# Isocost Line

Assume you own and operate a chocolate manufacturing company. What are the two basic inputs required by your company for manufacturing? It's obvious that it requires labor and capital. The company suddenly suffers the high pay demanded by the workers, which would eventually harm the company's profitability. What would you do to make sure your company is profitable? Let's start by learning about the isocost line, its properties, and isoquants. Let us get right into the article.

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## Define Isocost Line

Before jumping directly into defining the isocost line, let us have a quick look at the cost of the firm in the long run.

In the long run, a specific firm has the freedom of choice to make several business decisions. A firm can expand or contract its capital and labor force as per its requirement. Firms have the flexibility to select different combinations of labor and capital to minimize their production cost.

An isocost line is a graph showing various possible combinations of inputs (labor and capital) that can be purchased for an estimated total cost. Any combination of inputs on an isocost line provides the same total cost for the output.

Wider cost considerations for the firms

On the isocost line, a firm can select from a variety of input combinations that result in the same output. However, firms make decisions on a combination of inputs depending on their area of operation. If a firm is located in an area with low labor costs, it may choose to build a labor-intensive production facility to reduce production costs.

An isocost line is a graph that depicts potential input (labor and capital) combinations that can be acquired at an estimated total cost.

To learn more on the topic of firm's production, don't forget to check out these articles:- Costs in Economics;- Production Cost For a Firm.

## Isocost Line Equation

Now, let's dive deeper into the isocost line equation to further comprehend the concept.

We know that an isocost line shows all the possible combinations of labor and capital for a certain amount of cost. Now, to find an isocost line equation, let us assume that $$C$$ is the total cost of producing a particular amount of output, and $$r \times K$$ and $$w \times L$$ denote the rental cost of capital and total wage of labor, respectively.

The equation of the isocost line is:

$$C=r \times K + w \times L$$

$$\hbox{Where:}$$

$$K$$ - the amount of capital employed

$$r$$ - the rental rate of capital

$$L$$ - the amount of labor employed

$$w$$ - the wage rate.

You have come learning this far. Great Job! Why not check out our articles:- Total Cost Curve;- Cost Curves.

## The Slope of the Isocost Line

Now, let us have a look at how we can determine the slope of the isocost line by using the isocost line equation.

The equation of an isocost line can be rearranged as the equation of a straight line. The equation of a straight line is written as follows:

$$y = ax+b$$

Now, let's rearrange the equation of the isocost line in the form of a straight-line equation.

$$C=r \times K + w \times L$$

$$r \times K = C-w \times L$$

$$K = C/r - (w/r)L$$

Fig. 1 - The Slope of the Isocost Line

Figure 1 depicts the isocost line I1, along with all the possible combinations of inputs for the total estimated cost. A firm can either use a combination of (L1 ; K1) or (L2 ; K2) or (L3 ; K3), depending on how they want to operate. If a firm decides to make its production labor-intensive, then it might choose the input combination at point C with L1 of labor and K1 amount of capital. Similarly, if a firm decides to make its production capital-intensive, then it will choose the combination at point A. It all depends on how the firm wants to operate and what helps them maximize its profit.

## Shifts of the Isocost Line

Let us have a look at what causes the shifts of the isocost line.

Fig. 2 - Shifts of the Isocost Line

The major reason behind the shifts of the isocost line is the change in the number of inputs used by a firm. Sometimes a firm might decide to expand its operations and increase its production, and sometimes it might look to reduce its production. Depending on the organizational strategy, the amount of inputs they use for production also varies.

In Figure 2 above, the initial isocost line is at I1. Now, if a firm decides to expand its operations, it will require an increased amount of inputs (labor and capital). In this case, the isocost line shifts to the right from I1 to I3 as the increased amount of inputs means increased total cost. Likewise, if a firm decides to contract its operations, the number of inputs they require will decrease. In this case, the isocost line will shift from I1 to I2.

Taking a break? Why not have a quick look at the following articles:- Fixed vs Variable Costs;- Accounting Profit vs Economic Profit

## Isocost Line and Isoquant

Let's have a look at the isocost line and isoquant together.

An isocost line helps us determine the combination of inputs for a defined amount of cost. An isoquant curve is a little bit different. An isoquant curve helps us determine the combination of inputs to produce the same amount of output.

