# Isoquant

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Isoquant_map.png
An isoquant map where Q3 > Q2 > Q1. A typical choice of inputs would be labor for input X and capital for input Y. More of input X, input Y, or both is required to move from isoquant Q1 to Q2, or from Q2 to Q3.

In economics, an isoquant 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. Another way of defining the isoquant is a curve that shows all possible quantities of inputs that result in the same level of output with a given production function. The isoquant is a parallel of the indifference curve concept that deals with producers instead of consumers. While the indifference curve helps to answer the utility-maximizing problem of consumers, the isoquant deals with the cost-minimization problem of producers. Isoquants are typically drawn on capital-labor graphs, showing the 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.

An isoquant shows that 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 isoquants on the map as you increase output. If the distance between 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.

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A) Example of an isoquant map with two inputs that are perfect substitutes.

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 since a logical firm would never increase an input to decrease output.

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 is effortlessly replaced by input Y in the production function. 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 compliments, 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 a certain ratio represented by the kink in the isoquant. The firm will combine the two inputs in the required ratio to maximize output and minimize cost. If the firm is not producing at this ratio, there is no rate of return for increasing the input that is already in excess.

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B) Example of an isoquant map with two inputs that are perfect compliments.

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