Series 7: Economic Systems

Series Overview

Where Series 1–6 build mathematical tools and apply them to physical geography — terrain, hydrology, climate, ice — this series works the other way around. We begin with a real industry system, ask geographic questions about it, and then develop the mathematics needed to answer them rigorously.

The subject matter is economic geography in the fullest sense: the spatial organisation of production, infrastructure, and exchange. The industries covered are not case studies chosen for illustration. They are the systems that structure where people live, how goods move, and what places can and cannot become. Understanding them as a systems-thinking geographer — quantitatively, spatially, critically — is a distinct and transferable skill.

Each cluster is an industry vertical. The mathematical tools introduced in one cluster recur and extend in later ones. By the end of the series, readers will have a working toolkit for reading any capital-intensive industry as a spatial system.

Pedagogical Philosophy

Domain first, mathematics second. We do not introduce a theorem and then look for applications. We encounter a real system — a pipeline network, a commodity market, a trade corridor — ask what is actually happening and why it matters geographically, and then develop the mathematics that lets us answer precisely.

Industries as geographic systems. Every industry has spatial structure: nodes where things are produced or transformed, edges along which they move, constraints that determine what is possible, and price signals that reveal where the constraints bind. Geographic analysis identifies these structures; mathematical modelling quantifies their consequences.

Transferable thinking across verticals. The graph-theoretic tools used to analyse pipeline capacity in Cluster P reappear when analysing port networks in Cluster T. The price surface concepts from crude oil netbacks recur in spatial arbitrage and trade margin analysis. The series is structured so that each cluster reinforces and extends the last.

Learning Objectives

By completing this series, readers will be able to:

Decompose an industry into its spatial components — identify nodes, flows, constraints, and price-forming mechanisms
Apply graph theory to infrastructure networks — directed graphs, capacity, max-flow min-cut, betweenness centrality
Model price formation across space — netback calculations, basis differentials, spatial arbitrage conditions
Quantify infrastructure constraints and their economic consequences — capacity utilisation, throughput economics, bottleneck identification
Read commodity market data geographically — connect price signals to physical infrastructure constraints
Construct and interpret network flow models — from pipeline systems to trade corridors and supply chains
Apply systems thinking across industry contexts — transfer tools and concepts from one vertical to another

Mathematical Threads

The series introduces and develops five interlocking mathematical concepts:

Graph theory and network flow — directed graphs, adjacency, max-flow min-cut, betweenness centrality. Introduced in Cluster EP (pipeline networks); extended in later clusters.

Price surface analysis — netback pricing, basis differentials, spatial arbitrage. The geographic insight that prices differ across space because of transport costs and constraints.

Throughput and capacity economics — utilisation rates, batch scheduling, inventory dynamics. The mathematics of moving things through constrained physical systems.

Transport hydraulics — pipe flow (Weymouth equation for gas, Darcy-Weisbach for liquids). The physics that sets the engineering constraints economic models must respect.

Mass balance and commodity transformation — fractionation yields, refinery product splits, input-output relationships. How physical transformation shapes what can be moved where.

Prerequisites

Assumed: Algebra, unit conversion, proportional reasoning. Comfort reading quantitative analysis.

Helpful but not required: Series 1 (particularly Model 9: Graph Theory and Flow Routing; Model 10: Gravity Models). Series 1 develops the mathematical foundations; this series applies them to economic systems.

Not assumed: Economics training. Domain knowledge of any specific industry. We build what we need from first principles.

Entry Points by Background

Geography students: Start at Model 1. The domain-first approach is designed for readers who understand place and space but may not have formal economics or mathematics training.

Economics students: The geographic framing — spatial constraints, infrastructure networks, regional price differentials — adds dimensions that standard economics training rarely covers. Models 4–5 (refined products logistics, integrated network) may be the most novel.

Industry professionals (energy, transport, logistics): The mathematical framing of systems you know operationally provides analytical tools for the kind of quantitative spatial reasoning that geographers bring to industry problems.

Readers of the Alberta in Context essay series: The models here are the quantitative underpinning of the arguments made in those essays. Reading both threads together — domain narrative alongside mathematical model — is the intended experience.

Model Sequence

Cluster EP — Energy Infrastructure

Alberta’s hydrocarbon pipeline system as a case study in network geography. Five models build from individual commodity streams to a unified network analysis.

Model 1: Alberta’s Crude Oil Pipeline Network The continental crude oil system — Enbridge, Trans Mountain, Keystone, Express. Volumetric flow rate, pipe hydraulics, capacity utilisation. Netback pricing: how transport tariffs and quality discounts shape the price received at the wellhead. Market direction and the geography of price discrimination.

Model 2: NGL and Condensate Pipeline Systems The fractionation cascade — separating ethane, propane, butane, and condensate from raw NGL mix. Mass balance and yield ratios. The diluent supply chain: condensate flows north to dilute bitumen; dilbit flows south to refineries. A closed loop of commodity dependency.