Fig. 3 - Isocost Line and Isoquant

Figure 3 is a graph representing the isocost line (I1) and an isoquant curve (Q1). For a firm to produce maximum output at the minimum cost, the firm should aim to produce at the point where isoquant is tangent to isocost. At the tangent point, the slope of both isocost and isoquant is the same.

The curve that assists us in determining the combination of inputs that results in the same amount of output is known as an isoquant curve.

## Isocost Line Properties

Let us now examine some of the properties of the isocost line to see how firms can produce given output at the lowest possible cost and how firms react when input prices change.

• The properties of the isocost line are as follows:1. Helps the firm to produce given output at minimum cost.2. Helps the firm to adjust between two inputs when the price of one input changes.

### Isocost Line Properties: Minimum Cost Output

Let us first have a look at how the firms can produce the required output at a minimum cost.

Fig. 4 - Minimum Cost Output

Figure 4 depicts various isocost lines and an isoquant curve. Every firm strives to create its output at the lowest possible cost. Figure 4 depicts a firm attempting to create output Q1. How can a firm produce at the lowest possible overall cost?

Assume the firm wishes to invest an I1 amount of money. However, any combination of labor and capital on I1 will not be sufficient to generate Q1. At the cost levels I2 and I3, output Q1 is possible. At I3, the output can be obtained by combining K3 units of capital and L3 units of labor or K1 units of capital and L1 units of labor. However, the same output can be generated at the lowest cost at isocost I2 by using K2 units of capital and L2 units of labor.

• The isoquant curve is tangent to the isocost line at point A in Figure 4, indicating that this is the point where a firm can create the most output at the lowest cost.

### Isocost Line Properties: Substituting Input When Input Price Changes

Now, let's look at how a firm substitutes inputs when relative input prices change.

Fig. 5 - Isocost Line Properties

Let us Assume that the price of one of the inputs, say, labor, has increased. When the price increases, the slope of an isocost line increases in magnitude, which makes the isocost line rotate clockwise. Hence, it becomes steeper. How will a firm manage such a situation? Well, the firm will substitute the amount of labor it uses with capital.

In Figure 4 above, the firm was initially producing a Q1 level of output using a combination of L1 units of labor and K1 units of capital. Because labor costs have risen, the firm has decided to utilize a new combination of K2 units of capital and L2 units of labor to achieve the same output. Hence, the new cost minimization point for the firm is at point B.

To gain a better understanding of the various forms of costs in economics, why not check out:- Sunk Costs;- Fixed Costs;- Opportunity Cost.

## Isocost Line - Key Takeaways

• An isocost line is a graph that depicts potential input combinations that can be acquired at an estimated total cost.
• The equation of the isocost line is: $C=r \times K + w \times L$
• An isoquant curve assists us in determining the combination of inputs that results in the same amount of output.
• The isocost line's properties include assisting a firm in producing a specific output at the lowest possible cost and aiding the adjustment between two inputs when the price of one input changes.

#### Flashcards inIsocost Line 10

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Why are isocost lines straight lines?

As the cost of two inputs (capital and labor) are fixed, the isocost lines are straight.

What is isocost with example?

An isocost line is a graph that depicts potential input (labor and capital) combinations that can be acquired at an estimated total cost. For example, a firm can buy 10 units of capital and 4 units of labor or 5 units of capital and 8 units of labor. Both of the combinations can be acquired for the estimated cost of 40.

What are the properties of isocost?

The isocost line's properties include assisting the firm in producing a specific output at the lowest possible cost and assisting them in adjusting between two inputs when the price of one input changes.

What is the difference between isoquant and isocost lines?

An isocost line helps us to determine the combination of input for a defined amount of cost whereas an isoquant curve helps us to determine the combination of input to produce the same amount of output.

How do you graph isocost lines?

We graph the isocost line by taking into account the two inputs (labor and capital) and the total estimated expenditure.

What are the types of isocost?

There is no particular type of isocost line. However, depending on the decisions of the firm regarding the production inputs, the isocost line might shift to the right or the left.

## Test your knowledge with multiple choice flashcards

In the long run, firms have the flexibility to select different combinations of labor and capital to minimize their production cost.

Any combination of input in an isocost line provides the same total cost for the output.

Which of the following is the equation of an isocost line?

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