In this article we will discuss about the iso-cost line of a firm and its properties.
Iso-Cost Line (ICL) of a Firm:
Equations (8.27) and (8.28) are the two different forms of the same equation. To make our analysis simple, we shall assume that (8.28) is the firm’s iso-cost equation.
This equation is:
= rXx + rYy [eqn. (8.28)].
Since rx, rY and TVC are constants, eqn. (8.28) is a linear equation in x and y, and the straight line obtained as a graph of this equation is called the iso-cost line of the firm. We can draw the straight line if we know the values of the parameters rx, rY and 
.
For example, if we have rx = Rs 20, rY = Rs 10 and 
= Rs 1,000, then the specific form of the iso-cost equation (8.28) will be:
1,000 = 20 X+ 10 y (8.31)
Eqn. (8.31) is a linear equation in the input quantities x and y. Some of the combinations of x and y that satisfy (8.31) are M1 (50, 0), E (40, 20), F (30, 40), G (20, 60), H (10, 80) and L1 (0, 100). These combinations are plotted in two-dimensional input space of Fig. 8.11.
The straight line, L1M1, joining these points gives us the iso-cost line of the firm for rx = 20, rY = 10 and 
= 1,000. The firm would have to spend Rs 1,000 for buying any combination of the inputs lying on this line.
If the input prices, rx and rY, remain unchanged, then we shall obtain a particular iso-cost line (ICL) for each particular value of 
. For example, at 
= Rs 1,000, we have obtained the ICL, L1M1.
But if TVC increases to Rs 1500, then the specific form of the firm’s iso-cost equation will be:
1500 = 20x + 10y (8.32)
The ICL that would be obtained in this case is L2M2 in Figure 8.11. Two particular points on this line are M2 (75, 0) and L2 (0, 150).
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We have seen, therefore, that different ICLs would be obtained for different levels of cost.
Properties of an Iso-Cost Line:
The ICLs possess the following properties:
(i) An ICL is a negatively sloped straight line. The equation of this line, as we have already obtained is
= rXx + rYy [(8.28)]
Also, it is obvious from (8.28) that the slope of the ICL = -rX/rY = negative (rX. rY > 0). Since rX = Rs 20 and rY = Rs 10 in our example, the slope of both (8.31) and (8.32) are -2.
(ii) The numerical value of the slope of an ICL is equal to rX/ rY , or, it is equal to the ratio of the input prices.
(iii) It is obtained from (8.28) that the x-and y-intercepts of the iso-cost line are 
/ rX and 
/ry, respectively. In other words, the x-intercepts of the ICL would be equal to the quantity of input X that the firm would be able to buy if it spends all its money (i.e., 
) on , and the y-intercept would be the quantity of input , and the y-intercept would be the quantity of input that the firm would be able to buy if it spends all its Money on Y.
(iv) rX , rY remaining the same, if the amount of money, to be spent on input, i.e., TVC< increases (decreases), the x-and y-intercept of the ICL would increases (decreases),and the ICL would have a parallel rightward (leftward) shift (slope, – rX/ry, is constant). In other word, a higher (lower) ICL represents a higher (lower) amount of expenditure.