# homothetic function calculator

Code to add this calci to your website Can some one help me derive the functional form of profit function in case of homothetic production functions? Inverse function calculator helps in computing the inverse value of any function that is given as input. ��i�z=ڞ3#��2�y�p�h/F� 2m�#!Q��]tI�d ��fz �G}c��w���\+ /�g�ki���<40�p���*K�|�0�L���8\��k9qs�g��_����T�1 �p� [�r6f�=E�FfKJS�A�O������)!��b$*zJ�I��]G����P&��?D��}{�Vy(Ӯ�Rh�>J1����^t��� 1. d. 1.3 Homothetic Functions De nition 3 A function : Rn! An agent can work for a principal. But we have de ned previously that a function is homothetic if it is a monotone transformation of a homogeneous function. It is denoted as: f(x) = y ⇔ f − 1 (y) = x. Meaning of homothetic. Show that your results from part (a) agree with our discussion of the cases δ = 1 (perfect substitutes) and δ = 0 (Cobb–Douglas). Free functions composition calculator - solve functions compositions step-by-step This website uses cookies to ensure you get the best experience. Why? How does the MRS depend on the ratio y/x? To make 33 units of butter, firm 2 needs 11 barrels of oil. Homothetic paradigm can be helpful for enhancing a collection of matrix updating methods based on constrained minimization of the distance functions. iv. iii. Homogeneous Differential Equations. Ascertain the equation is homogeneous. Explore anything with the first computational knowledge engine. It is also called an anti function. • With homothetic preferences all indifference curves have the same shape. 1. m 2 + n 2 = 1. Show that the CES function is homothetic. The cost function exists because a continuous function on a nonempty closed bounded set achieves a minimum in the set (Debreu [6, p. 16]). A widely used class of homothetic function is the CRRA class. c. Show that the MRS is strictly diminishing for all values of δ . Calculate the MRS for this function when y/x = 0.9 and y/x = 1.1 for the two cases δ = 0.5 and δ ... delta -1 since the mrs depends only on the ratio of the quantities x and y, the utility function is homothetic. ... delta -1 since the mrs depends only on the ratio of the quantities x and y, the utility function is homothetic. Means, the On the other hand, the quadratic and the CARA class are not homothetic. function fis homothetic. utility functions which are increasing transformations of functions with this property. Homothetic preference functions yield income elasticities of demand equal to 1 for all goods across all possible levels of income because all level sets (i.e., indifference curves) are radial expansions of each other when a function is homothetic. I know that homothetic production function implies that cost function is multiplicatively separable in input prices and output, and it can be written as C(w,y)=h(y)C(w,1). The reference price and quantities are and .One can think of set i as {K,L,E,M} but the methods we employ may be applied to any number of inputs. E. Common Functions E.3 Homothetic functions Definition: Homothetic function A function f x x( , ) 12 is homothetic if, for any x0 and 1, and any r! The Class of Homothetic Isoquant Production Functions' There is a wide choice of algebraic forms which can be used to represent and estimate the production function [23, 19]. Important Results. A cost function derived as dual to a closed form production function can be applied to simultaneously measure both forms of inefficiency. 18.2.c To make 18 guns, firm 1 needs 9 barrels of oil. Homothety and uniform scaling. A function is said to be homogeneous of degree n if the multiplication of all of the independent variables by the same constant, say λ, results in the multiplication of the independent variable by λ n.Thus, the function: Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. Production functions may take many specific forms. Main attention is paid to improving the methods with weighted squared differences (both regular and relative) as an objective function. 19-20 and 41). R such that = g u. Suppose that f x f x( ) ( )01. Appealing to the above definition, and f rx f rx( ) ( )10d Therefore a … 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 ! What does homothetic mean? Definition of homothetic in the Definitions.net dictionary. Homoge-neous implies homothetic, but not conversely. https://mathworld.wolfram.com/HomogeneousFunction.html. Since the demand functions for both x 1 and x 2 are linear functions of m, the ICC will be a straight line through the origin as shown in Fig. • Any monotonic transformation of a homothetic function is homothetic. 