2 edition of **On the use of homothetic functions in economic theory.** found in the catalog.

On the use of homothetic functions in economic theory.

Ashok Parikh

- 194 Want to read
- 14 Currently reading

Published
**1982**
by University of East Anglia] in [Norwich
.

Written in English

**Edition Notes**

Series | Economics discussion paper / University of East Anglia -- no.69 |

ID Numbers | |
---|---|

Open Library | OL20764368M |

graphs of homothetic functions. 1. introduction In economics, a production function is a mathematical expression which denotes the physical relations between the output generated of a rm, an industry or an economy and inputs that have been used. Explicitly, a production function is a map which has non-vanishing rst derivatives de ned by f: Rn +! R. Homothetic and Non-Homothetic CES Production Functions By RYuzo SATO* In economic theory the production func-tion is generally a concept stating quantita-tively the purely technological relationship between the output and the inputs of factors of production. An essential purpose of the concept is to describe the substitution possi-.

Book Description: A sequel to his frequently citedCost and Production Functions(), this book offers a unified, comprehensive treatment of these functions which underlie the economic theory of production.. The approach is axiomatic for a definition of technology, by mappings of input vectors into subsets of output vectors that represent the unconstrained technical possibilities of production. The constant function f(x) = 1 is homogeneous of degree 0 and the function g(x) = x is homogeneous of degree 1, but h is not homogeneous of any degree. (If h were homogeneous of degree k, then we would have 1 + t x = t k (1 + x) for all t and all x, which implies in particular that 1 + 2 x = 2 k (1 + x) (taking t = 2), which in turn implies.

Search the world's most comprehensive index of full-text books. My library. Example: y=3x 1 + 5x 2 with x 1 =t 2 and x 2 =4t 3 Applying chain rule gives =2t; =12t 2 Page 4 Homogeneous and Homothetic Function 1 DC-1 Semester-II Paper-IV: Mathematical methods for Economics-II Lesson: Homogeneous and Homothetic Function Lesson Developer: Sarabjeet Kaur College/Department: P.G.D.A.V College, University of Delhi Homogeneous.

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In consumer theory, a consumer's preferences are called homothetic if they can be represented by a utility function which is homogeneous of degree 1.

For example, in an economy with two goods {\displaystyle x,y}, homothetic preferences can be represented by a utility function {\displaystyle u} that has the following property: for every. Topics in Consumer Theory Homothetic and Quasilinear Utility Functions One of the chief activities of economics is to try to recover a consumer’s preferences over all bundles from observations of preferences over a few bundles.

If you could ask the consumer an inﬁnite. homogeneous functions, we need to ask ourselves whether there is a class of functions that are homogeneous, and yet possesses all the cardinal properties so that we may use them in our consumer theory analysis.

The good news is that there is, and they are known as Homothetic functions. De nition 4 A function h: Rn + 7. The fundamental property of a homothetic function is that its expansion path is linear (this is a property also of homogeneous functions, and thankfully it proves to be a property of the more general class of homothetic functions).

In consumption theory, this means that, keeping the prices or the price ratio constant, if we vary the income of. Notes on Microeconomic Theory. This note covers the following topics: The Economic Approach, Consumer Theory Basics, Homothetic and Quasilinear Utility Functions, The Traditional Approach to Consumer Theory, Producer Theory, Choice Under Uncertainty, Competitive Markets and Partial Equilibrium Analysis, Externalities and Public Goods, Monopoly.

This study is the result of an interest in the economic theory of production intermittently pursued during the past three years. Over this period I have received substantial support from the Office of Naval Research, first from a personal service consulting contract directly with the Mathematics Division of the Office of Naval Research and secondly from Project N6 onr at Princeton Univer.

Notes on Microeconomic Theory This note covers the following topics: The Economic Approach, Consumer Theory Basics, Homothetic and Quasilinear Utility Functions, The Traditional Approach to Consumer Theory, Producer Theory, Choice Under Uncertainty, Competitive Markets and Partial Equilibrium Analysis, Externalities and Public Goods, Monopoly.

