Fig 2a — Worker: Activity Patterns under Transport Stress

File: fig2a_worker.png
Section: §4.1 Behavioral Validation — Toy Case
Layout: 3 rows × 3 panels + 1 full-width V₀ panel

What the Figure Shows

This figure answers: what happens to a worker’s daily activity pattern and welfare when transport becomes more expensive or slower?

Two sensitivity dimensions are shown side by side:

  • Row 0 (top): Cost sensitivity — baseline → cost ×1.58 → cost ×3.0
  • Row 1 (middle): Time sensitivity — baseline → time ×1.20 → time ×2.0
  • Row 2 (bottom): Combined V₀ welfare panel — both cost and time sweeps on one plot

All snapshots are from 300-agent simulations. Panel titles show V₀ (day welfare) and shop rate (fraction of agents making at least one shopping trip).

Baseline Worker (col 0, both rows)

Shop = 38%, V₀ = 177

The baseline worker spends:

  • Morning at home before 8 am
  • Work 8 am–5 pm (orange block dominates)
  • Brief shopping in the late afternoon/evening (small red band)
  • Home by night

The shopping fraction (~38%) reflects the marginally positive net value of a shopping trip (+0.23 utils). This is a fragile equilibrium — small increases in transport cost or time will suppress it.

Row 0 — Cost Sensitivity

Cost ×1.58 (shop = 34%, V₀ = 177)

Travel costs increase by 58%. The shopping band shrinks slightly (38%→34%). The work block is unchanged — workers still commute. V₀ barely moves.

Why: The shopping trip has a net value of only +0.23. A 58% cost increase raises the round-trip travel overhead enough that the net value approaches zero — some agents stop shopping. But work, with a net value of +8.26, is unaffected.

Tipping point: Cost ×1.58 is the shopping tipping point — the level at which shopping net value hits zero. Above this, shopping becomes a net-negative activity for many agents.

Cost ×3.0 (shop = 33%, V₀ = 175)

At triple the travel cost, shopping further drops (to 33%) but persists. The distribution looks visually similar to baseline because most of the agent population has heterogeneous shopping propensities — some have enough leisure time or proximity to sustain shopping even at high cost.

V₀ drops modestly from 177 to 175. Work is completely unaffected — the orange block is identical. The welfare loss comes entirely from suppressed discretionary activity.

Key insight: Workers are cost-resilient because the commute has a large positive net value. Travel cost increases primarily hurt discretionary trips (shopping), not mandatory ones (work). Cost is not the binding constraint for workers.

Row 1 — Time Sensitivity

Time ×1.20 (shop = 24%, V₀ = 175)

Travel times increase by 20%. Shopping drops sharply from 38%→24% — a much larger effect than cost ×1.58 (which only caused 38%→34%). The grey travel bands widen visibly.

Why shopping is more sensitive to time than cost: The shopping trip net value is driven more by time overhead than monetary cost. A 20% time increase erases more net utility than a 58% cost increase. This is because the K=9 utility specification is calibrated with relatively high travel time value.

Tipping point: Time ×1.20 is the shopping time tipping point — comparable to cost ×1.58 for shopping suppression but reached at a much smaller multiplier.

Time ×2.0 (shop = 2%, V₀ = 167)

At double the travel time, shopping is almost entirely suppressed (2%). The grey travel bands are now clearly visible. Workers who do shop face much longer journeys — most agents rationally decide not to bother.

V₀ drops from 177 to 167 — a loss of 10 utils, far larger than any cost scenario. Workers are still commuting (orange block intact) but the commute now consumes significantly more of the day.

Why V₀ drops more for time than cost: The commute to work is non-negotiable for workers. When travel time doubles, the round-trip commute overhead doubles — this directly reduces the on-schedule work utility harvested per day. Cost increases have no such mechanism because transport monetary cost parameters are calibrated at lower levels.

Work tipping point (time ×4.5): Not shown in snapshots but marked in the V₀ panel. At ×4.5 travel time (+350%), even the commute net value (+8.26) goes negative — workers would prefer to stay home. This is the point at which the model predicts commute abandonment.

Row 2 — Combined V₀ Panel

x-axis: % increase from baseline (0% = baseline multiplier ×1.0)
Solid lines: Cost sensitivity
Dashed lines: Time sensitivity
Orange: Worker
Blue: Non-worker (shown for comparison)

Reading the Panel

Orange solid (worker — cost): Nearly flat across 0–500%. V₀ barely falls even at ×3.0 cost (+200%). Workers are cost-insensitive because the mandatory commute and shopping trip economics are dominated by time, not money.

Orange dashed (worker — time): Steep downward slope from +20% onward. By +350% (time ×4.5), worker V₀ has fallen ~50 units. Time is the binding transport constraint for workers — it directly increases commute overhead and suppresses discretionary trips.

Blue solid/dashed (non-worker): Both lines are nearly flat near 172.8 throughout. Non-worker welfare is home-dominant — transport changes barely affect it. This is the correct model prediction: non-workers have no mandatory transport exposure.

Tipping Point Annotations

Annotation What it means
shop time ×1.20 (20%) Shopping net value hits zero under +20% travel time
shop cost ×1.58 (58%) Shopping net value hits zero under +58% travel cost
work time ×4.5 (350%) Commute net value hits zero under ×4.5 travel time
work cost ×11.3 (off scale) Commute net value hits zero under ×11.3 travel cost — cost is very ineffective at suppressing work

The fundamental asymmetry: Time stress is far more dangerous to welfare than cost stress at the same percentage change. Shopping is suppressed at +20% time vs +58% cost. The work tipping time multiplier (×4.5) is less than 1/2 of the cost equivalent (×11.3).

Summary — Worker Story

  1. Mandatory work is robust. A worker’s commute survives large transport stress because its net value (+8.26) is far above zero.
  2. Shopping is fragile. A net value of only +0.23 means shopping is the first casualty of any transport deterioration.
  3. Time matters more than cost. For the same percentage increase, travel time suppresses activity more than monetary cost.
  4. Welfare (V₀) is the unified measure. It correctly captures both effects — the cost-insensitivity of work and the time-sensitivity of the full daily pattern.
  5. Non-workers are unaffected. The contrast (blue vs orange lines) shows that transport stress is a worker problem, not a population-wide welfare issue.