Cartography and Economic Reasoning: A Map That Misleads
A geography class receives two maps of the same region (population 4 million). Map A is a choropleth shading each district by total population; the largest district by area (a sparsely populated mountain district, 3,000 km², 80,000 people) appears darkest because it has the biggest absolute number of residents, while a tiny coastal district (200 km², 600,000 people) appears pale. Map B shades by population density. A student concludes from Map A that 'the mountain district is the most crowded and needs the most schools.' The teacher also asks the class to connect this to an economic concept: how should a planner allocate a fixed budget of 50 schools across districts using density and need, not raw totals?
1. Explain why Map A misleads, using the concepts of choropleth mapping, absolute vs. relative values, and the modifiable areal unit problem (MAUP). Compute the densities of the two districts to support your answer.
Read the worked answer
Density computation:
- Mountain district: 80,000 ÷ 3,000 km² = ≈ 26.7 people/km² (very sparse).
- Coastal district: 600,000 ÷ 200 km² = 3,000 people/km² (extremely dense).
- Ratio: the coastal district is about 112 times denser than the mountain district.
Why Map A misleads:
- Absolute vs. relative values - a choropleth of totals colors large areas dark simply because they are large. It measures area × density, not crowding. The mountain district looks dark only because it covers 15 times the coastal district's area.
- Choropleth misuse - choropleths are designed for rates/densities, not raw counts; raw counts should be shown with proportional symbols (circles), not shading.
- MAUP (Modifiable Areal Unit Problem) - the apparent pattern depends on how districts are drawn. Merge the coastal district with a rural hinterland and its average density collapses; split the mountain district and its numbers change. The 'unit' is arbitrary, so conclusions about 'which district is crowded' are artifacts of the boundaries.
Conclusion: Map A answers 'where are most people in total?' - not 'where is crowding greatest?' The student's inference is a unit-of-analysis error.
2. Using density plus one equity consideration, propose how to allocate 50 schools between the two districts, and identify the economic concept that governs the trade-off.
Read the worked answer
Framework: allocate by need per capita, not raw totals, while respecting a minimum-service floor.
Step 1 - Per-capita baseline:
- Coastal: 600,000 people → 75% of the 800,000 combined population of the two districts.
- Mountain: 80,000 → 10%.
- A pure per-capita split of 50 schools gives coastal ≈ 37–38, mountain ≈ 5.
Step 2 - Equity adjustment:
- The mountain district's low density means schools must serve wider catchments (transport cost, travel time). A purely per-capita rule would leave remote villages unserved. So reserve a minimum floor (e.g., 3–4 schools) for the mountain district even though its per-capita share is small.
Step 3 - Suggested allocation (example): coastal 35, mountain 6, reserve 9 for need-based adjustment (poverty, distance, existing capacity).
Economic concept governing the trade-off: opportunity cost and allocative efficiency vs. equity. Every school given to a sparse area for equity reasons is one not given to a dense area where marginal benefit per student is higher. The planner's task is marginal analysis: place each additional school where its marginal social benefit per dollar is highest, subject to an equity constraint (minimum access).
Key principle: density is the right relative measure for crowding; equity is the right corrective for geography. Neither raw totals nor pure per-capita rules alone are adequate.