Tangency and the Marginal Rate of Substitution
Using the tangency of the budget line and an indifference curve: the marginal rate of substitution at the optimum equals the price ratio.
Arjun spends $income a year on video games (good x) and cloud storage (good y). Arjun's utility is U(x, y) = ufunc, where x is the number of video games and y the number of terabyte-months of cloud storage per year. The price of video games is $px per game and the price of cloud storage is $py per terabyte-month; both can be bought in any fractional amount. Arjun currently buys xnow video games and ynow terabyte-months of cloud storage, which costs exactly $income. Comparing Arjun's marginal rate of substitution at this bundle with the price ratio, what should Arjun do to raise his utility without spending more?
Use it
from datasets import load_dataset
ds = load_dataset("narunraman/steer_me", "mrs_tangency")curl "https://steer-benchmark.cs.ubc.ca/api/sample?element_name=mrs_tangency&n=5&seed=42"
See the Reference for the parameters.