This document discusses production functions and related concepts. It defines a production function as relating the quantity of output to quantities of inputs. Key properties of production functions are outlined, including non-negativity, monotonicity, and concavity. Short-run production functions are discussed as holding some inputs fixed. Elasticities of production and substitution are introduced as measures of how output and inputs respond to changes. The document provides an example of computing these measures for a Cobb-Douglas production function.
An Efficient Elliptic Curve Cryptography Arithmetic Using Nikhilam Multiplica...theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Assignment Chapter - Q & A Compilation by Niraj ThapaCA Niraj Thapa
My name is Niraj Thapa. I have compiled Assignment Chapter including SM, PM & Exam Questions of AMA.
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Phương pháp chữa nói lắp toàn diện được Echo Việt nam www.echovietnam.org dịch từ quyển sách Comprehensive Stuttering Therapy và phát hành dưới sự cho phép của tác giả Phillip J. Roberts. Đây là một trong nhiều tài liệu miễn phí hỗ trợ cho người nói lắp Việt Nam. Mọi việc trích dẫn từ sách này phải ghi rõ xuất xứ của quyển sách. Mọi yêu cầu phát hành lại, in lại… phải được sự chấp thuận của Echo Việt Nam, đại diện là người sáng lập Trương Minh Sử Nhiên.
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Tôi cũng xin gửi lời cảm ơn đến tác giả Phillip J. Roberts, đã cho phép, tôi, tổ chức Echo Việt nam được phép dịch và phát hành để phục vụ rộng rãi cho cộng đồng nói lắp Việt nam.
Sài Gòn, tháng 10 năm 2009
Người sáng lập Echo Việt nam
Trương Minh Sử Nhiên
tmsnhien@gmail.com
An Efficient Elliptic Curve Cryptography Arithmetic Using Nikhilam Multiplica...theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Assignment Chapter - Q & A Compilation by Niraj ThapaCA Niraj Thapa
My name is Niraj Thapa. I have compiled Assignment Chapter including SM, PM & Exam Questions of AMA.
You feedback on this will be valuable inputs for me to proceed further.
Phương pháp chữa nói lắp toàn diện được Echo Việt nam www.echovietnam.org dịch từ quyển sách Comprehensive Stuttering Therapy và phát hành dưới sự cho phép của tác giả Phillip J. Roberts. Đây là một trong nhiều tài liệu miễn phí hỗ trợ cho người nói lắp Việt Nam. Mọi việc trích dẫn từ sách này phải ghi rõ xuất xứ của quyển sách. Mọi yêu cầu phát hành lại, in lại… phải được sự chấp thuận của Echo Việt Nam, đại diện là người sáng lập Trương Minh Sử Nhiên.
Tài liệu này tuyệt đối không được sử dụng với mục đích thương mại dưới mọi hình thức.
Đại diện, nhóm Echo Việt Nam, tôi xin chúc các bạn sớm thành công trong việc giao tiếp công chúng và đời thường. Thành công sẽ không là xa với nếu ai kiên trì tìm kiếm nó.
Tôi cũng xin gửi lời cảm ơn đến tác giả Phillip J. Roberts, đã cho phép, tôi, tổ chức Echo Việt nam được phép dịch và phát hành để phục vụ rộng rãi cho cộng đồng nói lắp Việt nam.
Sài Gòn, tháng 10 năm 2009
Người sáng lập Echo Việt nam
Trương Minh Sử Nhiên
tmsnhien@gmail.com
Phương pháp tự điều trị cho người nói lắp được Echo Việt nam www.echovietnam.org dịch từ quyển sách Self Therapy for stutterers của tác giả MALCOLM FRASER và phát hành dưới sự cho phép của tổ chức www.stutteringhelps.org. Đây là một trong nhiều tài liệu miễn phí hỗ trợ cho người nói lắp Việt Nam. Mọi việc trích dẫn từ sách này phải ghi rõ xuất xứ của quyển sách. Mọi yêu cầu phát hành lại, in lại… phải được sự chấp thuận của Echo Việt Nam, đại diện là người sáng lập Trương Minh Sử Nhiên.
Tài liệu này tuyệt đối không được sử dụng với mục đích thương mại dưới mọi hình thức.
