1. Isocost Lines
An isocost line is a line showing combinations of inputs that would yield the same cost.

2. We have already thought about the demand for labor by firms in the context of the short run, i.e., when at least one input is fixed in amount. In the next few sections we will consider the long run. So we turn to concepts called isocost lines and isoquants.

3. Isocost lines
An isocost line includes all possible combinations of labor and capital that can be purchased for a given total cost.
In equation form the total cost is
C= wE + rK,
where C = Total cost or budget level,
w= the wage rate,
E = the amount of labor taken,
r = the rental price of capital, and
K = the amount of capital taken. This equation can be re-expressed as
K = (C/r) - (w/r)E.

4. When we write the isocost line in the form
K = (C/r) - (w/r)E.
We see
If E=0, then K = C/r,
If K=0, then E = C/w,
And the slope of the line is –w/r.

5. example
As an example say w = $6 per unit and r = $10 per unit. Then if we have C = $100 we have
K = (C/r) - (w/r)E or K = (100/10) – (6/10)E
We see
If E=0, then K = C/r = 100/10 = 10,
If K=0, then E = C/w = 100/6 = 16.67,
And the slope of the line is –w/r = -6/10.
On the next screen we can view the isocost line in a graph.

6. graph of isocost line K
This is the isocost line at $100. If we wanted to see higher costs (given the same input prices) we would shift the line out in a parallel shift and a lower cost we have a shift in. 10 E
16.67

7. Isocost K
If the wage should fall the isocost line rotates counterclockwise, and if the wage rises the line rotates clockwise. E