# How an Isoquant Curve Explains Input and Output

![Isoquant Curve](https://www.investopedia.com/thmb/kJMrnQ7z233CbKc8WAwkVzLqPPU=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/isoquantcurve-0d9045a18ca64ee385dc5bd58a85422b.jpg)

*— Investopedia / Laura Porter*

> **Definition**
>
> An isoquant curve helps manufacturers adjust their levels of labor and capital to maintain output at the lowest cost.

## What Is an Isoquant Curve?

An isoquant curve illustrates the relative influence that inputs, commonly [capital](https://www.investopedia.com/ask/answers/051115/what-capital-relation-factors-production.asp) and labor, have on output or production. It helps companies adjust inputs to maintain production and maximize profits

### Key Takeaways

*   An isoquant is commonly used to show combinations of capital and labor.
*   The isoquant curve helps companies adjust their manufacturing operations to produce the most goods at the least cost.
*   The formula for the marginal rate of technical substitution (MRTS) is used to calculate the curve.  
    

## Capital and Labor

The isoquant curve displays the combinations of inputs that produce a set amount of output. An isoquant shows combinations of capital and labor and the technological tradeoff between the two: how much capital is required to replace a unit of labor at a certain production point to generate the same output.

Labor is often placed along the X-axis of the isoquant graph and capital along the Y-axis. The exact slope of the isoquant curve on the graph shows the rate at which a given input, either labor or capital, can be substituted for the other while keeping the same output level.

In the graph below, factor K represents capital and factor L is labor. The curve shows that when a firm moves down from point (a) to point (b) and uses one additional unit of labor, the firm can give up four units of capital (K) and yet remain on the same isoquant at point (b). If the firm hires another unit of labor and moves from point (b) to (c), the firm can reduce its capital (K) by three units but remain on the same isoquant.

![Isoquant curve](https://www.investopedia.com/thmb/QN5JS4vAP55g5byuIT74H1X8gK4=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/marginal_rate_of_substitution_final2-893aa48189714fcb97dadb6f97b03948.png)

*— Image by Julie Bang © Investopedia 2019*

## How Isoquant Is Calculated

To calculate an isoquant, use the formula for the [marginal rate of technical substitution (MRTS)](https://www.investopedia.com/terms/m/marginal-rate-technical-substitution.asp#:~:text=The%20marginal%20rate%20of%20technical,maintain%20a%20level%20of%20productivity.):

$\begin{aligned} &\text{MRTS(\textit{L}, \textit{K})} = - \frac{ \Delta K }{ \Delta L } = \frac{ \text {MP}_L }{ \text {MP}_K } \\ &\textbf{where:} \\ &K = \text{Capital} \\ &L = \text{Labor} \\ &\text{MP} = \text{Marginal products of each input} \\ &\frac{ \Delta K }{ \Delta L } = \text{Amount of capital that can be reduced}\\ &\text{when labor is increased (typically by one unit)} \\ \end{aligned}$

For example, in the graph of an isoquant where capital (represented with K on its Y-axis and labor (represented with L) on its X-axis, the slope of the isoquant, or the MRTS at any one point, is calculated as dL/dK.

> **Important**
>
> The marginal rate of technical substitution shows the rate at which a firm can substitute one input, such as labor, for another input, such as capital, without changing the output.

## Properties of an Isoquant Curve

**An isoquant curve slopes downward or is negatively sloped**. This means that the same level of production only occurs when increasing units of input are offset with fewer units of another input factor. This property coincides with the marginal rate of technical substitution (MRTS). For example, the same output is achieved when capital inputs increase, but labor inputs decrease.

**An isoquant curve, because of the MRTS effect, is convex to its origin**. This indicates that factors of production may be substituted with one another. The increase in one factor must be used in conjunction with the decrease of another input factor.

**Isoquant curves cannot be tangent to or intersect one another**. Curves that intersect are incorrect and produce invalid results, as a common factor combination on each of the curves will reveal the same level of output, which is impossible.

**Isoquant curves in the upper portions of the chart yield higher outputs**. At a higher curve, factors of production are more heavily employed. Either more capital or more labor input factors result in greater production.

**An isoquant curve should not touch the X or Y axis on the graph**. If it does, the rate of technical substitution is void and indicates that one factor is responsible for producing the given level of output without the involvement of any other input factors.

**Isoquant curves do not have to be parallel to one another**. The rate of technical substitution between factors may have variations.

**Isoquant curves are oval-shaped**. This allows firms to determine the most efficient factors of production.

## Isoquant Curve vs. Indifference Curve

The isoquant curve is the flip side of another [microeconomic](https://www.investopedia.com/articles/economics/08/understanding-microeconomics.asp) measure, the [indifference curve](https://www.investopedia.com/terms/i/indifferencecurve.asp). The mapping of the isoquant curve addresses cost-minimization problems for producers or the best way to manufacture goods.

The indifference curve, on the other hand, measures the optimal ways consumers use goods. It attempts to analyze consumer behavior and map out consumer demand.

It identifies the point at which an individual stops being indifferent to the combination of goods. When plotted on a graph, an indifference curve shows a combination of two goods (one on the Y-axis, the other on the X-axis) that gives a consumer equal satisfaction and [utility](https://www.investopedia.com/ask/answers/032615/what-concept-utility-microeconomics.asp).  

## What Is an Isoquant in Economics?

An isoquant, when plotted on a graph, shows all the combinations of two factors that produce a given output. Often used in [manufacturing](https://www.investopedia.com/terms/m/manufacturing.asp), with capital and labor as the two factors, isoquants can show the optimal combination of inputs that will produce the maximum output at minimum cost.

## Where Did the Term Isoquant Originate?

The term "isoquant" seems to have been coined by Ragnar Frisch, appearing in his notes for lectures on production theory at the University of Oslo in 1928-29. Whatever its origins, by the late 1930s, the isoquant graph was in widespread use by industrialists and industrial economists.

## What Is the Difference Between Isoquant and Isocost?

Both isocosts and isoquants are curves plotted on a graph. Used by producers and manufacturers, they display the best interplay of two factors that will result in the maximum output at minimum cost. An isoquant shows all combinations of factors that produce a certain output. An isocost shows all combinations of factors that cost the same amount.

## The Bottom Line

The isoquant curve is a sloping line on a graph that shows the various combinations of inputs that result in the same output. It's a microeconomic metric that businesses use to adjust the relative amounts of capital and labor they need to keep production steady.

> **Article Sources**
>
> 1.  Lloyd, Peter J. "[The Discovery of the Isoquant](https://read.dukeupress.edu/hope/article-abstract/44/4/643/12534/The-Discovery-of-the-Isoquant?redirectedFrom=fulltext)." _History of Political Economy,_ vol 44, no. 4, 2012, pp. 643-661.