ISOCOST LINE: MEANING, SLOPE AND SHIFTS

The combination of inputs used by a firm for production is determined by the output that it wants to produce.

Aside from that, the quantity of output a firm produces is determined by the amount of money it wants to spend on production and the costs of its factor inputs.

An isocost line shows the combination of factors inputs that a firm can afford given the amount it wants to spend on production.

It shows the combination of factor inputs available at a given cost.

It depicts the input bundles each of which costs the same amount.

It is the locus of all points showing the various combinations of factor inputs that can be purchased with a fixed amount of money.

An isocost also shows the combination of capital and labour that can be purchased from a given total cost.

Indeed, every point on the isocost represents the total cost for a given combination of labour and capital.

That is, the total cost will be:

$$C=wL+rK$$

Where C is the total cost of production

            w is wages, which is the price of labour

             L is units of Labour

             r is interest rate/rent, which is the price of capital

            K is units of capital.

Let's pretend there are two inputs and the producer only has N30 to spend on the inputs.

Given that the price of labour per hour is N6 and that the price of capital is N3.

bundles (C=N30)labour (N6 per hour)machine rental (N3 per hour)
a010
b18
c26
d34
e42
f50

As can be observed from the table at all combinations,

$$C=wL+rK$$

In bundle a,

$$30=6(0)+3(10)$$

In bundle b,

$30=6(1)+3(8)$$

In bundle c,

$$30=6(2)+3(6)$$

Isocost line

The above information can be represented n an isocost line or a graphical representation of the plausible combination of two inputs that can be utilized by a firm given its money constraint.

Representing the above information on an isocost line, it is:

The slope of isocost line:-w/r

The slope of isocosts is the relative price of labour and capital.

Because the price of labour is wages, W, and the price of capital is the rental income, R, it follows that the slope of isocost can be represented as:

$$=\frac{-w}{r}$$

Assuming two inputs, Labor and capital, the slope of isocost is known as the wage-rental ratio.

In other words, the slope of isocost is the ratio of wage rate to the rental cost of capital.

The slope of isocost shows the rate at which capital can be substituted for labour with no change in cost.

With K on the y-axis and L on the x-axis, the slope of any isocost line equals $\frac{-W}{r}$

Shifts in isocost line

There are two reasons why an isocost line shifts:

1. When a firm's expenditure on production changes.

2. When the price of any of the inputs, or both inputs, changes.

How does a change in a firm's production expenditure affect isocost?

When a firm increases its expenditure on labour and capital, the Isocost line shifts outwards, indicating that the firm now has more money to spend on labour and capital.

The isocost line shifts outwards when a firm production expenditures increase, showing that the firm now has more money to spend on labour and capital.

The reverse is also true. When a firm decreases its production expenditure ( on labour and capital), then the isocost lines will shift inward, indicating that less money can be spent on labour and capital.

How does a change in factor prices shift the isocost?

An increase in the prices of labour/capital  means that few labour/capital can be acquired given the limited money the firm has to expend on production.

Given the limited amount of money the firm has to spend on production, an increase in wage rate/rental income rate means that only a small amount of labour/capital can be acquired.

This will result in an inward shift in the isocost line, as illustrated below:

By the same reasoning, a decrease in the wage rate/rental rate would result in an outward shift in the isocost line, suggesting that more labour/capital can be acquired.

Changes in the slope of the isocost line

As earlier, the slope of isocost is the wage-to-rent ratio.

It is the relative price of labour and capital

Do changes in factor price causes changes in the isocost?

A change in factor price (s) will affect the slope of isocost only if the change is non-proportionally.

That is, wage rate and rental income do not increase or decreased by the same proportion.

When factor prices change proportionally, such that the wage rate and rental income increase or decrease in the same proportion, the slope of the isocost is unaffected.

Do changes in firm expenditure on production affect the slope of isocost?

The answer is no. The slope of isocost is the relative price of labour to capital, which has nothing to do with the amount of money a company spends on production.

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To summarize, a change in the firm expenditure on production as well as a change in the price of any input would shift the isocost line.

In addition, a non-proportional change in input costs will modify the slope of the isocost, although a change in the firm production budget will not.

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