In economics, an
isoquant (derived from quantity and the Greek word iso, meaning equal) 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 inputs.While an indifference curve
mapping helps to solve the utility-maximizing problem of consumers, the
isoquant mapping deals with the cost-minimization problem of producers.
Isoquants are typically drawn along with isocost curves in capital-labor graphs, showing the technological tradeoff between capital and labor in the production function,
and the decreasing marginal returns of both inputs. Adding one input
while holding the other constant eventually leads to decreasing marginal
output, and this is reflected in the shape of the isoquant. 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. Isoquants are also called equal product curves.
An isoquant map where Q3 > Q2 > Q1. Typically inputs X and Y would
refer to labor and capital respectively. More of input X, input Y, or
both is required to move from isoquant Q1 to Q2, or from Q2 to Q3.
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Production Isoquant/Isocost Curve
An isoquant shows the extent to which the firm in question has the
ability to substitute between the two different inputs at will in order
to produce the same level of output. An isoquant map can also 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.
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 in
more output than any point on the isoquant. 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 firm would never increase an input to decrease output.
A) Example of an isoquant map with two inputs that are perfect substitutes.
B) Example of an isoquant map with two inputs that are perfect complements.
Shapes of Isoquants
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
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.
The only relevant portion of the isoquant is the one that is convex
to the origin, part of the curve which is not convex to the origin
implies negative marginal product for factors of production. The higher
the isoquant, the higher the production.