New York University Department of Economics V C. Wilson Mathematics for Economists May 7, Homogeneous Functions For any α∈R, a function f: Rn ++ →R is homogeneous of degree αif f(λx)=λαf(x) for all λ>0 and x∈RnA function is homogeneous if it is homogeneous of.

This product is the book alone and does NOT come with access to MyMathLab Global. Buy Essential Mathematics for Economic Analysis, 5th edition, with MyMathLab Global access card (ISBN ) if you need access to MyMathLab Global as well, and save money on this resource.

INTRODUCTION Ever since their introduction by Shepherd inHomothetic Production Functions (HPFs) have been subject to an intensive analysis and development by economists.

Assumption of homotheticity simplifies computation, Derived functions have homogeneous properties, doubling prices and income doesn't change demand, demand functions are homogenous of degree 0 The slope of the MRS is the same along rays through the origin.

Let ≽ be a preference ordering on a set view of economic considerations, a common and reasonable assumption is the convexity of the ordering (i.e.

for all x ∈ E, the set {y ∈ E/y ≽ x} is convex).Then the utility functions which represent the ordering are quasi-concave but in general, a concave representation does not exist.

Economics A Graduate Economic Theory Fall Ted Bergstrom Economics Department, UCSB. Welcome to the Economics A Website. If you are taking this course, please check this site regularly. I will use this site for posting announcements about assignments.

The syllabus that you see is a bit like the weather report. Homothetic Functions De nition 3 A function: Rn. R is called homothetic if it is a mono-tonic transformation of a homogenous function, that is there exist a strictly increasing function g: R. R and a homogenous function u: Rn.

R such that = g u. It is clear that homothetiticy is ordinal property: monotonic transforma. Cite this entry as: Crouzeix JP. () Homogeneous and Homothetic Functions.

In: Durlauf S.N., Blume L.E. (eds) The New Palgrave Dictionary of Economics. This paper gives an outline of evolution of the concept and econometrics of production function, which was one of the central apparatus of neo-classical economics.

It shows how the famous Cobb-Douglas production function was indeed invented by von Thunen and Wicksell, how the CES production function was formulated, how the elasticity of substitution was made a variable and finally how Sato’s.

With homothetic utility functions, you can use the same model for rich or poor people/countries. So, if you want to have this feature, and do use expected utility theory, you MUST stick to CRRA.

The theory of production functions. In general, economic output is not a (mathematical) function of input, because any given set of inputs can be used to produce a range of outputs.

To satisfy the mathematical definition of a function, a production function is customarily assumed to specify the maximum output obtainable from a given set of inputs. The production function, therefore, describes. Economic Inquiry. Volume 9, Issue 1. ON HOMOTHETICITY OF PRODUCTION FUNCTIONS.

WHITAKER. University of Virginia. Search for more papers by this author. McCALLUM. University of Virginia *The authors are indebted to the referees for valuable comments on an earlier draft. Homogeneous functions Definition Multivariate functions that are “homogeneous” of some degree are often used in economic theory.

A function is homogeneous of degree k if, when each of its arguments is multiplied by any number t > 0, the value of the function is multiplied by t example, a function is homogeneous of degree 1 if, when all its arguments are multiplied by any number t. A sequel to his frequently cited Cost and Production Functions (), this book offers a unified, comprehensive treatment of these functions which underlie the economic theory of production.homothetic definition: Adjective (not comparable) 1.

(mathematics) of a function of two or more variables in which the ratio of the partial derivatives depends only on the ratio of the variables, not their value 2. (economics) in which the ratio of goods.production function, being a Cobb-Douglas production function, is also homothetic, meaning that if we solve for the ratio of optimal inputs, l*/k*, this term should not depend on the quantity produced.

Anyhow, to derive the associated cost function, we first need to solve for optimal quantities of the inputs, k and l, as functions of w, v and q.