The amount by which one output can be increased if another is reduced by a small amount, per unit of the decrease, holding total inputs constant. The marginal rate of transformation can be calculated at the level of the firm, the industry, a country, or the world as a whole. It measures opportunity costs, and is given by the gradient of the production possibility frontier. If the production possibility frontier is defined implicitly by G(X, Y) = 0, where G(X, Y) is differentiable, the marginal rate of transformation is defined by