**Technology: Properties and Empirical Aspects — Transcript & Summary | SozAI**
Source: https://sozai.app/transcript/technology-properties-empirical-aspects/

Introduction to technology in production analysis, covering technology sets, production functions, and key properties like monotonicity and convexity.

## Key Takeaways

- Technology in production is defined as the set of all feasible input-output combinations.
- Monotonicity ensures that increasing inputs does not reduce output feasibility.
- Convexity guarantees that combinations of feasible input bundles are also feasible.
- Leontief production functions model perfect complements, while perfect substitutes are rare in empirical data.
- Understanding these properties is essential for empirical estimation and efficiency measurement in production analysis.

## What the video covers

- The video introduces fundamental concepts of technology in production analysis, focusing on its empirical construction and properties.
- Technology is viewed from both Leontief's perspective and the production economics point of view as feasible input-output combinations.
- The one input-one output case is used to conceptualize the technology set and production function as the boundary of feasible production.
- Extension to two inputs and one output introduces the concept of isocost curves and the technology set as the region including and to the right of the isocost.
- Special cases of technology include Leontief production functions with perfect complements and perfect substitutes between inputs.
- Key properties of technology sets discussed include monotonicity (free disposability) and convexity.
- Monotonicity means more inputs should not reduce output feasibility; free disposability applies to both inputs and outputs.
- Convexity implies that weighted combinations of feasible input bundles remain feasible, ensuring the technology set is convex.
- Mathematical formalizations of these properties are provided, including definitions of the technology set and input-output bundles.
- The session sets the foundation for constructing production functions and measuring technical efficiency in future lessons.

## Chapters

1. 00:00 Introduction and Overview of Technology Concepts
2. 00:53 Production Possibility Set and Isocost with Two Inputs
3. 01:51 One Input-One Output Technology Set Conceptualization
4. 03:17 Technology Set with Two Inputs and One Output
5. 04:27 Leontief Production Function and Perfect Complements
6. 06:02 Perfect Substitutes and Empirical Observations
7. 07:03 Monotonicity and Free Disposability of Inputs and Outputs
8. 09:11 Mathematical Formalization of Free Disposability
9. 10:46 Convexity Property of Technology Set
10. 14:32 Summary and Future Directions on Production Function Construction

Answers

## Questions about this video

What is the definition of technology in production economics?

Technology is defined as the set of all feasible input-output combinations or technologically feasible bundles that can produce output from given inputs.

What does monotonicity mean in the context of technology sets?

Monotonicity means that having more inputs should not reduce the ability to produce output; increasing inputs should maintain or increase output feasibility.

How is convexity important in production technology?

Convexity ensures that any weighted combination of two feasible input bundles is also feasible, implying the technology set is convex and allowing for smooth production possibilities.

## Full Transcript — Download SRT & Markdown

00:05

Speaker A

[music] [music] Welcome back to the course Applied Production Analysis Using MATLAB. In today's session, we'll be covering very fundamental concepts related to technology, its properties including its empirical construction.

00:32

Speaker A

We see technology from Leontief's perspective and technology from the production point of view. How technology is related to the production function.

00:44

Speaker A

We take the case of one input, one output. That is the very simple case of conceptualizing technology set and production function.

00:53

Speaker A

Extending that, we see how to conceptualize production possibility set and production function in the context of isocost in the context of two inputs and one output. And we go through two important properties of production possibility set or technology set that

01:14

Speaker A

is monotonicity and convexity. From a Leontief's perspective, technology is like the set of skills, methods, and the ways that you convert inputs into output. Similarly, in production economics point of view, we name technology as the set of all

01:42

Speaker A

feasible combinations of inputs and output or set of all technologically feasible inputs and output.

01:51

Speaker A

So with that, actually we can conceptualize the same in the context of one input, one output. In case of one input, one output case,

02:20

Speaker A

we can conceptualize the technology set output here, input here. And in this case, the technology set is the region below the production function or production function we can call it as the boundary of technology set.

02:52

Speaker A

So here in this context, one input and one output case, this production possibility set or the technology set shows all combinations of input and output which are technologically possible and the boundary we can call it as the production function.

03:17

Speaker A

Moving ahead, we can conceptualize technology set in the context of two inputs and one output.

03:37

Speaker A

Say we have two inputs X1 and X2. And in this context, as many of you know, we conceptualize technology in terms of isocost which shows the locus of combination of X1 and X2 which you can use for

04:02

Speaker A

production of a particular level of output. And here a point towards the right side of this isocost, say we are producing Y unit of output throughout the points of this isocost. In this context, any point toward the right side of that isocost as well

04:27

Speaker A

should be technologically feasible. In that case, the region toward the right side of the isocost including the boundary is the technology set.

04:43

Speaker A

And if you consider a point over here, producing the same amount of output is not technologically feasible because it involves lower amount of both X1 and X2.

04:57

Speaker A

You may come across the case where both X1 and X2 that we have mentioned over here are perfect complements. In that case, we get a Leontief production function. Say X1 and X2 are perfect complements. That means you need equal proportionate amount of

05:21

Speaker A

X1 and X2. Say you can consider the case of a car and driver.

