Halsey 50–50 plan (wage incentive): Given base hourly rate R, standard time S, and actual time T, what is the total wage for the job?

Introduction / Context:
The Halsey 50–50 plan is a classic time-based wage incentive system. It pays a guaranteed time wage for the actual time worked, and then shares the value of the time saved (relative to a pre-set standard) equally between the worker and the employer. Understanding the exact wage formula prevents confusion with similar plans like Rowan or straight piecework.

Given Data / Assumptions:

• Base (time) rate = R currency units per hour.
• Standard time allowed for the job = S hours.
• Actual time taken by the worker = T hours.
• “50–50” means 50% sharing of time-saved value with the worker.

Concept / Approach:
Time saved equals S − T (if T < S). Under Halsey 50–50, the bonus equals 0.5 * (S − T) * R. Total wage is the time wage for actual hours plus the bonus. This is different from the Rowan plan, which scales the bonus as a fraction of standard time (proportional to T / S).

Step-by-Step Solution:

Verification / Alternative check:
If T = S (no saving), bonus is zero and pay reduces to TR. If T is much smaller than S, the worker earns a greater bonus but still shares only half the saving value, aligning incentives and cost control.

Why Other Options Are Wrong:

• TR: Ignores incentive; this is guaranteed pay only.
• TR + (S − T)R: Gives 100% of saving to the worker; not Halsey 50–50.
• TR * [1 + (S − T)/S]: This is the Rowan form, not Halsey.
• R * S: Pays for standard time regardless of actual effort; not this plan.

Common Pitfalls:
Confusing Halsey with Rowan; forgetting to multiply time saved by the base rate R; applying the formula when T ≥ S (then bonus should be zero).

Final Answer:
TR + 0.5 * (S - T) * R