Đại diện, nhóm Echo Việt Nam, tôi xin chúc các bạn sớm thành công trong việc giao tiếp công chúng và đời thường. Thành công sẽ không là xa với nếu ai kiên trì tìm kiếm nó.
Tôi cũng xin gửi lời cảm ơn đến tổ chức Stuttering Helps, đã cho phép, tôi, tổ chức Echo Việt nam được phép dịch và phát hành để phục vụ rộng rãi cho cộng đồng nói lắp Việt nam.
Sài Gòn, 22 tháng 10 năm 2010
Người sáng lập Echo Việt nam
Trương Minh Sử Nhiên
tmsnhien@gmail.com
1
ECONOMICS 581: LECTURE NOTES
CHAPTER 4: MICROECONOMIC THEORY: A DUAL APPROACH
W. Erwin Diewert March 2011.
1. Introduction
In this chapter, we will show how the theory of convex sets and concave and convex
functions can be useful in deriving some theorems in microeconomics. Section 2 starts
off by developing the properties of cost functions. It is shown that without assuming any
regularity properties on an underlying production function, the corresponding function
satisfies a large number of regularity properties. Section 3 shows how the cost function
can be used to determine a production function that is consistent with a given cost
function satisfying the appropriate regularity conditions. Section 4 establishes the
derivative property of the cost function: it is shown that the first order partial derivatives
of the cost function generate the firm’s system of cost minimizing input demand
functions. Section 5 shows how the material in the previous sections can be used to
derive the comparative statics properties of the producer’s system of cost minimizing
input demand functions. Section 6 asks under what conditions can we assume that the
technology exhibits constant returns to scale. Section 7 indicates that price elasticities of
demand will tend to decrease in magnitude as a production model becomes more
aggregated.
Section 8 notes that the duality between cost and production functions is isomorphic or
identical to the duality between utility and expenditure functions. In this extension of the
previous theory, the output level of the producer is replaced with the utility level of the
consumer, the production function of the producer is replaced with the utility function of
the consumer and the producer’s cost minimization problem is replaced by the problem
of the consumer minimizing the expenditure required to attain a target utility level. Thus
the results in the first 5 sections have an immediate application to the consumer’s system
of Hicksian demand functions.
The final sections of the chapter return to producer theory but it is no longer assumed that
only one output is produced; we extend the earlier analysis to the case of multiple output
and multiple input technologies.
2. Properties of Cost Functions
The production function and the corresponding cost function play a central role in many
economic applications. In this section, we will show that under certain conditions, the
cost function is a sufficient statistic for the corresponding production function; i.e., if we
know the cost function of a producer, then this cost function can be used to generate the
underlying production function.
2
Let the producer’s production function f(x) denote the maximum amount of output that
can be produced in a given time period, given that the producer has access to the
nonnegative vector ...
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
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Abstract Power system engineers are always striving hard to run the system with effective utilization of real and reactive powers generated by the generating plants. Reactive power is used to provide better voltage profile as well as to reduce system losses. Membership functions are written for fuel cost, losses, stability index and emission release. As minimization of real power loss over the transmission lines, an attempt is made in this paper to optimize each objective individually using Fuzzy logic approach. In this paper basic assumption is Decision Maker (DM) has imprecise or fuzzy goals of satisfying each of the objectives, the multi objective problem is thus formulated as a fuzzy satisfaction maximization problem which is basically a min-max problem. The multi objective problem is handled using the fuzzy decision satisfaction maximization technique which is an efficient technique to obtain trade off solution in multi objective problems. The developed algorithm for Optimization of each objective is tested on IEEE 30 bus system. Simulation results of IEEE 30 bus network are presented to show the effectiveness of the proposed method. Keywords: Real power, Reactive power, losses, membership functions, fuzzy logic and trade off solution
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One such alternative that has garnered significant attention and acclaim is Nitrux Linux 3.5.0, a sleek, powerful, and user-friendly Linux distribution that promises to redefine the way we interact with our devices. With its focus on performance, security, and customization, Nitrux Linux presents a compelling case for those seeking to break free from the constraints of proprietary software and embrace the freedom and flexibility of open-source computing.
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Pakdata Cf is a groundbreaking system designed to streamline and facilitate access to CNIC information. This innovative platform leverages advanced technology to provide users with efficient and secure access to their CNIC details.