05:27

Speaker A

Say one driver can ride only one car at a time and one car can be driven by only one driver at a time. So in this case, actually we can conceptualize the production function f of X1, X2

05:45

Speaker A

but it will take a case of minimum of X1 or X2. As I mentioned, even if you have an additional car but having only one driver, that does not contribute anything to the production function.

06:02

Speaker A

Similarly, you may have a case where X1 and X2 are perfect substitutes. In that case, the isocost takes a form of a straight line.

06:15

Speaker A

But in numerical literature, we may not come across these two cases. We may come across the case of Leontief production function. But this case of perfect substitutability between factors of production is rarely found. Most of the empirical cases we will find a

06:34

Speaker A

smoothly behaved curve that is the isocost that is given over here. So now we'll talk about the properties of technology set

07:03

Speaker A

or properties of technology we can call. The first property that we are discussing is monotonicity.

07:16

Speaker A

By monotonicity we mean having more input should not hurt us from a production point of view.

07:26

Speaker A

Alternatively, we call it as the free disposability as well. In some literature, you may see it as predisposability.

07:45

Speaker A

By monotonicity of redisposability we mean if you are able to produce Y amount of output by using X amount of input, you should be able to produce at least Y amount of output by using any input bundle which is greater than X.

08:08

Speaker A

And in literature, you may see predisposability from both input and output point of view. So we can have free disposability of input and we can have predisposability of output as well.

08:32

Speaker A

So we'll formalize the concept of predisposability of input which is going to be very foundational for our conceptualization or empirical estimation of technology set and production function especially in the context of nonparametric approaches to formalize predisposability of input.

08:51

Speaker A

Before that, we define T as the technology set which consists of all combinations of technologically feasible input-output bundles starting with X and Y as an input-output bundle which we consider as technologically feasible or actually being produced by

09:23

Speaker A

using X unit of input, one we are able to produce Y unit of output. So now we are bringing in X0, a different bundle of the input that we are considering which is expected to be greater than X

09:46

Speaker A

that is the initial bundle that we are referring to. So in this case, as per disposability of input, you can see that we can conceptualize a new bundle that is X0, Y should also be technologically feasible.

10:08

Speaker A

This is a mathematical way of defining free disposability of input. We can extend the same for multiple inputs and the same way for multiple outputs.

10:21

Speaker A

Right? Coming to the free disposability of output, it's very logical, very intuitive in some sense. Say X and Y are technologically feasible bundles that we have already discussed in the case of predisposability of input.

10:39

Speaker A

Now we can conceptualize Y0 as a level of output which is less than Y.

10:46

Speaker A

So in that case, as per free disposability of output, X, Y0 should also be technologically feasible. In a very simple mathematical example, say by using 10 units of input, initially firm is producing 100 units of output. By free disposability of

11:12

Speaker A

output, that means this should also be technologically possible to produce using the same amount of input but 80 units of output, where we are disposing 20 units in a philosophical manner.

11:30

Speaker A

Moving ahead, we have another important property of technology that is convexity. It's a very popular terminology that you keep seeing in the operations research or linear programming or even in the microeconomic literature.

11:54

Speaker A

Say we are talking about an output bundle Z and consider the case that the amount of output that Z can be produced by using or let's consider the case of Y as the output just to keep it consistent with what we have discussed

12:17

Speaker A

earlier. Say there are two ways to produce Y. Say X1 unit of input one and Z1 unit of input two.

12:31

Speaker A

We consider it as technologically feasible. Say alternatively you can use X2 unit of input one and Z2 unit of input two to produce the Y unit of output that we are considering.

12:52

Speaker A

Now by convexity, since these two points are technologically feasible, a convex combination or a weighted combination of these two bundles should also be technologically feasible. That means lambda X1 plus 1 minus lambda X2 as the amount of input one

13:29

Speaker A

and lambda Z1 plus 1 minus lambda Z2 as the input of input bundle of X2, that input two should also be technologically feasible. So here you can see the weight that is sum of weights associated with our

14:10

Speaker A

two bundles gets into one which is basically a property associated with convexity. So from a diagrammatic point of view, we can say that say f of X is the production possibility from here that you are considering given Y and X in a simple one input, one output

14:32

Speaker A

case and this is the production possibility set or the technology set and we say that it is convex. That means any point that you take within the technology set, say here, here, and the line connecting these two points should

14:50

Speaker A

also fall within the set. So that is the property that is the characteristic th

15:00

Speaker A

So uh these two properties or in in some sense these three properties predisposability of input predisposability of output and this convexity these are going to be very foundational for our conceptualization of production possibility set or the technology set and the production

15:19

Speaker A

possibility frontier whether it is uh one input one output case or two input one output case or even sometime uh we can conceptualize it as a two output and one input case. So it's going to be very foundational. So in this session we

15:37

Speaker A

covered the case of one input one output production possibility set which is the boundary of and the boundary of the same is called production function. We consider the case of two inputs, one output and in that context we were using

15:53

Speaker A

an isocorn and uh the properties of important properties of production possibility set which is predisposability of input, predisposability of output and the convexity.

16:09

Speaker A

In the upcoming sessions, we'll be constructing a production function that satisfy these properties and see how this can be utilized for measuring technical efficiency as a measure of performance.

16:23

Speaker A

[music] [music]

Topics: technology production function production possibility set isocost monotonicity convexity Leontief production function free disposability input-output bundles technical efficiency

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