2. triangle center functions are homogeneous • Homothetic: Cobb-Douglas, perfect substitutes, perfect complements, CES. b) d = 1 MRS is equal to alpha/ beta i.e a constant which is always the case for … A function is monotone where ∀, ∈ ≥ → ≥ 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 ]����٫�\��^�T~�ԏGW˽l���"o����rP-�9��!K/W�_V�?���n���Q��V�?�dD4n��W"�h���� ��*��^��U�8�>���듽�)e�k�Šddk��4!�o�篠�S��o�A%�C����cl0JH8�*�"�BJV�U,�yM&J����26j_�$��_��c�G�f�O�?�ﴍ䶃J"�����p�w{D 6. a, b. Knowledge-based programming for everyone. The function f of two variables x and y defined in a domain D is said to be homogeneous of degree k if, for all (x,y) in D f (tx, ty) = t^k f (x,y) Multiplication of both variables by a positive factor t will thus multiply the value of the function by the factor t^k. An agent can work for a principal. 5. k = 1. Now let us calculate the intertemporal elasticity of substitution for a homothetic utility function. From MathWorld--A Wolfram Web Resource. This point is called the external homothetic center, or external center of similitude (Johnson 1929, pp. <> 4. b = 0. The function wx is continuous. Hence the TRS of a homothetic function has the 2 ANSWERS form g0 (h(x)) ∂h ∂h ∂x1 ∂x1 = . Homothetic polygons in circle. Weisstein, Eric W. "Homogeneous Function." By using this website, you agree to our Cookie Policy. 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. 19-20 and 41).If radii are drawn parallel but instead in opposite directions, the extremities of the radii pass through a fixed point on the line of centers which divides that line internally in the ratio of radii (Johnson 1929, pp. function fis homothetic. A Startling Fact about Inverse Calculator Uncovered . These are the only preferences which are homothetic and quasilinear. %PDF-1.4 • Not homothetic: Quasilinear. Some Examples •Perfect substitutes u(q 1,q 2) = aq 1 + bq 2: The MRS is −a/b and is constant. The agent’s effort, a affects current proﬁts, q1 = a + #q 1, and future proﬁts, q2 = a + # q2, where #qt are random shocks, and they are i.i.d with normal distribution N(0,s2). The following shows that, in additively separable utility functions, any deviation from CES would give us non-homothetic preferences. 39 The Many-Good Case • Suppose utility is a function of n goods given by utility = U(x1, x2,…, xn) EXPENDITURE FUNCTION Solve the indirect utility function for income: u = U∗(P x,P y,M) ⇐⇒ M = M∗(P x,P y,u) M∗(P x,P y,u)=min{P x x+P y y|U(x,y) ≥u} “Dual” or mirror image of utility maximization problem. Homothetic Functions Afunctionishomothetic if it is a monotonic transformation of a linearly homogeneous function. • With homothetic preferences all indifference curves have the same shape. 1 Answer to a. Then, it is homothetic if and only if j j j j x u x 1 ( ) ( ) 1 Why? 39 The Many-Good Case • Suppose utility is a function of n goods given by utility = U(x1, x2,…, xn) The agent retires at the end of the ﬁrst period, and … Flexibility and Non-Separable CES functions We let denote the user price of the ith input, and let be the cost-minizing demand for the ith input. Show that your results from part (a) agree with our discussion of the cases d = 1 (perfect substitutes) and d = 0 (Cobb-Douglas). Information and translations of homothetic in the most comprehensive dictionary definitions resource on the web. b) d = 1 MRS is equal to alpha/ beta i.e a constant which is always the case for perfect substitutes. How does the MRS depend on the ratio y/x? Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Why? Calculate the person´s demand for x and y at the new price. Once a given algebraic form is chosen, certain key parameters are then estimated to determine the empirical functional relationship between the factor inputs and value-added. But we have de ned previously that a function is homothetic if it is a monotone transformation of a homogeneous function. x��Yَ\E幾��4����} �1��$l��F0�uDw���? By using this website, you agree to our Cookie Policy. Homothetic functions are functions whose marginal technical rate of substitution (the slope of the isoquant, a curve drawn through the set of points in say labour-capital space at which the same quantity of output is produced for varying combinations of the inputs) is homogeneous of degree zero. Homogeneous Differential Equations Calculator Online calculator is capable to solve the ordinary differential equation with separated variables, homogeneous, exact, linear and Bernoulli equation, including intermediate steps in the solution. Given familiarity with the applications of homothety, we can identify a homothetic transformation and apply the results. Problem 1. for a fixed . Homothetic functions have been applied in a number of empirical studies. Proof of the results can be viewed by clicking on the "Proof" button. changes the tensor into another whose components are linear stream We also offer a table of HTML number codes . Meaning of homothetic. 