An isoquant (derived from quantity and the Greek word iso, meaning equal), in
microeconomics
Microeconomics is a branch of mainstream economics that studies the behavior of individuals and firms in making decisions regarding the allocation of scarce resources and the interactions among these individuals and firms. Microeconomics fo ...
, is a
contour line
A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a plane section of the three-dimensional grap ...
drawn through the set of points at which the same quantity of output is produced while changing the quantities of two or more inputs. The x and y axis on an isoquant represent two relevant inputs, which are usually a factor of production such as labour, capital, land, or organisation. An isoquant may also be known as an “Iso-Product Curve”, or an “Equal Product Curve”.
Isoquant vs. Indifference Curve
While an
indifference curve
In economics, an indifference curve connects points on a graph representing different quantities of two goods, points between which a consumer is ''indifferent''. That is, any combinations of two products indicated by the curve will provide the c ...
mapping helps to solve the utility-maximizing problem of consumers, the isoquant mapping deals with the cost-minimization and profit and output maximisation problem of producers. Indifference curves further differ to isoquants, in that they cannot offer a precise measurement of utility, only how it is relevant to a baseline. Whereas, from an isoquant, the product can be measured accurately in physical units, and it is known by exactly how much isoquant 1 exceeds isoquant 2.
Nature and Practical Use of an Isoquant
In managerial economics, isoquants are typically drawn along with
isocost
In economics, an isocost line shows all combinations of inputs which cost the same total amount.Chiang, Alpha C., ''Fundamental Methods of Mathematical Economics'', third edition, McGraw-Hill, 1984. Although similar to the budget constraint in co ...
curves in
capital-labor graphs, showing the technological tradeoff between capital and labor in the
production function
In economics, a production function gives the technological relation between quantities of physical inputs and quantities of output of goods. The production function is one of the key concepts of mainstream neoclassical theories, used to define ...
, and the decreasing marginal returns of both inputs. In managerial economics, the unit of isoquant is commonly the net of capital cost. As such, isoquants by nature are downward sloping due to operation of diminishing
marginal rates of technical substitution (MRTS).
The slope of an isoquant represents the rate at which input x can be substituted for input y. This concept is the MRTS, so MRTS=slope of the isoquant. Thus, the steeper the isoquant, the higher the MRTS. Since MRTS must diminish, isoquants must be convex to their origin. Adding one input while holding the other constant eventually leads to decreasing marginal output.
The contour line of an isoquant represents every combination of two inputs which fully maximise a firms’ use of resources (such as budget, or time). Full maximisation of resources is usually considered ‘efficient’. Efficient allocation of factors of production occur only when two isoquants are tangent to one another. If a firm produces to the left of the contour line, then the firm is considered to be operating inefficiently, because they are not maximising use of their available resources. A firm cannot produce to the right of the contour line unless they exceed their constraints.
![TE-Production-Isoquant](https://upload.wikimedia.org/wikipedia/commons/9/93/TE-Production-Isoquant.png)
A family of isoquants can be represented by an isoquant map, a graph combining a number of isoquants, each representing a different quantity of output.An isoquant map can indicate decreasing or increasing
returns to scale based on increasing or decreasing distances between the isoquant pairs of fixed output increment, as output increases. If the distance between those isoquants increases as output increases, the firm's production function is exhibiting decreasing returns to scale; doubling both inputs will result in placement on an isoquant with less than double the output of the previous isoquant. Conversely, if the distance is decreasing as output increases, the firm is experiencing increasing returns to scale; doubling both inputs results in placement on an isoquant with more than twice the output of the original isoquant. A firm can choose to utilise the information an isoquant gives on
returns to scale, by using it as insight how to allocate resources.
![Isoquant x vs y input intensity](https://upload.wikimedia.org/wikipedia/commons/7/70/Isoquant_x_vs_y_input_intensity.jpg)
Knowing how to allocate resources is a concept pertinent to managerial economics. Isoquants can be useful to graphically represent this issue of
scarcity
In economics, scarcity "refers to the basic fact of life that there exists only a finite amount of human and nonhuman resources which the best technical knowledge is capable of using to produce only limited maximum amounts of each economic good. ...
. They show the extent to which the firm in question has the ability to substitute between two different inputs (x and y in the graph) at will in order to produce the same level of output (see: Graph C)). They also represent different quantity combinations of two goods which adhere to a
budget constraint. Thus, they can be used as a tool to help management make better informed decisions regarding production and profit dilemmas, such as cost or waste minimization, and revenue and output maximization.
