Commute vs Core
Alonso-Muth-Mills spatial economics: housing gets cheaper the further out you go, but commuting gets costlier. The optimal location is the bottom of the U-shaped total cost curve.
All figures are in today's money: every rate on this page is real, i.e. above inflation. Why?
Housing Market
5%/km exponential drop from centre.
Commuting Mechanics
Gas + wear & tear, or ticket equivalent.
Try 4 for hybrid: the optimal location shifts far outward.
Fixed costs incurred when living outside center (e.g. errands, weekend trips).
Value of Time
Standard range: an hour off is worth somewhat less than an hour of work.
Your Location
| Metric | Value |
|---|---|
| Optimal Distance vs your 15 km | 27 km |
| Monthly Cost Gap above optimal | €136 |
| Hours Lost / Month round-trip commute time | 13.7 h |
| Direct Cash Outflow (Rent + Transport only, ignores time value) | €1,399 |
Alonso-Muth-Mills Cost Curve
Monthly cost (€) by distance from centre. The U-shape forms where the falling rent line meets the rising commuting cost.
- Optimal: Reference line: Optimal.
- You: You: a labelled point on the path.
- Bid-Rent Theory: the optimal location (the curve's minimum) is where the marginal rent saving exactly equals the marginal commuting cost increase.
- True hourly rate (three-location card): money left after housing and commute cash, divided by every hour the job costs you: paid work hours plus unpaid round-trip commute time: (net income − rent − commute cash) ÷ (work hours + commute hours). Work hours are 8 hours on every paid working day, about 19.6 a month (47 working weeks a year), or your 16 commuting days if that is more, giving 157 h/mo: a day worked from home is still paid. Core city (0 km) pays the full centre rent but loses zero hours to commuting; You is wherever you actually live; Optimal is the U-curve minimum itself, so unlike You and Core, its distance (and therefore its true hourly figure) moves when you change Time value, because Time value shapes where that minimum sits. Time value plays no other part in any of the three figures: commute hours sit in the denominator as unpaid hours the job costs you, valued at zero per hour, never at your Time value.
- Wage of the train seat: literally what your time on that train is worth. Commute time itself earns no salary, only the cost it lets you avoid. Expressed as a share of your derived €31.91/hr rate, this is also the old time-value break-even point: commuting pays off below 251.6% time value and stops paying off above it. Time value is currently set to 75%.
- Remote Work's impact: Lower "Days commuting" from 16 down to 4. The commuting cost line flattens dramatically and the Optimal marker slides far to the right. This is the spatial-economics explanation for why remote work has structurally decentralised cities since 2020.
Rent by distance
rent(d) = 2,500 × e^(−decay × d)
- d: one-way distance from the centre, km
- decay: rentDecay / 100 (or the auto-calculated rate)
Auto-calculated decay rate (only when "Auto-calculate decay rate" is on; otherwise rentDecay above is used as typed)
decayPct = −ln(1,200 ÷ coreRent) ÷ 20 × 100
- outerRent: rent observed at the outer reference point
- outerDistance: distance of that reference point, km
Commuting cost by distance
transport(d) = d × 0.35 × 2 × 16 + (d > 0 ? 50 : 0) timeHrs(d) = (d ÷ 35) × 2 × 16 commute(d) = transport(d) + timeHrs(d) × hourlyRate × timeValuePct / 100
- commuteCostKm: cash cost per km
- daysPerMonth: commuting days per month
- commuteSpeed: door-to-door speed, km/h
- transportOverhead: fixed monthly cost incurred once you live outside the centre
- hourlyRate: see Hourly rate below
Hourly rate
hourlyRate = 5,000 ÷ (max(daysPerMonth, 47 × 5 ÷ 12) × 8)
- monthlyNetIncome: monthly net income
- daysPerMonth: commuting days per month; only counts once it exceeds an average month of working days
- 47 × 5 ÷ 12: ≈ 19.6 paid working days in an average month (47 working weeks a year)
Total cost and the optimal location
- rent(d): see Rent by distance above
- commute(d): see Commuting cost by distance above
- optD: an optimum at 50 km means 50 km or further, because the sweep stops there
Wage of the train seat
- core.rent: rent(0)
- you.rent: rent(userDistance)
- you.transport: transport(userDistance)
- you.timeHrs: timeHrs(userDistance)
Assumptions behind every figure: how this site models the market →
Every model leaves things out. Here is what this one does not see:
- Fatigue, delay and the days you simply cannot make the trip. The time cost here is average minutes, not the 90th-percentile morning.
- Career visibility and promotion pace: being near the office for spontaneous facetime, after-work events and simply "being in the room" is not priced. Living further out scores as costless on this axis, when in many career tracks it isn't.
- The cumulative physical and mental toll of a long daily commute (stress, lost sleep, lost exercise time) has no line item. Only the minutes are converted to money, not the wear on the body doing them.
- The exponential rent-decay curve is a smooth citywide average; real neighbourhoods have their own micro-markets (a good school, a subway stop, a noisy road) that don't sit exactly on any curve, so the single "optimal km" this model prints is more precise than any real housing market can deliver.