Iso-cost Line/ Producers Budget Line
The ISO-cost line is a graphical representation of the iso-cost schedule showing the various combinations of any two possible factor inputs that a producer can hire at the given income at the given price level of factor inputs.
Mathematically, it is expressed as;
Pl * Ql + Pk * Qk= C
or W.L + R*K= C…(i)
L= c/w, k=0
K= c/r, l=0
Here,
Pl= Price per labor
Ql= Units of labor
Pk= Price of capital
Qk= Units of capital
c= Total budget of producer
w= Wages of labor
l= Units of labor
r= Rate of interest of capital
k= Capital amount
Suppose the producer has Rs.2000 to hire labor and capital having per unit price Rs.200 and Rs.100 respectively. Lets explain this with the help of below table and graph:
| Combinations | Units of Labor (L) | Units of Capital (K) | Budget (B) = 200*L + 100*K = 2000 |
| A | 0 | 20 | 200*0 + 100*20 = 2000 |
| B | 2 | 16 | 200*2 + 100*16 = 2000 |
| C | 4 | 12 | 200*4 + 100*12 = 2000 |
| D | 6 | 8 | 200*6 + 100*8 = 2000 |
| E | 8 | 4 | 200*8 + 100*4 = 2000 |
| F | 10 | 0 | 200*10 + 100*0 = 2000 |
In the above figure, if the producer spends all of his or her budget on labor, then
He or she can hire: L = 2000/200 = 10
Here, K = 0, B (10, 0)
If the producer spends all of his or her budget on capital then,
He or she can spend: K = 2000/100 = 20
Here, L= 0, A (0, 20)
If we join this two ending points, a producer budget curve AB is formed. A producer can utilize his or her budget in the given straight budget line.
Note:
- Any combination outside the budget line is unattainable due to limited budget.
- Any combination inside the budget line is attainable but the budget is not fully spent.
- Slope of producer budget line changes when there is a change in price of the factor inputs such as change in wages rate of labor and interest rate of capital.
- Slope of producer budget line remains same or unchanged if there is change in producer’s budget.
