### Isocost Line

The combination of factor-inputs with which a firm produces output depends upon the quantity of output that the firm wants to produce. Besides, the combination of factor-inputs also depends upon the amount of money that the firm wants to spend and prices of the factor-inputs.

An isocost line is a graphical representation of various combinations of two factors (labor and capital) which the firm can afford or purchase with a given amount of money or total outlay. It is an important tool for determining what combination of factor-inputs the firm will choose for production process.

Suppose a producer has Rs. 200 and he wants to spend his entire outlay on two factors – labor and capital. Further suppose that the price of Labor is Rs. 4 per unit and the price of capital is Rs 5 per unit. If the firm spends its whole outlay of Rs 200 on labor only, he can buy 50 units of labor. And, if the firm spends its entire outlay on capital only, then he can buy 40 units of capital.

Mathematically, an isocost line can be expressed as

C = w L + r K

Where,

C = cost of production

w = price of labor or wages

L = units of labor

r = price of capital or interest rate

K =units of capital

A firm can purchase only such combinations of factor-inputs which satisfy the given equation. For example, a producer can purchase combinations like ’25 units labor + 20 units capital’, ‘30 units labor + 16 units capital’ or ’12.5 units labor + 30 units capital’ because all of them fulfill the equation at given prices and outlay.

This concept is clearly explained by the figure given below.

Figure: isocost line

In the given diagram, x-axis represents units of labor and y-axis represents units of capital. Therefore, OB in the figure represents 50 units of labor and OA represents 40 units of capital.

If we join points A and B, we get isocost line for Rs. 200. And, the straight line which joins points A and B will pass through all combinations of labor and capital which the firm can buy with the outlay of Rs 200, if it spends the entire sum on them at the given prices.

This way, an isocost line is also known as price line or outlay line. It is a counterpart of budget line of indifference curve analysis.

The slope of the isocost line is equal to the ratio of price of factor-inputs. Mathematically, slope of an isocost line is expressed as

And this slope remains the same throughout the isocost line.

### Shift in Isocost Line

An isocost line may shift due to two reasons. They are

- Change in total outlay to be made by the firm
- Change in price of a factor-input

### Change in total outlay to be made by the firm

When the firm decides to increase the total money to be spent on purchase of inputs while prices of the inputs remain the same, the producer becomes able to afford such combinations of inputs which were initially unattainable to him. This causes isocost line to shift to a new position higher to the initial line.

Figure: shift in isocost line due to change in total outlay

In the above figure, AB is the initial isocost line. When the firm increased its total outlay, the isocost line shifted rightwards to a higher position A’B’ where the producer could purchase combinations of inputs with higher units of labor and capital. Likewise, if the firm reduces its total outlay, the isocost line will shift leftwards to A”B”.

Whether the isocost line shifts toward the left or toward the right, it will always remain parallel to the original line. It is because the slope of an isocost line is calculated as

Since we assume that no changes are made in the prices of either of the inputs, the slope remain the same for all budget line at any given outlay. And, any lines with same slope are parallel to each other.

### Change in price of a factor-input

When price of factor-input changes, the isocost line swings or rotates. The direction in which the isocost line will swing depends upon the factor whose price has changed.

**Case I: Change in price of labor**

Figure: shift in isocost line due to change in price of labor

Let us suppose that a firm has total outlay of Rs. 200 and AB is initial isocost line. Let us also suppose that the price of labor was decreased by certain amount, as a result of which the producer became able to purchase more units of labor at the same outlay. However, the producer can’t increase purchasing units of capital as price of capital is constant. Therefore, the position of price line is changed in the x-axis but unchanged in y-axis.

Simply, decrease in price of labor causes anti-clockwise rotation and increase in price of labor causes clockwise rotation.

**Case II: Change in price of capital**

Figure: shift in isocost line due to change in price of capital

Once again, let us assume that a firm has total outlay of Rs. 200 but this time let us suppose that the price of capital has changed and not of labor.

In this case, the producer will be able to buy more units of capital at same outlay but won’t be able to increase the purchasing units of labor. As a result, the isocost line shifts its position in y-axis and not in x-axis.

In the diagram, we can see that isocost line AB shifts to new position A’B as a result of decrease in price of capital. Likewise, the line shifts to A”B as a result of increase in price of capital.

In other words, decrease in price of capital causes clockwise shift in isocost line and increase in price of capital causes anti-clockwise shift.