# Isoquants Optimal Production Function: Properties, Types

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## What is an Isoquant?

Isoquants, which you might already know, are like treasure maps for producers. They show all the different combinations of inputs that can produce the same level of output. Imagine isoquants as the contours on a map that connect all the points with the same altitude, but here, itโs all about output levels. The steeper the isoquant, the more output it represents.

An isoquant is a curve that shows all the combinations of inputs that yield the same level of output. โIsoโ means equal and โquantโ means quantity. Therefore, an isoquant represents a constant quantity of output.

## Definition of Isoquant

โAn Iso-quant curve may be defined as a curve showing the possible combinations of two variable factors that can be used to produce the same total product.โ

Peterson

โThe Iso-product curves show the different combinations of two resources with which a firm can produce an equal amount of product.โ

Bilas

โAn Iso-quant is a curve showing all possible combinations of inputs physically capable of producing a given level of output.โ

Ferguson

โThe Iso-product curve shows the different input combinations that will produce a given output.โ

Samuelson

For example, an isoquant for 100 units of output could show all the combinations of labor and capital that could be used to produce 100 units of output. Some of the combinations on the isoquant might be 50 units of labor and 50 units of capital, or 25 units of labor and 75 units of capital, or any other combination that adds up to 100 units of output.

## Properties of isoquants

Isoquants have a few key properties:

• They are downward-sloping. This is because as you add more of one input, you need to use less of the other input to keep the output constant.
• They are convex to the origin. This is because of the law of diminishing marginal returns. As you add more of one input, the marginal productivity of that input declines, so you need to use more of the other input to keep the output constant.
• They are not perfectly straight lines. This is because the marginal rate of technical substitution (MRTS) is not constant. The MRTS is the amount of one input that you can give up in exchange for one unit of another input while keeping the output constant. The MRTS declines as you move down the isoquant, meaning that you have to give up more of one input to get one unit of another input.

## Types of Isoquants

Now, letโs talk about the various types of isoquants and their characteristics. We have three main types: the right-angle isoquant, the L-shaped isoquant, and the smooth, bowed-outward isoquant. Itโs like we have squares, L-shapes, and curvy lines in our isoquant gallery.

### Linear isoquants

These show that the two inputs are perfect substitutes. This means that they can be used in any proportion to produce the same level of output. For example, if labor and capital are perfect substitutes, then a firm could produce 100 units of output with 50 units of labor or 50 units of capital.

### Input-output isoquants

These show that the two inputs are perfect complements. This means that they must be used in fixed proportions to produce the same level of output. For example, if labor and capital are perfect complements, then a firm could produce 100 units of output with 50 units of labor and 50 units of capital, but it could not produce 100 units of output with 25 units of labor and 75 units of capital.

### Kinked isoquants

These show that there is a limited range of substitutability between the two inputs. This means that there are some combinations of inputs that can be used to produce the same level of output, but there are other combinations that cannot be used. For example, a kinked isoquant might show that a firm can produce 100 units of output with 50 units of labor and 50 units of capital, or with 75 units of labor and 25 units of capital, but it cannot produce 100 units of output with any other combination of inputs.

### Smooth, convex isoquants

These show that the two inputs are imperfect substitutes. This means that they can be used in some proportions to produce the same level of output, but the marginal rate of technical substitution (MRTS) declines as the firm uses more of one input and less of the other input. The MRTS is the amount of one input that the firm can give up in exchange for one unit of another input while keeping the output constant.

## How are isoquants used?

Isoquants are used to analyze the production decisions of firms. Firms want to produce a certain level of output at the lowest possible cost. Isoquants can help firms to find the optimal combination of inputs to produce a given level of output.

Isoquants can also be used to analyze the impact of changes in input prices on production costs. For example, if the price of labor increases, the isoquant will shift inward, meaning that the firm will need to use more capital to produce the same level of output. This will increase the firmโs production costs.

Ok i think it becomes complicated so letโs take an example so assume that if youโre producing shoes, the right-angle isoquant would be like youโre using only labour or only capital with no substitution, making it quite rigid. On the other hand, the L-shaped isoquant would imply that you can only produce a certain output by using a fixed combination of inputs โ quite inflexible, donโt you think?

But hey, here comes the superstar โ the smooth, bowed-outward isoquant! With this one, you can mix and match inputs to your heartโs content, achieving the same output in various ways. Itโs like being able to bake a cake using different recipes and still ending up with a delicious treat!

Now, letโs see what these isoquants look like on a graph and how to interpret them. Just think of the graph as a giant puzzle board where we place our isoquant pieces. The axes represent our inputs, like labour and capital. Each isoquant is a piece on the board, and we can slide them around to find the best input combinations.

Suppose youโre producing books, and you can use either more labour or more capital. As we move along the isoquant from left to right, weโre using more labour and less capital, while moving from right to left means more capital and less labour. Easy peasy, right?

Now, letโs have some real-world fun with examples of isoquants in economics. Think about a pizza shop, and the isoquants show all the ways they can produce the same number of pizzas. They can have a team of skilled chefs and fewer ovens or more ovens and fewer chefs, all leading to the same delicious outcome!

Now, imagine youโre a superhero economist, and you use isoquant analysis to save the day. You swoop in to help a car manufacturer figure out the best combination of workers and machines to produce cars efficiently. And voilร , youโve optimised their production process!

Alright, letโs switch gears for a moment and talk about isocost lines. These are like budget lines that show all the different combinations of inputs that cost the same amount. Remember, every superhero economist needs to be cost-conscious too!

Assume, yourself as the manager of an ice cream parlour. You have a certain budget, and you can spend it on workers or machines to make ice cream. The isocost lines will help you find the sweet spot, where you get the most ice cream for your money!

Now, letโs put isoquants and isocosts on the same graph and see what happens. Itโs like a dance-off between your production options and your budget. The magic happens where the isoquant and isocost lines intersect. Thatโs where youโre getting the most output for the least cost โ the ultimate win-win situation!

But beware, there are some key differences between isoquants and isocosts. While isoquants focus on output levels, isocosts are all about the expenses. Itโs like comparing your superhero powers โ one is all about strength, while the other is all about agility!

Now, you might wonder how isoquants and indifference curves are related. Well, imagine yourself in the shoes of a savvy consumer, trying to find the perfect balance between the goods you want and the money you have. The indifference curves show all the combinations of goods that give you the same level of satisfaction, and the isoquants help producers find the optimal combination of inputs. Itโs like a cosmic connection between consumers and producers!