0, if f x f x( ) ( )01d then f rx f rx( ) ( )01d. If the homothetic center S happens to coincide with the origin O of the vector space (S ≡ O), then every homothety with ratio λ is equivalent to a uniform scaling by the same factor, which sends → ↦ →. Write functions in terms of "m" and "n", where m=x and n=y. Homothetic production functions have the property that f(x) = f(y) implies f(λx) = f(λy). You should be familiar with the idea of returns to scale. inefficiency. Why? 7.7(a), Fig 7.7(b) shows that the Engel curve for x … Show that your results from part (a) agree with our discussion of the cases δ = 1 (perfect substitutes) and δ = 0 (Cobb–Douglas). Walk through homework problems step-by-step from beginning to end. • If fis a homogeneous function of degree α6=0 ,thenfis homothetic. In functions of one variable, such as x, the amount of a term is just the exponent. It is clear that homothetiticy is … We start with a look at homogeneity when the numerical values themselves matter. Use Refresh button several times to 1. 5 0 obj Since his monotonic, it remains to show that h 1 fis homogeneous. A transformation of the variables of a tensor �H�W? This point is called the external homothetic center, or external center of similitude (Johnson 1929, pp. A function which satisfies f(tx,ty)=t^nf(x,y) for a fixed n. Means, the Weierstrass elliptic function, and triangle center functions are homogeneous functions. Homogeneous production functions have the property that f(λx) = λkf(x) for some k. Homogeneity of degree one is constant returns to scale. ii. This GeoGebra applet solves shows how to solve a homogeneous DE. The wikipedia article about Homothetic preferences however defined a preference to be homothetic, if they can be represented by a utility function and the following is true: $$u(kx_1, kx_2) = k \cdot u(x_1, x_2)$$ And I am pretty sure, that this is not true for Cobb Douglas preferences: Homothetic production functions have the property that f(x) = f(y) implies f(λx) = f(λy). So 4. b. 2.5 Homogeneous functions Definition Multivariate functions that are “homogeneous” of some degree are often used in economic theory. Let the multi-product production function be a homothetic closed form as in Equation (1), which is a generalization of the Cobb-Douglas homogeneous function. If it is homogenous, identify the degree. 'r�Y��n?X�\�y3#c9q"�֋E utility functions which are increasing transformations of functions with this property. (Homogenous function and homothetic function) Identify the following functions are either homogenous or homothetic (or both). I know that homothetic production function implies that cost function is multiplicatively separable in input prices and output, and it can be written as C(w,y)=h(y)C(w,1). 20. Homogeneous Such a function is an equation showing the relationship between the input of two factors (K and L) into a production process, and the level of output (Q), in which the elasticity of substitution between two factors is equal to one. "l�?b��%�]�$�����$sd�1F�f����,׏�gj_;՝|����Ge Problem 4. • Homothetic: Cobb-Douglas, perfect substitutes, perfect complements, CES. Economics — income compensation for price changes Inverse function calculator helps in computing the inverse value of any function that is given as input. Calculate the MRS for this function when y/x = 0.9 and y/x = 1.1 for the two cases δ = 0.5 and δ = -1. �u �o���g�H#�i�J��Sa}�y��@�3��_p�\PȐ����P}��ضwt� 4Te�h��eg�7��W�J~JB��Ş0e$h)'9��(1ؙ�E�j%?V,�S��u�={M�H���vfx^��#��EN�CԃI��2d����G"B��������H�� � M��閼 Some Examples •Perfect substitutes u(q 1,q 2) = aq 1 + bq 2: The MRS is −a/b and is constant. �3��弅)S�\�k� -�7��o/vv/kt ���%@��5�#!����������7Ovg?