It should be noted that, given the properties of community’s PPC and indifference curves, PPC has a common point of tangency with one and only one indifference curve. The slope of the common tangent also measures what is termed the Autarky Price Ratio, or “the equilibrium relative commodity prices in isolation”.
Panel H represents the two-sector general equilibrium position of the “Home” country, or country H, and panel F represents the two-sector general equilibrium position of the “Foreign” country, or country F. For country H, the general equilibrium is attained at point E on its PPC where indifference curve 2 is tangent to it.
The slope of the tangent KK, is equal to KN/NE. It means that in country H, pre-trade equilibrium in the exchange sector is attained when price per unit of item X is equal to KN/NE units of item Y, and price per unit of item Y is NE/KN units of item X. Similarly, pre-trade equilibrium in the production sector of H is attained when it is producing OM of item X and ON of item Y.
Similarly, for country F, indifference curve 2 is tangent to its PPC at point E’. We find that in this case, in pre-trade exchange equilibrium, each unit of item X is priced at (K’N’/N’E’) units of item Y and each unit of item Y is priced at (N’E’/K’N’) units of item X. Correspondingly, the equilibrium production quantities of goods X and Y are OM’ and ON’, respectively.
Returns to Scale:
The above conclusions are also applicable even when both X and Y are produced under constant returns to scale and PPC is a straight line. In this case, MRTx.y remains constant throughout the length of PPC and two-sector general equilibrium is attained, as before, by the tangency of one of the indifference curve of the community with its PPC. Moreover, in this case also, there is one and only one such point.
Since MRTx.y is constant throughout the length of PPC, autarky prices remain unchanged irrespective of the output- combination of goods X and Y. The point of tangency only determines the quantities of X and Y to be produced.