Aggregation of Fixed Factor Supply
Splitting a fixed supply of a factor between two competitive firms so that their values of marginal product are equal, and finding the market rental rate.
You own all kbar hours of time on the only sound stage in town available and rent them out in a competitive market to two firms, a film producer (firm 1) and an advertising producer (firm 2). Each firm takes the rental rate per hour as given and rents the amount that maximizes its profit, and the rate adjusts until the whole supply is rented. With K hours, firm 1 produces f1 minutes of finished footage per month, which it sells at $p1 per minute, and firm 2 produces f2 finished commercials per month, which it sells at $p2 per commercial; the firms have no other costs that depend on K. The two production functions have different exponents on K. In equilibrium, how many hours does the film producer (firm 1) rent? Round to two decimals.
Use it
from datasets import load_dataset
ds = load_dataset("narunraman/steer_me", "fixed_factor_aggregation")curl "https://steer-benchmark.cs.ubc.ca/api/sample?element_name=fixed_factor_aggregation&n=5&seed=42"
See the Reference for the parameters.