School Funding & Class-Size Policy Lab

Policy Levers

Per-pupil funding $10,000

Class-size cap 22 students/teacher

Teacher salary $58,000

Support-program share 15%

District Outcomes

Achievement score

50.0

Teachers needed

Est. dropout rate

9.0%

Materials budget/pupil

$3,364

How it works

840 students are fixed. Raising the class-size cap needs fewer teachers for the same students, which frees more of the per-pupil budget for materials and support — but research on class size (e.g. Tennessee's STAR experiment) finds a real, if modest, achievement cost to bigger classes. The model:

teachers      = ceil(students / classSize)
salaryCost/pupil = salary / classSize
materials/pupil  = funding − salaryCost/pupil   (deficit if negative)
general   = materials × (1 − supportShare)
support   = materials × supportShare

classEffect   = clamp(−1.2×(classSize−15), −18, +6)
fundingEffect = 18 × (1 − e^(−general/3000))      // diminishing returns
teacherEffect = 14 × sqrt(clamp((salary−30000)/60000, 0, 1))
supportEffect =  8 × (1 − e^(−support/1500))

achievement = clamp(50 + classEffect + fundingEffect
                     + teacherEffect + supportEffect, 0, 100)
dropout% = clamp(20 − 0.15×achievement − 7×(support/1500)
                  + 0.2×max(0, classSize−20), 1, 28)

Funding & teacher salary both show diminishing marginal returns — the first dollars help far more than the last, matching the broad finding across school-finance studies that spending effects saturate.
Support-program share reallocates part of the materials budget toward interventions for at-risk students: it barely lifts the headline score but meaningfully cuts dropout.
Each classroom cluster in the 3D view is colored by its own noisy draw around the district-wide achievement score — real schools vary around the average even under one policy.
If salaries + class size push salary cost above the funding cap, the district runs a materials deficit (shown in red) — an unfunded mandate.

Low achievement Mid achievement High achievement Teacher

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