Isocost Lines
Recall that a universally accepted objective of any firm is to maximise profit.
If the firm maximises profit, it will necessarily minimise cost for producing a
given level of output or maximise output for a given level of cost. Suppose
there are 2 inputs: capital (K) and labour (L) that are variable in the relevant
time period. What combination of (K,L) should the firm choose in order to
maximise output for a given level of cost?
If there are 2 inputs, K,L, then given the price of capital (P
k
) and the price of
labour (P
L
), it is possible to determine the alternative combinations of (K,L) that
can be purchased for a given level of expenditure. Suppose C is total
expenditure, then
C= P
L
* L + P
k
* K
This linear function can be plotted on a graph.
ISOCOST
K
C/P
k
A
B
O
C/P L
L
•
N
•
P
Figure 7.7: Isocost line
If only capital is purchased, then the maximum amount that can be bought is
C/P
k
shown by point A in figure 7.7. If only labour is purchased, then the
maximum amount of labour that can be purchased is C/P
L
shown by point B in
the figure. The 2 points A and B can be joined by a straight line. This straight
line is called the isocost line or equal cost line. It shows the alternative
combinations of (K,L) that can be purchased for the given expenditure level C.
Any point to the right and above the isocost is not attainable as it involves a
level of expenditure greater than C and any point to the left and below the
isocost such as P is attainable, although it implies the firm is spending less than
C. You should verify that the slope of the isocost is
1

k
L
k L
P
P
P
C
*
P
C
∆ L
∆ K
EXAMPLE :
Consider the following data:
P
L
= 10, P
k
= 20 Total Expenditure = 200.
Let us first plot the various combinations of K and L that are possible. We
1 The nagative sign is due to the fact that the slope of the isocost is negative.15
consider only the case when the firm spends the entire budget of 200. The
alternative combinations are shown in the figure (7.8).
P r o d u c t i o n F u n c t i o n
K
A
10
9
8
7
6
5
4
3
2
1
O
B
L
C
2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0
Figure 7.8: Shifting of Isocost
The slope of this isocost is ½. What will happen if labour becomes more
expensive say P
L
increases to 20? Obviously with the same budget the firm
can now purchase lesser units of labour. The isocost still meets the Yaxis at
point A (because the price of capital is unchanged), but shifts inwards in the
direction of the arrow to meet the Xaxis at point C. The slope therefore
changes to 1. You should work out the effect on the isocost curve on the
following:
(i) decrease in the price of labour
(ii) increase in the price of capital
(iii) decrease in the price of capital
(iv) increase in the firms budget with no change in the price of labour and capital
the answer
1. Statistical data can be organized and presented on a number line. Numerical information displayed on a number line is called a "line plot." 2. The hourly wages earned by the principal wage earner in ten families is shown in the chart at the right. The data range from $8.00 per hour to $20.25 per hour. In order to represent each on a number line, the scale shown must include these values. A "W" is used to represent each hourly wage. If more than one "W" has the same location on the number line, additional "W's" will be placed one above the other. A line plot on hourly wages is shown below. 3. Have the students discuss what information can be gained from the line plot. For example, what is the usual wage? Are any wages very different from the rest? 4. Discuss the possibility of using different symbols to distinguish between sets of data on the same line plot or to differentiate between values within the same set. Family Hourly Wage A $8.00 B $10.50 C $20.25 D $9.40 E $11.00 F $13.75 G $8.50 H $10.50 I $9.00 J $11.00 W W W W W W W W W W 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Point out that graphs do not have to start with "0."
A line of bestfit.
A straight line, a telephone line, a shipping line, a fishing line.
A line intersect is a point on a line where another line or object crosses the line.
the answer
The ISOcost line shows combinations of inputs that yield the same level of cost. It is not the same as the profit line, which represents combinations of outputs that generate the same level of profit. Profit lines are typically used to analyze profitmaximizing decisions, while ISOcost lines are used to analyze costminimizing decisions.
A line along which the cost of something  usually a combination of two factors of production  is constant. Since these are usually drawn for given prices, which are therefore constant along the line, an isocost line is usually a straight line, with slope equal to the ratio of the (factor) prices.
Isocost lines are straight because they represent all the possible combinations of inputs that can be purchased for a given total cost. Since the cost per unit of input is constant along a straight line, different combinations on the line will have the same total cost. This allows firms to find the most costeffective way to produce a given level of output.
yes
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Final coordination line
Final coordination line
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