** Production Optimization: **Generally, a profit-maximizing firm wants to determine which combination of factors of production (or inputs) would minimize its cost of production for a given output. This can be known by combining the firm’s production and cost functions, namely isoquants and iso-cost lines, respectively. Let us understand what we mean by isoquants.

**Isoquants:** An isoquant is a representation of all the input-output combinations that can produce the same level of output. Because an isoquant curve reflects all inputs that provide an equal quantity of output, the producer is indifferent as to which combination he uses.** Therefore, isoquants are also called **

**Equal-product curves****Production indifference curves or****iso-product curves.**

**The concept of isoquant can be easily understood with the help of the following table: **

**Various combinations of X and Y to produce a given level of output**

Factor Combination | Factor X | Factor Y | The Marginal Rate of Technical Substitution (MRTS) |

A | 1 | 12 | – |

B | 2 | 08 | 4 |

C | 3 | 05 | 3 |

D | 4 | 03 | 2 |

E | 5 | 02 | 1 |

When we plot the various combinations of factor X and factor Y, we get a curve IQ as shown in the below figure of Equal Product Curve or Isoquant:

**Equal Product Curve or Isoquant**

Isoquants are similar to indifference curves. Isoquants are negatively sloped, convex to the origin due to the diminishing marginal rate of technical substitution (MRTS), and are non-intersecting. However, there is one significant distinction between the two: Whereas the amount of happiness received by the consumer cannot be quantified in an indifference curve, the level of production acquired by the producer can be easily quantified. While isoquant IQ1 represents 100 units, curves IQ2, IQ3, and so on can be created to indicate increasing levels of production. A higher level of output is represented by a curve on the right, while a lower level of output is represented by a curve on the left. Having understood the concept of isoquants, let us understand what we mean by iso cost.

** Isocosts or equal-cost lines: **The isocost line, also known as the budget line or the budget constraint line, shows the various alternative combinations of two factors which a firm can buy with a given outlay. Assume that a company has Rs. 1,000 to spend on X and Y. If factor X costs Rs. 10 and the factory costs Rs. 20, the firm can spend on factor X and factor Y in a variety of ways. It can spend the full sum on X and thus purchase 100 units of X while purchasing zero units of Y, or it can spend the entire sum on Y and purchase 50 units while purchasing zero units of X. It can have any combination of X and Y in the middle. The total cost to the company remains the same regardless of which combination it chooses. In other words, all points on a budget line would cost the firm the same amount. The iso-cost line can also be depicted graphically. The units of factor X are shown on the X-axis, while the units of factor Y are shown on the Y-axis. When we spend an entire amount of $1,000 on factor X, we get OB of factor X, and when we spend an entire amount of $1,000 on factor Y, we get OA of factor Y. The straight line AB, which joins points A and B, will pass through all possible combinations of factors X and Y that the firm can buy with an outlay of $1,000. Line AB is called the Iso-cost line.

*Iso Cost Line Diagram: *

The above figure of iso-cost lines shows various iso-cost lines representing different combinations of factors with different outlays. Isoquants, which represent technical conditions of production for a product, and iso-cost lines, which represent various “levels of cost or outlay” (given the prices of two factors), can aid a company’s production optimization. It may strive to reduce the cost of producing a certain level of production or maximize the output for a certain cost or outlay. Assume the firm has already decided on the level of output to be produced. The question that then arises is which factor combination the firm should try to produce the predetermined output level. The firm will aim to use the least expensive combination of factors. By superimposing the isoquant that represents the predetermined level of output on the iso-cost lines, the least cost combination of components can be discovered. This is shown in the below figure:

*Least-Cost Combination of Factors: Producer’s Equilibrium:*

Assume the company has agreed to make 1,000 units (represented by iso-quant P). This can be produced by any factor combination lying on P, such as A, B, C, D, E, etc. The cost of producing 1,000 units would be minimum at the factor combination represented by point C, where the iso-cost line MM1 is tangent to the given isoquant P. All other points, such as A, B, D, and E, have higher costs since they are on higher iso-cost lines as compared to MM1. Thus, the factor combination represented by point C It is the optimum combination for the producer. It represents the least cost of producing 1,000 units of output.

The tangency point of a particular isoquant with an iso-cost line thus represents the least cost combination of factors for producing a given output.

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