How the equilibrium is solved

A policy change (a tariff, a tax, a carbon price) shifts every price in the economy at once. Agora doesn't guess the outcome — it solves for the new competitive equilibrium: the set of prices at which every market clears simultaneously. Here is that solve, and it lights up live while a query runs.

The formal model

Agora is a calibrated open-economy computable general equilibrium (CGE) model, solved exactly. Below is the structure — the objects, the equilibrium conditions, and how they are computed and calibrated.

1 · Competitive equilibrium

Let \(p \in \mathbb{R}^{n}_{++}\) be a price vector over \(n\) goods and factors. Each agent optimises given \(p\); aggregate excess demand is \(z(p)=\sum_i d_i(p)-\sum_j y_j(p)\). A competitive equilibrium is a price \(p^*\) with

Existence follows from Brouwer/Kakutani fixed-point arguments (Arrow–Debreu, 1954); Walras' law \(p\cdot z(p)\equiv 0\) makes one market redundant, so we normalise a numéraire.

2 · Production — nested CES (KLEM)

Each sector \(j\) combines capital \(K\), labour \(L\), energy and materials in a nested constant-elasticity structure:

3 · Trade — Armington imports & CET exports

Domestic and imported varieties are imperfect substitutes (Armington, 1969); output splits between home sales and exports by a constant-elasticity-of-transformation frontier:

4 · Demand — Linear Expenditure System

Households (one or more) allocate income by Stone–Geary/LES preferences with committed quantities \(\bar q_k\) (Stone, 1954):

5 · Government, carbon & welfare

Income tax \(\tau\) and tariffs finance the government; a carbon price adds an output tax proportional to each sector's CO₂ intensity, optionally recycled through \(\tau\). Welfare is the money-metric equivalent variation

reported as a percent of the benchmark, and scaled by observed GDP into an exact money figure.

6 · Solving & calibration

The system is solved by tâtonnement with Newton polishing to machine precision — the numerical realisation of Scarf's (1967) constructive fixed-point computation. Parameters are recovered by exact calibration: the benchmark SAM is, by construction, an equilibrium, so shares and scale terms are chosen to reproduce it before any policy is applied.

Intellectual lineage

Every part of the engine descends from a specific advance in mathematical economics. Agora is their theory, made computable.

Benchmarking

The engine is exact and fast: it solves a full 45-sector open economy in tens of milliseconds and satisfies the market-clearing conditions to machine precision. Every figure below is recorded on this instance.

The architecture

An exact economy, explained clearly

Agora pairs an exact general-equilibrium engine with a language model. The engine owns every number; the model reasons and explains on top; a deterministic guard keeps the prose faithful to the engine. You get the depth of a CGE study with the readability of a briefing note.

Design principle

Language models are fluent but will invent a plausible number if asked. Agora removes that failure mode by construction: the truth lives in the solver, the model only phrases it, and a guard in code enforces the boundary. The result is a policy tool a minister can both trust and understand.

How to use Agora

Ask a policy question in plain English. Agora interprets it, solves the exact equilibrium, and writes a full explanation — mechanism, winners and losers, and an honest bottom line. Pick a country, type a question, or click a sample below.

Policy levers you can ask about

Lever	Example phrasing	What it does
Tariffs	"raise tariffs 15%", "free trade", "halve tariffs"	Scales the country's real tariff schedule
Income tax	"cut income tax 10%", "raise income tax 5 points"	Shifts the income-tax rate in percentage points
Carbon price	"add a carbon price of 0.05, recycle the revenue"	Output tax by CO₂ intensity, optional recycling
Reform ranking	"which reform gives the biggest welfare gain?"	Searches for the binding constraints
Comparisons	"compare free trade vs a tax cut — who wins?"	Solves several scenarios and lines them up