Let us make an in-depth study of the general equilibrium between exchange and production.

General equilibrium in exchange must be consistent with general equilibrium in production to have a general equilibrium within the economy.

This means that we need to derive a transformation curve (or ppc) which is a reflection of the contract curve in the box diagram depicting general equilibrium of production. Thus, the transformation curve gives all possible equilibrium combinations of goods X and F that could be produced by employing all available inputs.

Although this gives the same information as is given by the contract curve, it is plotted on a graph with the axis representing curve which is derived from Fig. 15.2. Point W on the contract curve in Fig. 15.2 depicts tangency of isoquants x2 and y2, which represent the production of x2 of X and y2 of Y.

These quantities are plotted as point Won the transformation curve in Fig. 15.3. Similarly, point Z is drawn in Fig. 15.3. For every point on the contract curve in Fig. 15.2, there is a corresponding point on the transformation curve in Fig. 15.3. If good Y is not produced, then the maximum amount of X, X*, can be produced, which corresponds to the origin Y; OY in Fig. 15.2.

If we select a point that is not on the contract curve, such as point F in Fig. 15.2, we see that this translates into a point that is not on the transformation curve, e.g. point Fin Fig. 15.3. We can see that point F could not represent a general equilibrium in production since the economy is capable of producing more of X without reducing the output of Y by moving to point W.

Finally, the slope of the transformation curve is called the marginal rate of transformation (MRT).

The condition necessary for general equilibrium between exchange and production is MRS = MRT. General equilibrium in exchange occurs when both individuals have the same MRS, which is a point on the contract curve. When the MRS = the MRT, there is a general equilibrium between exchange and production.