The Production Possibility Curve (PPC) graphically represents the maximum output combinations of two goods that an economy can produce with its available resources and technology.
The slope of the PPC at any given point indicates the opportunity cost of producing one more unit of one good in terms of the other good.
Mathematically, the slope represents the rate at which the output of one good must decrease to increase the output of the other good by one unit.
The Marginal Rate of Transformation (MRT) quantifies this trade-off. It is defined as the ratio of the decrease in the output of one good to the increase in the output of another good.
$ MRT = -\frac{\Delta Y}{\Delta X} $
Where $\Delta Y$ is the change in the quantity of good Y, and $\Delta X$ is the change in the quantity of good X. The negative sign indicates the inverse relationship shown by the downward-sloping curve.
The absolute value of the slope of the PPC represents the marginal rate of transformation, reflecting the actual rate at which the economy can transform one good into another by reallocating resources.
In the above diagram, the consumer surplus is represented by the area of :