Model 3: Natural Gas Transmission from Alberta The NOVA intra-Alberta gathering network and its export corridors. The Weymouth equation: how pipe diameter, pressure differential, and gas properties determine throughput capacity. AECO vs Henry Hub: the basis differential as a measure of infrastructure constraint. Annual revenue foregone from the Canada-US price gap.

Model 4: Refined Products Distribution Gasoline, diesel, and jet fuel from Alberta’s refineries to western Canadian consumers. Batch scheduling and product sequencing in multi-product pipelines. Throughput rates, transit times, terminal inventory, and days of supply. The supply security arithmetic for an isolated market like British Columbia.

Model 5: The Integrated Network Alberta’s full hydrocarbon system as a directed network graph. Max-flow min-cut applied to each commodity stream. Betweenness centrality: which hubs are most critical to network function? The netback price surface across all market destinations. Sankey diagram of integrated commodity flows.

Cluster TR — Trade and Transport

Canada’s goods trade as a spatial system: the gravity model as a geographic instrument, corridor analysis, port hierarchy, modal choice, and integrated network flow. Five models build from bilateral trade prediction to a full multi-modal network under a Windsor Corridor disruption scenario.

Model 6: Canada’s Trade Gravity Model The gravity equation — GDP, distance, and the border effect. Why Canadian provinces trade less with each other than distance predicts, and why Alberta’s geography compounds the penalty. Calibration from bilateral trade data; the Anderson-van Wincoop structural form.

Model 7: Canada’s Trade Corridor Systems Three continental corridor systems — Windsor-Detroit (auto/manufacturing), Vancouver-Prince Rupert (Pacific gateway), Halifax-Montréal (Atlantic). Link capacity, chokepoint identification, Wardner equilibrium under demand variation. Leaflet map of the full corridor network.

Model 8: Canada’s Port Economics Port hierarchy from Vancouver to Thunder Bay. Throughput functions, economies of scale, queuing theory at constrained facilities. Hinterland catchment areas and the spatial economics of mode competition. TEU-equivalent cost structure by cargo type.

Model 9: Freight Modal Split Cost functions for rail, truck, and marine by commodity class. Break-even distance thresholds. CN/CP duopoly and its geographic consequences. Discrete choice (logit) model: how shipper decisions aggregate to system-level modal share.

Model 10: The Integrated Trade Network Canada’s goods trade as a 12-node directed network: seven regional nodes, three gateway ports, two cross-border exchange points. Max-flow min-cut for each commodity class. Betweenness centrality reveals which nodes bind the system. The Windsor problem: corridor disruption propagation and redundancy arithmetic. Sankey diagram of integrated commodity flows.

Cluster UE — Urban Economic Systems

The spatial economics of cities: why land is expensive near the centre, why firms cluster, how city sizes follow a power law, and what actually drives a city’s economy. Five models build from the bid-rent gradient to a fully integrated urban system, with Calgary, Toronto, and Vancouver as running case studies.

Model 11: The Bid-Rent Model Von Thünen’s agricultural rent gradient → Alonso’s urban extension → the Muth-Mills household model. Bid-rent functions, spatial equilibrium, and the utility-maximisation derivation that shows why offices cluster at the centre, retail rings them, and residential fills the outer city. The density gradient as an economic output, not a planning choice.

Model 12: Agglomeration Economies Marshall’s three externalities — labour pooling, input sharing, knowledge spillovers — and Jacobs’ urbanisation economies. The wage-density elasticity: a doubling of employment density raises wages by 4–8%. Location quotients as a measurement tool. Calgary’s energy agglomeration vs Toronto’s diversified base: why specialisation concentrates risk.

Model 13: Zipf’s Law and the City Size Distribution The rank-size rule: the nth-largest city has 1/n times the population of the largest. Gibrat’s Law and the random growth model that generates a power law in the limit. Log-log regression on 30 Canadian CMAs. Why Alberta’s Edmonton-Calgary near-parity is unusual — and what it reveals about the province’s economic structure.

Model 14: The Urban Economic Base Export base theory, location quotients, and the economic base multiplier. If basic employment falls by 1, total employment falls by 2–3 (the multiplier). The oil-price transmission mechanism: energy sector contraction → multiplier amplification → city-wide employment effect. Calgary worked example: 40,000 direct losses imply ~88,000 total.

Model 15: The Integrated Urban System All four mechanisms as one system. Mermaid causal flowchart: rent gradient → agglomeration → productivity → city rank → multiplier → back to rent. A 30% oil-price shock traced through each layer via waterfall chart. Radar comparison of Calgary, Toronto, and Vancouver on five dimensions. Monocentric vs polycentric structure, and the policy tools that work through the bid-rent mechanism.

Cluster RE — Resource Economics

The economics of finite resources: optimal depletion theory, who survives a price crash, how governments capture resource rents, and why resource-rich regions often grow more slowly than resource-poor ones. Alberta runs as the continuous case study from wellhead to Heritage Fund.

Model 16: The Hotelling Rule The fundamental theorem of non-renewable resource economics: price must rise at the rate of interest, or the owner is better off waiting. Derivation via intertemporal NPV maximisation. Scarcity rent vs extraction cost. How low interest rates (2010–2021) accelerated oil sands investment — and what rising rates imply for the depletion path.

