In economics, an expansion path (also called a scale line[1]) is a line connecting optimal input combinations as the scale of production expands.[2] A producer seeking to produce the most units of a product in the cheapest possible way attempts to increase production along the expansion path.[3]
Economists Alfred Stonier and Douglas Hague defined expansion path as "that line which reflects least cost method of producing different levels of output, when factor prices remain constant."[4] The points on an expansion path occur where budget level and the purchaser's indifference curve are tangents. As a producer's budget level increases, each of these points can be connected in a line. A line joining tangency points of isoquants and isocosts (with input prices held constant).[5] If an expansion path forms a straight line, the production technology is considered homoethetic.[6] In this case, the ratio is always the same, and the inputs can be adjusted based on this ratio for any budget. A Cobb–Douglas production function has an expansion path which is a straight line through the origin.[6]