Elasticity of Substitution
Computing the elasticity of substitution of a CES technology from its function, from two cost-minimising input ratios, or using it to predict how the input ratio responds to a wage rise.
Arjun runs a recycling plant that turns plastic waste into pellets. Its weekly output, in tonnes of pellets, is Q = (a * L^ρ + b * K^ρ)^(1/ρ) with params, where L is the number of hours of sorter labor and K the number of hours of shredder time used per week. Arjun pays $wage per hour of sorter labor and $rent per hour of shredder time and chooses the input mix that minimizes cost. If the wage rises by x% and the rental rate stays the same, by what percentage does the cost-minimizing number of hours of shredder time per hour of sorter labor (K/L) change? Round to two decimals.
Use it
from datasets import load_dataset
ds = load_dataset("narunraman/steer_me", "elasticity_of_substitution")curl "https://steer-benchmark.cs.ubc.ca/api/sample?element_name=elasticity_of_substitution&n=5&seed=42"
See the Reference for the parameters.