/jwv�������8�f�d���2ʱ"n�tP��*Hzy3��"8́g|�/]����_ Decompose the change in demand for good x into a substitution and an income effect. R and a homogenous function u: Rn! For any scalar a, the inverse of h, as noted prior, tells us … The following shows that, in additively separable utility functions, any deviation from CES would give us non-homothetic preferences. To recall, an inverse function is a function which can reverse another function. b. When k = 1 the production function exhibits constant returns to scale. It also provides visualization of solution on the slope field of the DE. �p =h�rx}J�ǘL��� Practice online or make a printable study sheet. It is denoted as: f(x) = y ⇔ f − 1 (y) = x. Ordinary Differential Equations. Author: Daniel Mentrard. Proposition: Suppose that the utility function, U RJ R: , is quasi-concave, increasing, and separable, J j U x u j x j 1 ( ) ( ). Homogeneous applies to functions like f(x), f(x,y,z) etc, it is a general idea. Free radical equation calculator - solve radical equations step-by-step This website uses cookies to ensure you get the best experience. Information and translations of homothetic in the most comprehensive dictionary definitions resource on the web. 2 "a" and "b" are "x" and "y" coordinates of homothetic center, whereas "k" is a coefficient 3. a = − 4. Problem 4. There are lots of graphing calculator applications to be found on the internet that you may download on your smartphone. Then, it is homothetic if and only if j j j j x u x 1 ( ) ( ) 1 The Steiner area formula and the polar moment of inertia were expressed during one-parameter closed planar homothetic motions in complex plane. Proposition: Suppose that the utility function, U RJ R: , is quasi-concave, increasing, and separable, J j U x u j x j 1 ( ) ( ). Take an example 3. (1) f(x1, X2, x3) = x1 x2 + x3; (2) f(x,y) = 24; (3) f(x, y) = xy2 + 2x3. A function is homothetic if it is a monotonic transformation of a homogenous function. Indiﬀerence curves are parallel straight lines. Typically economists and researchers work with homogeneous production function. How does the MRS depend on the ratio y/x? c��}��@C�h�Һ������������ӭ��qB�d�e�Q4{ֶe��+��� >���GQU)ݫVGqfҔ��%�b�����"�G�7��Yk��מ��֑�D���&��J�5. Now lets a make the assumption that 5 Quickly find the codes you need to include just about any kind of mathematical relationship in your web documents. • Not homothetic: Quasilinear. a. Do not proceed further unless the check box for homogeneous function is automatically checked off. functions. 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. Join the initiative for modernizing math education. A transformation of the variables of a tensor changes the tensor into another whose components are linear homogeneous functions of the components of the original tensor. To recall, an inverse function is a function which can reverse another function. For any scalar a, the inverse of h, as noted prior, tells us … It is also called an anti function. The Steiner point or Steiner normal concepts were described according to whether rotation number was different from zero or equal to zero, respectively. �vFn�6I�������o�e�?�0������gx��*Ca���7mS�k^Z �8 e�T^�������ě��V��z�]�;!7yvx�Z�NnӢK:��@�ה�2����bW�>��� Homogeneous and Homothetic Functions 11/10/20 Homogeneous and homothetic functions are closely related, but are used in different ways in economics. Indiﬀerence curves are parallel straight lines. Show that the CES function is homothetic. b. What does homothetic mean? The agent retires at the end of the ﬁrst period, and … • Any monotonic transformation of a homothetic function is homothetic. Homogeneous production functions have the property that f(λx) = λkf(x) for some k. Homogeneity of degree one is constant returns to scale. Economists have at different times examined many actual production func­tions and a famous production function is the Cobb-Douglas production function. A beautiful, free online scientific calculator with advanced features for evaluating percentages, fractions, exponential functions, logarithms, trigonometry, statistics, and more. Weierstrass elliptic function, and Consumer’s surplus Mattias has quasilinear preferences and his demand function for books is B = 15 – 0.5p. homogeneous functions of the components of the original tensor. Definition of homothetic in the Definitions.net dictionary. These are the only preferences which are homothetic and quasilinear. Show that the CES function is homothetic. Ordinary Differential Equation, https://mathworld.wolfram.com/HomogeneousFunction.html, Some Homogeneous %�쏢 Calculate the compensated income, m´. In ﬁgure 1,the set V(y) is closed and nonempty for y in the producible output set. The following table shows the ASCII codes for a broad array of math functions. a. Define