Iso-cost Line
Iso-cost line is the locus of various combinations of inputs which can be produced by the producer at a given outlay and
factor prices. The iso-cost line is important for determining what combination of input the firm will choose for
production.
Let w and r be the price of inputs L and K respectively, and CO be the total outlay (cost) of production then the equation
of iso-cost line is,
Co = w..L + r..K
Now suppose that a producer has a total budget of Rs 100 and and for producing a certain level of output, he has to
spend this amount on two factors labor and capital. Price of factors labor and capital are Rs. 20 and Rs. 10
respectively. All the possible combination of two inputs are as follows:
Combination
Labor
Capital
Total cost
A
0
10
100
B
1
8
100
C
2
6
100
D
3
4
100
E
4
2
100
F
5
0
100
The above table shows all the different combinations of inputs that can purchase for a given cost. If we plot
these combinations on graph, we get the budget line as shown in the following figure:
Y
Capital
10 A
8
B
C
6
D
4
E
2
0
1
2
3
4
Labor
F
5
X
In the given diagram, x-axis represents units of labor and y-axis represents units of capital. If the firm spent all of its
total outlay on capital, it could purchase OA (10) units of capital. If the firm spent all of its total outlay on labor, it could
purchase OF (5) units of labor. If we join these two points A and F, we get Iso-cost line for the firm. The firm can
purchase any combination of labor and capital shown on its iso-cost line. An iso-cost line is also known as price line or
outlay line.
Mathematically, an Iso-cost line can be expressed as
Co = w L + r K
or, r K = Co - w L
Co
w
K = r − r L ………….(i)
Differentiating equation (i) w. r. t. ‘L’, we get,
𝒅𝑲
𝒘
= − 𝒓 = Slope of Iso-cost line
𝒅𝑳
Shift in Iso-cost Line
An Iso-cost line may shift due to two reasons. They are
1. Change in total outlay to be made by the firm
2. 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 Iso-cost line to shift to a new position higher to the initial line.
Figure: shift in Iso-cost line due to change in total outlay
In the above figure, A’B’ is the initial Iso-cost line. When the firm increased its total outlay, the Iso-cost 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 Iso-cost line will shift leftwards to AB. Whether the
Iso-cost line shifts toward the left or toward the right, it will always remain parallel to the original line.
Change in Price of a Factor-Input
When price of factor-input changes, the Iso-cost line swings or rotates. The direction in which the Iso-cost line will
swing depends upon the factor whose price has changed.
Case I: Change in Price of Labor
Figure: Shift in Iso-cost line due to change in price of labor
Let us suppose that a firm has total outlay of Rs. 100 and AB is initial Iso-cost 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 Iso-cost line due to change in price of capital
Once again, let us assume that a firm has total outlay of Rs. 100 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 Iso-cost line shifts its position in y-axis and not in x-axis.
In the diagram, we can see that Iso-cost 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 Iso-cost line and increase in price of capital causes
anti-clockwise shift.