In economics, an expansion path (also called a scale line) is a line connecting optimal input combinations as the scale of production expands. A producer seeking to produce the most units of a product in the cheapest possible way attempts to increase production along the expansion path.
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." 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 joining tangency points of isoquants and isocosts (with input prices held constant). If an expansion path forms a straight line, the production technology is considered homothetic (or homoethetic). 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.
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