1. Observer-relative accounting
ρᴾ = a / b ρᶠ = (a − f) / (b + f) gap = f(a+b) / (b(b+f))
Same hour of work, two valid bookkeepings. a is overhead the person counts, b is real output the person values, f is the facade portion of a the firm folds into output. The wedge is the gap between the two ratios — large enough to make the person's dashboard red while the firm's stays green.
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2. Hedonic decay
m(t) = m∞ + (1 − m∞)·e^(−t/τₘ) ⇒ ρᴾ(t) = ρ₀ / m(t)
Same desk, same hours, less will to start the day. The numerator (overhead) did not change; the denominator (perceived output value) did. A multiplier m(t) decays from 1 toward a job-match floor m∞ on time scale τₘ. Under realistic parameters, a new job at ρ₀ = 0.6 (well in the safe zone) can drift past ρ* purely because the pride-and-novelty multiplier collapses.
3. Population sigmoid B(t)
B(t) = Φ( (μ₀ + δ·t − μ*) / √(σ² + σ*²) )
Lift from individual to population. With heterogeneous drift (within-person spread σ) and heterogeneous threshold (between-person spread σ*), the burnout fraction follows a sigmoid in time. δ is cohort-mean log-ρ drift per week, μ* is the median log-threshold. The dot marks the chosen observation time.
4. Optimal stopping (Charnov MVT)
u(t) = u₀·m(t) A(T) = (1/(s+T))·∫₀ᵀ u(τ)dτ ⇒ quit at u(t*) = A(t*)
Given the decay is real, when exactly should you quit? Charnov's Marginal Value Theorem (1976), originally for birds foraging in a patch: leave the current patch when its current intake rate equals the long-run average rate over the cycle of search-plus-forage. Same equation governs jobs. s is the search / transition cost in weeks; current utility u(t) decays with m(t). The intersection marks t*.
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Paper PDFs:
unified (v4 + 4 mechanisms)
· v4 — optimal stopping
· v3 — hedonic decay
· v2 — observer + heterogeneity
· v1 — ratio
Figures source: code/burnout
· LaTeX: sources/burnout-paper.tex