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The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024Neo4j
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Paper: https://eprint.iacr.org/2023/1886
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What will you get from this session?
1. Insights into integrating generative AI.
2. Understanding how this integration enhances test automation within the UiPath platform
3. Practical demonstrations
4. Exploration of real-world use cases illustrating the benefits of AI-driven test automation for UiPath
Topics covered:
What is generative AI
Test Automation with generative AI and Open AI.
UiPath integration with generative AI
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...Neo4j
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In this work, we equipped AFL, a popular fuzzer, with DIAR and examined two critical Linux libraries -- Libxml's xmllint, a tool for parsing xml documents, and Binutil's readelf, an essential debugging and security analysis command-line tool used to display detailed information about ELF (Executable and Linkable Format). Our preliminary results show that AFL+DIAR does not only discover new paths more quickly but also achieves higher coverage overall. This work thus showcases how starting with lean and optimized seeds can lead to faster, more comprehensive fuzzing campaigns -- and DIAR helps you find such seeds.
- These are slides of the talk given at IEEE International Conference on Software Testing Verification and Validation Workshop, ICSTW 2022.
3. Outline Introduction Properties Quantities of interest An example Short-run production functions Transformation functions 3 ECON377/477 Topic 1.2
4. Introduction Consider a firm that uses amounts of N inputs to produce a single output The technological possibilities of such a firm can be summarised using the production function: q = f(x) where q is output and x = (x1, x2, …, xN)׳ is an Nx1 vector of inputs We assume these inputs are under the control of the decision maker 4 ECON377/477 Topic 1.2
5. Properties Non-negativity: the value of f(x) is a finite, non-negative, real number Weak essentiality: the production of positive output is impossible without the use of at least one input Non-decreasing in x (monotonicity): additional units of an input will not decrease output , i.e. if x0≥ x1, then f(x0)≥ f(x1) ECON377/477 Topic 1.2 5
6. Properties Concave in x: Any linear combination of the vectors x0 and x1 will produce an output that is no less than the same linear combination of f(x0) and f(x1) Formally, f(θx0) + (1 – θ)x1 ≥ θ f(x0) + (1 – θ)f(x1) If the production function is continuously differentiable, concavity implies that all marginal products (MPs) are non-increasing (the law of diminishing marginal productivity) 6 ECON377/477 Topic 1.2
7. Properties The diagram on the next slide depicts a production function defined over a single input, x The values of q are all non-negative and finite real numbers for the values of x represented on the horizontal axis (non-negativity) The function passes through the origin (weak essentiality) The MP of x is positive at all points between the origin and point G (monotonicity) but monotonicity is violated on the curved segment GR 7 ECON377/477 Topic 1.2
8. q MP at G = 0 G E AP at E is the slope of the ray through the origin and E R q = f(x) Point of optimal scale D x 0 Concavity violated Feasible region Monotonicity violated
9. Properties As we move along the production function from the origin to point D, MPx increases Thus, the concavity property is violated at these points But concavity is satisfied at all points on the curve segment DR 9 ECON377/477 Topic 1.2
10. Properties Extending the graphical analysis to the multiple-input case is difficult In such cases it is common practice to plot the relationship between two of the variables while holding all others fixed We now consider a two-input production function and plot the relationship between the inputs x1 and x2 while holding output fixed at the values q0 10 ECON377/477 Topic 1.2
11. Properties We also plot the relationship between the two inputs when output is fixed at the values q1 and q2, where q2 > q1 > q0 (output isoquants), shown in the diagram on the next slide If properties are satisfied, these isoquants are non-intersecting functions that are convex to the origin, as depicted The slope of the isoquant is the marginal rate of technical substitution (MRTS) that measures the rate at which x1 must be substituted for x2 in order to keep output at its fixed level 11 ECON377/477 Topic 1.2
12. x2 F F(x1,x2) = q2 MRTS at F = slope of the isoquant at F F(x1,x2) = q1 F(x1,x2) = q0 x1 0 12 ECON377/477 Topic 1.2
13. Properties An alternative representation of a two-input production function is provided in the diagram on the next slide The lowest of the four functions plots the relationship between q and x1: The value of x2 is held fixed The other functions plot the relationship between q and x1 when x2 is fixed at different values 13 ECON377/477 Topic 1.2
