivative of its cost function with respect to that input's price.
Question template
Consider a bicycle workshop that services racing bikes. The bicycle workshop produces at the lowest possible cost. Its weekly cost, in dollars, of producing Q services when an hour of mechanic labor costs w dollars and an hour of workstand time costs r dollars is C(w, r, Q) = cfunc. The bicycle workshop pays w = $wage and r = $rent and produces Q = output services a week. How many hours of mechanic labor does the bicycle workshop use per week? Round to two decimals.
Use it
from datasets import load_dataset
ds = load_dataset("narunraman/steer_me", "shephards_lemma")curl "https://steer-benchmark.cs.ubc.ca/api/sample?element_name=shephards_lemma&n=5&seed=42"
See the Reference for the parameters.