Consumption beyond PPF from trade

Linear PPF, opportunity cost, and terms of trade

Comparative advantage for this small open economy is read off a single comparison: if the world pays more Y per X than the domestic opportunity cost of X, the country has a comparative advantage in X and should specialize completely in X under free trade; if the world pays less Y per X than that opportunity cost, comparative advantage lies in Y. When terms of trade exactly equal the opportunity cost of X there is no strict price signal to specialize, and this calculator requires an explicit specialize flag if you still want the geometry without claiming gains. Complete specialization places production at a corner of the PPF; trade then moves the country along a straight consumption possibility frontier whose slope is the world relative price, not the domestic opportunity-cost slope. A two-good linear production possibility frontier is fully described by the intercepts max_x and max_y: if every domestic resource produces only good X the country obtains max_x units of X and zero of Y; if every resource produces only Y it obtains max_y of Y and zero of X. Feasible autarky bundles satisfy x over max_x plus y over max_y less than or equal to one with non-negative quantities. The domestic opportunity cost of one more unit of X is therefore max_y over max_x units of Y given up, and the opportunity cost of one more unit of Y is max_x over max_y units of X. Terms of trade tot_y_per_x state how many units of Y the world market delivers for each unit of X exported—the relative world price of X expressed in Y.

Input contract, specialization, and response fields

Optional specialize is auto, x, or y (default auto); auto picks X when ToT exceeds the opportunity cost of X and Y when ToT is smaller. Optional decimals is an integer from zero through twelve controlling half-up rounding on every computed field (default six). POST a JSON body with three required positive finite numbers: max_x and max_y as the PPF intercepts, and tot_y_per_x as world units of Y per unit of X. Optional export_share is a number strictly greater than zero and at most one (default one half) giving the fraction of specialized-good output that is exported. Missing fields, non-finite values, non-positive intercepts or terms of trade, export_share outside the open-closed unit interval, specialize outside the allowed set, and auto mode when ToT equals the opportunity cost of X all fail with invalid_input and are not billed. On success the response echoes the inputs, reports opportunity_cost_x_in_y and opportunity_cost_y_in_x, recommended_specialize and specialized_in, the production corner, export and import flows for both goods, the consumption bundle, CPF intercepts cpf_max_x and cpf_max_y, ppf_index equal to consumption_x over max_x plus consumption_y over max_y, boolean beyond_ppf, intercept gains versus the domestic PPF, consumption and autarky incomes valued in Y at world prices, trade_gain_value_y, and a short formula string. Example: max_x one hundred, max_y fifty, tot_y_per_x one, export_share one half specializes in X, exports fifty X for fifty Y, consumes fifty of each, and yields ppf_index one point five, so the consumption point lies clearly outside the domestic frontier.

Where a consumption-beyond-PPF trade API earns its keep

Keep requests small, pin the rounded consumption and ppf_index fields in tests, and you get reproducible trade-gain numbers for homework, LMS plugins, and edge workers without standing up a full trade-simulation stack of your own.