You may be confused sometimes between isocost and isoquant. In this article, we are going to discuss both in detail and also address the profit maximization issue.

## What is isoquant?

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The combining of two variables generating output is seen in an isoquant.

In this diagram, the isoquant introduces both labor and capital combinations capable of generating a cumulative production of 4,000. Above in the isoquant, it can be seen that:

Twenty capitals with eighteen labors (more capital intensive)

Nine capitals and Thirty-five labors (More labor-intensive)

The rule of decreasing returns normally forms an isoquant concave. The fall in the marginal output (MP) of fixed resources hiring extra employees.

## The marginal rate of factor substitution

*MRS = ΔK/ ΔL*

The marginal rate of substitution is the amount of one factor (e.g. K) that can be replaced by one factor (e.g. L). If 2 units of capital could be replaced with one-factor labor, the MRS would be 2.

**MRS = ΔK/ ΔL**

=2/1

=2

### The diminishing marginal rate of factor substitution

If 2 L and 40 K are employed. It would then save 10 K for an extra job. This saves considerably. The organization must pay only one new employee so can save 40.

However, with 9 Labor, an added employee makes only 2 capital saves. The longer these employees are thus working, the lower the pace at which the other element will be substituted. There is one thing that hardly any money is spared by hiring more employees. This happens because reduced labor yields are very high – jobs are effectively mutually exclusive.

The performance stays the same by going down the isoquant. The output obtained by more labor, then, needs to balance the output lost by more capital.

*MPP (L) x ΔL = MPP (K) x ΔK*

Deriving from this equation we get:

*MPP (L) / MPP (K) = ΔK / ΔL*

## Map of Isoquant

There are various performance ratios on an isoquant diagram. For instance;

I_{1} can suggest the combinations that can yield 4,000 TPP between capital and labor.

I_{2} will display capital and job combinations capable of delivering 5,000 TPP.

I_{5} is more powerful than I4

In the short term, an organization is faced with a certain isoquant. However, a business can invest in growing the stock of resources in the long run and achieve better returns with the same amount of work.

## What is Isocost?

An isocost displays the combination of variables, which cost the same.

A labor and capital unit cost £6,666 each. In this case;

The net expense of recruiting 30K and 30L is £200, 00 + £200,000

The average expense of hiring 10 K and 50 L is £66,666 + 333,333 = £400,000.

### Change in labor costs

In this case, the cost of labor and capital originally amounted to both £5,000. ( E.g. 60L = 60 x 5 000 pounds = 300 thousand pounds)

But if Labor rates go up to £10,000, the isocost would move to the left. Today, to retain costs of £300,000, only 30 staff (30 x £10,000) could employ a company.

Therefore, the angle of the isocost is P_{L} / P_{K}

## Profit maximization

An organization wants to make the best possible isoquant and lowest possible isocost for optimizing benefit.

We have one isocost and three isoquants in this case. The highest production that a corporation would manage with the isocost of £400,000 will be 4,000 TPP. If 13K and 48 Labor were produced, so only a TPP of 3500 will be produced.

There is no cumulative PTP(Publicly Traded Partnership) of 4,500 without an extra expense of £400,000.

### Profit maximization – the lowest cost manufacturing process

Another way to optimize earnings is to strive for production of 4,00 and find the lowest possible isocost. In this case, it is a TC of £400,000 that impacts the Tangent TPP.

## Isoquant Curve – Assumptions

Isoquant’s curve illustrates how the change in one production element influences the other as the output stays stable.

We have to assume the following to form an isoquant curve:

* Optimum Combinations:* Productive and of same performance and efficiency are all possible combinations of production factors.

* Two output factors:* only two factors engage in the manufacturing function as it is possible to say

Q = f(L,K)

* Steady Manufacturing Methodology:* The process remains unchanged in its production process or technology.

* Technical substitution Possible:* production variables should be such that one can, including labor and money, replace one with the other.

* Divisible output factors:* The producing factors must be quantifiable or separated into fewer or less units.

## Isoquant Types

During the isoquant curves, we are presented with the various options that may or may not be practically applicable.

### Linear Isoquant

The one factor that replaces the other entirely in the manufacturing process is a very unrealistic strategy. The capital is replaced by the labor as the isoquant curve crosses the x-axis.

Even, if the curve crosses the y-axis, the output is achieved without employing any labor by capital itself.

### Smooth Convex Isoquant

The isoquant of which only two variations are possible, A and B, so that the two output variables are unable to substitute each other.

Thus, from A to B there is a straight convex curve.

### Right-angled isoquant or Leontief

If the two output variables cannot be replaced by each other, a right angle isoquant curve is formed.

Here, at the edge of the curve or ‘L,’ there is the optimal output stage. Also, the output is always equal.

### Kinked Isoquant

The development factors may be substituted to one another to a minimal degree in such an isoquant curve.

Besides, this substitution is facilitated by a minimal number of manufacturing methods.

## Isocost and Isoquant at a glance

Isocost curve is the budget line of a manufacturer, whereas isoquant is his curve of indifference. The same product curve or curve of development or a constant product curve is often referred to as Isoquant. Isoquant demonstrates different combinations of two input factors that provide the same output level per unit of time.

The expense minimization takes place where an isoquant is just tangent to an isocost line (but not crossed). The price ratio of variables when this occurs is the same as the marginal output ratio. Symbolically;

**PL / PK = MPL / MPK**