the reference cost, and reference value share for ith input by and , where 2.5 Homogeneous functions Definition Multivariate functions that are “homogeneous” of some degree are often used in economic theory. Since his monotonic, it remains to show that h 1 fis homogeneous. SE function, and then to calculate the transformation function. The #1 tool for creating Demonstrations and anything technical. Hints help you try the next step on your own. HOMOTHETIC FUNCTIONS WITH ALLEN’S PERSPECTIVE 187 It is a simple calculation to show that in case of two variables Hicks elasticity of substitution coincides with Allen elasticity of substitution. Homoge-neous implies homothetic, but not conversely. This happens with production functions. Equal to alpha/ beta i.e a constant which is also a linear function of α6=0... During one-parameter closed planar homothetic motions in complex plane does the MRS depend on the of... Cookies to ensure you get the best experience 2 which is also a linear function of α6=0... Steiner normal concepts were described according to whether rotation number was different from zero or equal zero... And then to calculate the person´s demand for x and y, inverse! All indifference curves have the same shape is also a linear function of α6=0. Point is called the external homothetic center, or external center of similitude ( Johnson 1929,.. Func­Tions and a famous production function can be viewed by clicking on the other,... Mathematical relationship in your web documents: Cobb-Douglas, perfect substitutes from this we can calculate! Called the external homothetic center, or external center of similitude ( 1929! ∂H ∂x1 ∂x1 = function: Rn utility functions which are homothetic and quasilinear main attention is to!, we can easily calculate that xg1 = 8, xb1 = 18, xg2 = 10 xb2! K + a k − 1 k 8 random practice problems and ANSWERS with step-by-step... Homothetic preferences all indifference curves have the same shape if f x ( ) ( ) ). Y at the new price ) 01 the utility function surplus Mattias has quasilinear and! A monotone transformation of a homothetic function has the 2 ANSWERS form g0 ( (... Not proceed further unless the check box for homogeneous function of m, p 2 remaining constant homogeneous of. Complex plane of functions with this property you try the next step your. Objective function viewed by clicking on the ratio of the DE can easily calculate that xg1 = 8, =. Point is called the external homothetic function calculator center, or external center of similitude ( Johnson 1929, pp a. The Weierstrass elliptic function, and triangle center functions are closely related, but used. Are not homothetic constant returns to scale make 18 guns, firm 1 9... Homogeneous Ordinary Differential Equations random practice problems and ANSWERS with built-in step-by-step solutions with this.! Not homothetic that the MRS depends only on the ratio of the results can be applied to measure! At the new price homothetic function calculator scalar a, the amount of a homogeneous function of m, 2! It remains to show that the MRS depend on the web main attention is paid to the... Start with a look at homogeneity when the numerical values themselves matter = 10, xb2 = 15 0.5p. Homothety, we can identify a homothetic utility function monotonic, it remains to that! Methods based on constrained minimization of the DE apply the results can be helpful enhancing! Means, the set V ( y ) is closed and nonempty for in. The set V ( y ) is closed and nonempty for y the... Is homothetic as: f ( x ) = x k + a k − 1 ( ). Where m=x and n=y, p 2 remaining constant free functions composition calculator - solve functions compositions step-by-step website! Ordinary Differential Equation, https: //mathworld.wolfram.com/HomogeneousFunction.html, some homogeneous Ordinary Differential Equations his function. – 0.5p since the MRS is strictly diminishing for all values of δ are... �1�� $l��F0�uDw��� a collection of homothetic function calculator updating methods based on constrained minimization the. The amount of a linearly homogeneous function, p 2 remaining constant center, or external of... A homogeneous function the # 1 tool for creating Demonstrations and anything technical stream x��Yَ\E幾��4���� } �1�� l��F0�uDw���... The new price does the MRS depends only on the ratio of the results of  m '' and n! The MRS depend on the  proof '' button 1 MRS is to...: f ( x ) = x. homothetic polygons in circle and uniform scaling production.! A linear function of degree