Model 17: Supply Cost Curves and Break-Even Prices The global oil supply stack: Middle East conventional to Arctic frontier, ordered by break-even price. Alberta’s position — high-cost, landlocked, quality-discounted — as a triple penalty. Operating cost vs full-cycle cost: why producers keep pumping below the break-even threshold. The WCS discount as an infrastructure problem in price form.

Model 18: Royalty Regimes and Resource Rents Revenue royalties vs profit-based taxes: certainty vs efficiency. The Norwegian Government Pension Fund model: 78% marginal tax, $1.7T accumulated. Alberta’s Heritage Fund: deposits stopped in 1987 at $12B, now ~$18B after 40 years. Same oil, different policy. Dutch disease: how a resource boom can hollow out the non-resource economy.

Model 19: The Resource Curse The paradox: resource-rich regions often underperform resource-poor ones over the long run. Three mechanisms — Dutch disease, volatility, institutional. Harold Innis and the staples trap: export commodity infrastructure locks in dependence. Herfindahl-Hirschman Index of export concentration: Alberta vs Ontario vs BC. The historical record on deliberate diversification attempts.

Model 20: The Integrated Resource System Alberta as a complete case study. Mermaid causal diagram from oil price through extraction decision, cost curves, royalty calculation, government revenue, and Heritage Fund to diversification (or its absence). Three price scenarios (2025–2040): $90+, $65–75, $45–55. Sensitivity table across price and royalty regime combinations. The energy transition overlay: how decarbonisation rewrites the Hotelling depletion path.

Cluster MK — Markets and Price Formation

How commodity prices form, how they travel across space, how futures markets encode geographic risk, and how price volatility hits landlocked producers harder than connected ones. The series closes by assembling a full price surface — a geographic map of what every producer actually receives.

Model 21: Commodity Price Formation Benchmark crudes (WTI, Brent, Dubai), benchmark gas (Henry Hub, AECO, TTF), and the formula pricing that links physical trade to these benchmarks. Quality differentials: why heavy sour crude trades at a persistent discount to light sweet. The netback calculation: WTI at $75 minus Trans Mountain tariff minus quality discount equals $53 at the Alberta wellhead vs $67 for a Texas producer at the same WTI.

Model 22: Spatial Arbitrage and the Law of One Price Samuelson’s spatial price equilibrium: trade flows until the price gap equals the transfer cost. The price band theorem. When the law of one price fails: the AECO-Henry Hub basis differential as a pipeline constraint showing up as a price signal. Revenue loss arithmetic: a $1.50/GJ differential on 14 Bcf/day implies ~$7.7B in annual foregone revenue.

Model 23: Futures Markets as Geographic Instruments The cost-of-carry model: futures price as spot price adjusted for interest, storage cost, and convenience yield. Contango vs backwardation. WTI going negative in April 2020: what actually happened physically. Geographic basis: Alberta producers hedging with WTI futures retain the WCS-WTI differential as unhedged basis risk. The forward curve as a forward-looking infrastructure signal.

Model 24: Price Volatility and Its Geographic Consequences WTI annualised volatility ~30–40% vs S&P 500 ~15–20%. GARCH(1,1) and volatility clustering. The transmission chain from price volatility to provincial fiscal capacity. Geographic amplification: when WTI falls, the WCS-WTI differential often widens simultaneously — a double penalty for landlocked producers. Revenue at risk: the 5th-percentile scenario for Alberta royalty revenue.

Model 25: The Integrated Price System The price surface: a geographic map where every point’s price equals the global benchmark minus transport cost minus quality discount. The infrastructure feedback loop — low wellhead prices defer investment, which maintains constraints, which maintains the basis differential. Scenario analysis 2025–2030 under three infrastructure states. Mermaid causal diagram of the full feedback system. Closing retrospective on all five clusters and the analytical toolkit assembled across the series.

Estimated Time Investment

Per model: 2–4 hours (reading, working through examples, exploring visualisations)

Cluster EP (5 models): 10–20 hours for thorough engagement

Cluster TR (5 models): 10–20 hours for thorough engagement

Cluster UE (5 models): 10–20 hours for thorough engagement

Cluster RE (5 models): 10–20 hours for thorough engagement

Cluster MK (5 models): 10–20 hours for thorough engagement

Accelerated path per cluster: 6–10 hours (focus on visualisations and worked examples, skim derivations)

Start with Cluster EP: Alberta’s Crude Oil Pipeline Network — energy infrastructure, pipeline hydraulics, netback pricing.

Start with Cluster TR: Canada’s Trade Gravity Model — bilateral trade, border effects, gravity equation.

Start with Cluster UE: The Bid-Rent Model — land rent, urban gradients, the price of access.

Start with Cluster RE: The Hotelling Rule — optimal depletion, scarcity rent, the price path of a finite resource.

Start with Cluster MK: Commodity Price Formation — benchmarks, netbacks, and what a producer actually receives.

Companion reading: Alberta in Context — the narrative essay series that applies these models to the political economy of a landlocked province.