15. Quantities of interest If the production function is twice-continuously differentiable we can use calculus to define a number of economic quantities of interest For example, two quantities we have already encountered are the MP and the MRTS Related concepts that do not depend on units of measurement are the output elasticity and the direct elasticity of substitution, which is usually denoted as σin the two-input case 15 ECON377/477 Topic 1.2
16. Quantities of interest In the next slide, an infinitesimal movement from one side of point A to the other results in an infinitesimal change in the input ratio but an infinitely large change in the MRTS, implying that σ = 0 Thus, in the case of a right-angled isoquant, an efficient firm must use its inputs in fixed proportions That is, no input substitution is possible ECON377/477 Topic 1.2 16
18. Quantities of interest In the next slide, a movement from D to E results in a large percentage change in the input ratio but leaves the MRTS unchanged This result implies that the isoquant is a straight line and inputs are perfect substitutes 18 ECON377/477 Topic 1.2
19. x2 D σ = infinity E x1 0 19 ECON377/477 Topic 1.2
20. Quantities of interest In the next slide, an intermediate (and more common) case is depicted where σ lies somewhere between zero and infinity 20 ECON377/477 Topic 1.2
21. x2 σ lies between zero and infinity x1 0 21 ECON377/477 Topic 1.2
22. Quantities of interest In the multiple-input case it is possible to define at least two other elasticities of substitution: the Allen partial elasticity of substitution (AES) and the Morishima elasticity of substitution (MES) The DES is sometimes regarded as a short-run elasticity because it measures substitutability between xn and xm while holding all other inputs fixed 22 ECON377/477 Topic 1.2
23. Quantities of interest Economists use the term, short-run, to refer to time horizons so short that at least one input is fixed The AES and MES are long-run elasticities because they allow all inputs to vary When there are only two inputs, DES = AES 23 ECON377/477 Topic 1.2
24. Quantities of interest The MP measures the output response when one input is varied and all other inputs are held fixed But we are often interested in measuring output response when all inputs are varied simultaneously If a proportionate increase in all inputs results in a less than proportionate increase in output, then we say the production function exhibits decreasing returns to scale (DRS) 24 ECON377/477 Topic 1.2
25. Quantities of interest If a proportionate increase in inputs results in the same proportionate increase in output, the production function is said to exhibit constant returns to scale (CRS) If a proportionate increase inputs leads to a more than proportionate increase in output the production function exhibits increasing returns to scale (IRS) There are many reasons why firms may experience different returns to scale 25 ECON377/477 Topic 1.2
26. Quantities of interest A widely used measure of returns to scale is the elasticity of scale or total elasticity of production The production function exhibits locally DRS, CRS or IRS as the elasticity of scale is less than, equal to or greater than 1 For the Cobb-Douglas production function defined over N inputs: q = ax1β1x2β2 … xNβN The output elasticities are En = Σβnfor n = 1, …, N 26 ECON377/477 Topic 1.2
27. An example Refer to pages 18-19 for an example illustrating the computation of MPs and elasticities in a two-input Cobb-Douglas production function 27 ECON377/477 Topic 1.2
28. Short-run production functions Short-run production functions are obtained by holding one or more inputs fixed Consider equation (2.10) on page 18 of CROB: q = 2x10.5x20.4 If x2 were fixed at 100 in the short run, the short-run production function would be: q = 2x10.51000.4, = 12.619x10.5 This function is depicted in the diagram on the next slide, along with another function based on the assumption that x2 is fixed at 150, when: q = 14.841x10.5 28 ECON377/477 Topic 1.2
30. Short-run production functions A family of short-run production functions could be constructed in this way, each of which satisfies the four properties outlined above As a group, this family could be viewed as a long-run production function because it depicts the production possibilities of the firm when both inputs vary 30 ECON377/477 Topic 1.2
31. Transformation functions The production function concept can be generalised to more than one output The technological possibilities of a firm that uses N inputs to produce M outputs can be summarised by the transformation function: T(x,q) = 0 where q = (q1, q2, …, qM)׳ is an Mx1 vector of outputs Transformation functions are special cases of distance functions, which are discussed in detail later 31 ECON377/477 Topic 1.2