### Producer’s Equilibrium

The primary objective of any business firm is to maximize profit. And, a producer is said to be in equilibrium when he attains maximum profit from limited outlay or limited output.

A producer may find out his equilibrium condition by the help of isoquant map and a family of isocost line.

An isoquant represents various combinations of two factor-inputs which yield same level of output to the producer while an isoquant map is a set of different isoquants, all of which represents unique level of output.

On the other hand, an isocost is a line formed by combining points which represents various combinations of two factor-inputs, given the prices of inputs and the total outlay available to the producer. And, a family of isocost is a set of isocost lines which shows various combinations of inputs at different level of outlay.

### Optional Choice of Inputs

A producer may maximize his profit through two ways. They are

- A producer can either minimize the cost of production for any given level of output.
- Or, maximize the output at any given level of outlay.

Let us examine these two options separately.

### Least Cost Combination: Minimization of Cost for Given Level of Output

Sometimes, the producer may have a particular level of output in mind, for example, constructing a building, making a dress, or producing X amount of certain commodity, etc.

To produce this given level of output the producer will have to choose the combination of factor-inputs in such a way that his cost of product is as less as possible so that his profit is maximized. Thus, a producer will try to produce given level of output with least cost combination.

The concept is explained by the help of an isoquant and a family of isocost in the following diagram.

**Figure: minimizing cost for a constant level of output**

Let us suppose that an entrepreneur decided to produce 500 units of a commodity. His desired level of output can be obtained by employing any combination of labor and capital that the isoquant (Iq) pass through.

In the figure, we have only one isoquant which denotes that the level of output is fixed, i.e. 500 units. On the other hand, there are three isocost lines (AB, A’B’ and A”B”) which indicates different level of outlay (cost).

Since the isoquant (Iq) pass through points such as C, D and E, the producer can attain his desired level of output by employing any of the combinations of labor and capital that lie at these points. However, C and D being situated on the higher isocost line will be ignored by the producer as he will require higher level of outlay to purchase these combinations.

On the other hand, the producer won’t be able to choose any combinations from the isocost line AB because no combination of labor and capital lying on that line will be able to produce 500 units of output.

Hence, the producer will be in equilibrium where the isocost line is tangent to the isoquant, i.e. at point E. In this situation, the slope of isoquant is equal to the slope of isocost line.

### Maximization of Output for a Given Level of Outlay (Cost)

Sometimes, there may be situation where the producer has fixed outlay from which he has to produce as much output as possible in order to maximize his profit.

How a producer attains equilibrium is such condition is explained by the help of an isocost line and an isoquant map.

**Figure: maximizing output for a given level of outlay**

Let us suppose that this time the producer has decided to incur an outlay of Rs. 5000 on labor and capital. Since the total outlay is fixed, there is single isocost line AB which represents various combinations of labor and capital that the producer can afford at Rs. 5000.

Similarly, in the figure, we have an isoquant map (three isoquants) Iq_{1}, Iq_{2} and Iq_{3} which represents various level of outputs, i.e. 300 units, 400 units and 500 units, respectively.

Since the isocost line AB passes through the points C, E and D, the producer can spend his total outlay on purchasing any combinations of capital and labor lying on these points to produce outputs. But, as we can see that the points C and D lie on the lower isoquant, the producer will choose the combination at point E.

It is because, by the property of isoquants,

level of output in Iq_{3} > level of output in Iq_{2} > level of output in Iq_{1 }

Although the level of output is greater in Iq_{3} as compared to Iq_{2} and Iq_{1}, the producer cannot choose any combination at Iq_{3} as it is away from the isocost line.

Hence, we can once again say that the producer will be in equilibrium at the point where the slope of isoquant is equal to the slope of isocost.