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Examples and exercises on the output expansion path
Economics curves {{economics-stub
In economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and interac ...
, an expansion path (also called a scale lineJain, TR; Khanna OP (2008). ''Economics.'' VK Publications, ) is a path connecting optimal input combinations as the scale of production expands.Hirschey, Mark (2008). ''Managerial economics.'' Cengage Learning, It is often represented as a curve in a graph with quantities of two inputs, typically physical capital
Physical capital represents in economics one of the three primary factors of production. Physical capital is the apparatus used to produce a good and services. Physical capital represents the tangible man-made goods that help and support the pr ...
and labor
Labour or labor may refer to:
* Childbirth, the delivery of a baby
* Labour (human activity), or work
** Manual labour, physical work
** Wage labour, a socioeconomic relationship between a worker and an employer
** Organized labour and the labour ...
, plotted on the axes. A producer seeking to produce a given number of units of a product in the cheapest possible way chooses the point on the expansion path that is also on the isoquant
An isoquant (derived from ''quantity'' and the Greek word ', , meaning "equal"), in microeconomics, is a contour line drawn through the set of points at which the same quantity of output is produced while changing the quantities of two or more in ...
associated with that output level.Prusty, Sadananda (2010). ''Managerial Economics.'' PHI Learning Pvt. Ltd.,
Economists Alfred Stonier and Douglas Hague defined “expansion path” as "that line which reflects the least–cost
Cost is the value of money that has been used up to produce something or deliver a service, and hence is not available for use anymore. In business, the cost may be one of acquisition, in which case the amount of money expended to acquire it i ...
method of producing different levels of output, when factor prices remain constant."Stonier, Alfred W.; Hague, Douglas C. (1980). ''A textbook of economic theory, 5th edition.'' Longmans The points on an expansion path occur where the firm's isocost curves, each showing fixed total input cost, and its isoquants, each showing a particular level of output, are tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points o ...
; each tangency point determines the firm's conditional factor demands
In economics, a conditional factor demand is the cost-minimizing level of an input (factor of production) such as labor or capital, required to produce a given level of output, for given unit input costs ( wage rate and cost of capital) of the in ...
. As a producer's level of output increases, the firm moves from one of these tangency points to the next; the curve joining the tangency points is called the expansion path.Salvatore, Dominick (1989). ''Schaum's outline of theory and problems of managerial economics.'' McGraw-Hill,
If an expansion path forms a straight line from the origin, the production technology is considered homothetic (or homoethetic).Rasmussen, Svend (2011). ''Production Economics: The Basic Theory of Production Optimisation.'' Springer, In this case, the ratio
In mathematics, a ratio () shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
of input usages is always the same regardless of the level of output, and the inputs can be expanded proportionately so as to maintain this optimal ratio as the level of output expands. A Cobb–Douglas production function
In economics and econometrics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the amounts of two or more inputs (particularly phy ...
is an example of a production function that has an expansion path which is a straight line through the origin.
See also
* Income-consumption curve, the closest analog in consumer theoryReferences
External links
Examples and exercises on the output expansion path
Economics curves {{economics-stub