A Simplified Model:
Let us assume a closed economy (that, an economy without international trade) having only two sectors, viz., production and exchange (representing consumption). In this economy, the concept of general equilibrium implies a simultaneous equilibrium in both sectors.
In other words, it is that situation where the economy does not want to change either its production pattern or its demand preference pattern. It prefers to continue with its existing allocation of productive resources and the current production levels of both X and Y.
Similarly, it does not want to revise (that is, re-draw) its set of indifference curves and continues with the existing prices of X and Y in terms of each other.
Conditions of Equilibrium:
Such a position of general equilibrium is attained when one of the community indifference curves is tangential to PPC of the economy. This is so because, at this common point of tangency, the slopes of the two curves equal each other so that MRTXY (as measured by the slope of its PPC) equals MRSXY (as measured by the slope of its indifference curve).
Image Source: i.ytimg.com
ADVERTISEMENTS:
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”.
Diagrammatic Illustration:
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.
ADVERTISEMENTS:
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.