A firm can determine the ''least cost combination'' of inputs to produce a given output, by combining isocost curves and isoquants, and adhering to
First Order Condition
In calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine whether each point is a local maximum, a local minimum, or a saddle point. Derivative tests can also give information abou ...
s.
The least cost combination is where the ratio of marginal products is equal to the ratio of factor prices. At this point, the slope of the isoquant, and the slope of the isocost, will be equal (see intersection of graph D). A firm has incentive to produce at the least cost combination because it is at this point, the related costs of desired production are minimised.
As with indifference curves, two isoquants can never cross. Also, every possible combination of inputs is on an isoquant. Finally, any combination of inputs above or to the right of an isoquant results represents a higher level of output, and vice versa. Although the marginal product of an input decreases as you increase the quantity of the input while holding all other inputs constant, the marginal product is never negative in the empirically observed range since a
rational
Rationality is the quality of being guided by or based on reasons. In this regard, a person acts rationally if they have a good reason for what they do or a belief is rational if it is based on strong evidence. This quality can apply to an abi ...
firm would never increase an input to decrease output.
Shapes of an Isoquant
If the two inputs are perfect substitutes, the resulting isoquant map generated is represented in fig. A; with a given level of production Q3, input X can be replaced by input Y at an unchanging rate. The perfect substitute inputs do not experience decreasing marginal rates of return when they are substituted for each other in the production function.
If the two inputs are perfect complements, the isoquant map takes the form of fig. B; with a level of production Q3, input X and input Y can only be combined efficiently in the certain ratio occurring at the kink in the isoquant. The firm will combine the two inputs in the required ratio to maximize profit.
Isoquants are typically combined with
isocost
In economics, an isocost line shows all combinations of inputs which cost the same total amount.Chiang, Alpha C., ''Fundamental Methods of Mathematical Economics'', third edition, McGraw-Hill, 1984. Although similar to the budget constraint in co ...
lines in order to solve a cost-minimization problem for given level of output. In the typical case shown in the top figure, with smoothly curved isoquants, a firm with fixed unit costs of the inputs will have isocost curves that are linear and downward sloped; any point of tangency between an isoquant and an isocost curve represents the cost-minimizing input combination for producing the output level associated with that isoquant. A line joining tangency points of isoquants and isocosts (with input prices held constant) is called the
expansion path
In economics, 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 econom ...
.
[Salvatore, Dominick (1989). ''Schaum's outline of theory and problems of managerial economics,'' McGraw-Hill, ]
Non convexity
Under the assumption of declining marginal rate of technical substitution, and hence a positive and finite elasticity of substitution, the isoquant is convex to the origin. A locally nonconvex isoquant can occur if there are sufficiently strong returns to scale in one of the inputs. In this case, there is a negative elasticity of substitution - as the ratio of input A to input B increases, the marginal product of A relative to B ''increases'' rather than decreases.
A nonconvex isoquant is prone to produce large and discontinuous changes in the price minimizing input mix in response to price changes. Consider for example the case where the isoquant is globally nonconvex, and the isocost curve is linear. In this case the minimum cost mix of inputs will be a corner solution, and include only one input (for example either input A or input B). The choice of which input to use will depend on the relative prices. At some critical price ratio, the optimum input mix will shift from all input A to all input B and vice versa in response to a small change in relative prices.
See also
{{Commons category, Isoquants
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Microeconomics
Microeconomics is a branch of mainstream economics that studies the behavior of individuals and firms in making decisions regarding the allocation of scarce resources and the interactions among these individuals and firms. Microeconomics fo ...
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Production, costs, and pricing
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Production theory basics
Production is the process of combining various inputs, both material (such as metal, wood, glass, or plastics) and immaterial (such as plans, or knowledge) in order to create output. Ideally this output will be a good or service which has value a ...
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Marginal rate of technical substitution
In microeconomic theory, the marginal rate of technical substitution (MRTS)—or technical rate of substitution (TRS)—is the amount by which the quantity of one input has to be reduced (-\Delta x_2) when one extra unit of another input is used ( ...
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Lerner diagram Factor price equalization is an economic theory, by Paul A. Samuelson (1948), which states that the prices of identical factors of production, such as the wage rate or the rent of capital, will be equalized across countries as a result of internati ...
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Budget constraint
References
Production economics