page_title: Production–possibility frontier
section_title: Marginal rate of transformation
hierarchical_section_title: Production–possibility frontier / Properties / Marginal rate of transformation
context_page_description: A production–possibility frontier, production possibility curve, or production possibility boundary, or Transformation curve/boundary/frontier is a curve which shows various combinations of the amounts of two goods which can be produced within the given resources and technology/a graphical representation showing all the possible options of output for two products that can be produced using all factors of production, where the given resources are fully and efficiently utilized per unit time. A PPF illustrates several economic concepts, such as allocative efficiency, economies of scale, opportunity cost, productive efficiency, and scarcity of resources.
  This tradeoff is usually considered for an economy, but also applies to each individual, household, and economic organization. One good can only be produced by diverting resources from other goods, and so by producing less of them.
  Graphically bounding the production set for fixed input quantities, the PPF curve shows the maximum possible production level of one commodity for any given production level of the other, given the existing state of technology.
context_section_description: The slope of the production–possibility frontier (PPF) at any given point is called the marginal rate of transformation (MRT). The slope defines the rate at which production of one good can be redirected (by reallocation of productive resources) into production of the other. It is also called the (marginal) "opportunity cost" of a commodity, that is, it is the opportunity cost of X in terms of Y at the margin. It measures how much of good Y is given up for one more unit of good X or vice versa. The shape of a PPF is commonly drawn as concave to the origin to represent increasing opportunity cost with increased output of a good. Thus, MRT increases in absolute size as one moves from the top left of the PPF to the bottom right of the PPF.
  The marginal rate of transformation can be expressed in terms of either commodity. The marginal opportunity costs of guns in terms of butter is simply the reciprocal of the marginal opportunity cost of butter in terms of guns. If, for example, the (absolute) slope at point BB in the diagram is equal to 2, to produce one more packet of butter, the production of 2 guns must be sacrificed. If at AA, the marginal opportunity cost of butter in terms of guns is equal to 0.25, the sacrifice of one gun could produce four packets of butter, and the opportunity cost of guns in terms of butter is 4.
caption: Marginal rate of transformation increases when the transition is made from AA to BB.