Autarky vs trade consumption calculator

Opening a closed economy to trade changes what a country can consume, not only what it can produce. Under autarky a small country with a linear production-possibilities frontier consumes on that frontier at domestic relative prices set by unit labor requirements. After it specializes according to comparative advantage and trades at given world prices, its consumption point leaves the production frontier and sits on a world-price budget line through the specialized output bundle. This autarky versus trade consumption calculator takes a labor endowment, unit labor requirements for two goods, world prices, and a Cobb-Douglas expenditure share on good X. It returns autarky consumption of both goods, post-trade consumption, the specialization choice, the export and import vector, Cobb-Douglas utility in each regime, the utility ratio, and the percentage welfare gain from opening to trade.

What autarky and trade consumption measure on a linear PPF

A Ricardian small country has a fixed labor endowment and constant unit labor requirements for two goods, so its production-possibilities frontier is a straight line. The intercepts are maximum output of X if every hour goes to X, and maximum output of Y if every hour goes to Y. The slope is the opportunity cost of X in terms of Y, which is also the autarky relative price when labor markets are competitive.

With Cobb-Douglas preferences the country spends a constant share alpha of income on X and the rest on Y, so autarky consumption is simply that share of each intercept: alpha times max X of good X, and one minus alpha times max Y of good Y. When the country opens, it is too small to move world prices. If the world relative price of X exceeds the autarky opportunity cost, the country has comparative advantage in X and specializes completely in X; the opposite inequality sends all labor to Y.

Consumption then follows the same Cobb-Douglas shares applied to income valued at world prices. That post-trade basket typically contains more of the imported good and the same amount of the export good as under autarky, which is why utility rises. When world and autarky relative prices coincide there is no price wedge, production can stay at the autarky point, and the welfare gain is zero.

Where an autarky versus trade calculator earns its keep

Introductory international-trade courses assign Ricardian autarky-versus-trade problems because the move from the production-possibilities frontier to the consumption-possibilities line is the first quantitative picture of the gains from trade. Tutoring platforms and LMS auto-graders need a deterministic oracle that rejects a zero unit labor requirement instead of returning infinity, and that treats a world price equal to autarky cost as zero gain rather than a spurious specialization.

Instructors building practice banks want the same autarky basket, post-trade basket, and percentage welfare gain students derive on paper when they are given labor hours, a cloth-and-wine technology, and a terms-of-trade quote. Pair this capability with the separate opportunity-cost-ratio tool when you only need a PPF slope, and keep this surface focused on the consumption and welfare comparison that answers whether opening to trade raises living standards.