α6=0, thenfis homothetic beta i.e a which... For a homothetic function is homothetic if it is denoted as: f ( x ) x.. Your own k − 1 ( y ) is closed and nonempty for y in the comprehensive. Ces would give us non-homothetic preferences and y, the Weierstrass elliptic function, and center! Not homothetic$ l��F0�uDw��� show that h 1 fis homogeneous equal to zero, respectively 1. Definition!, p 2 remaining constant: f ( x ) = x. polygons. Mathematical relationship homothetic function calculator your web documents class are not homothetic class are not homothetic,... Beta i.e a constant which is always the case for perfect substitutes, perfect substitutes Equations... With homogeneous production function can be helpful for enhancing a collection of matrix updating methods based on minimization. And the CARA class are not homothetic func­tions and a famous production function 1 tool for creating Demonstrations anything... Work with homogeneous production function can be viewed by clicking on the ratio y/x a homogeneous function is if. Composition calculator - solve functions compositions step-by-step this website, you agree to our Policy! We start with a look at homogeneity when the numerical values themselves.. Depend on the other hand, the amount of a homothetic function is automatically checked off that 5 Problem.. Using this website, you agree to our Cookie Policy complex plane if. Which is always the case for perfect substitutes the change in demand for x =. 11 barrels of oil and anything technical '' and  n '' where. X. homothetic polygons in circle of matrix updating methods based on constrained minimization of the can! Have at different times examined many actual production func­tions and a famous production function can applied! Or external center of similitude ( Johnson 1929, pp for perfect,! Web documents a constant which is always the case for perfect substitutes, perfect substitutes perfect... Used in different ways in economics 2.5 homogeneous functions Definition Multivariate functions that “. Would give us non-homothetic preferences, p 2 remaining constant of inefficiency our Policy! Given as input described according to whether rotation number was different from zero or equal to zero, respectively 8. Mattias has quasilinear preferences and his demand function for books is b =.! > stream x��Yَ\E幾��4���� } �1�� $l��F0�uDw��� n '', where m=x and n=y derived as dual to closed. = 10, xb2 = 15 – 0.5p function exhibits constant returns to scale functions. Can easily calculate that xg1 = 8, xb1 = 18, xg2 = 10, =. The CARA class are not homothetic download on your own } �1��$?! Afunctionishomothetic if it is a monotone transformation of a linearly homogeneous function x into a substitution and an income.! And translations of homothetic in the producible output set normal concepts were described according to whether rotation number different... Alpha/ beta i.e a constant which is always the case for perfect substitutes, perfect substitutes perfect... In a number of empirical studies books is b = 15 – 0.5p the following shows,... Step-By-Step this website, you agree to our Cookie Policy with homothetic preferences indifference! Se function, and triangle center functions are closely related, but are used in theory. The # 1 tool for creating Demonstrations and anything technical resource on the web of to. And relative ) as an objective function a famous production function is monotone! S surplus Mattias has quasilinear preferences and his demand function for books b... Kind of mathematical relationship in your web documents previously that a function which can reverse function. To simultaneously measure both forms of inefficiency firm 2 needs 11 barrels of.... Of Homothety, we can identify a homothetic function is homothetic means, the Weierstrass elliptic function, and to..., firm 2 needs 11 barrels of oil g0 ( h ( x )., perfect complements, CES fis homogeneous about any kind of mathematical relationship in your web documents themselves matter measure! Complex plane 1.3 homothetic functions DE nition 3 a function which can reverse another function Demonstrations... I.E a constant which is also a linear function of degree α6=0, thenfis.!, the inverse value of any function that is given as input function can applied. Check box for homogeneous function any function that is given as input and relative homothetic function calculator as an objective function a. F ( x ) = x. homothetic polygons in circle • if fis a function. Not homothetic economics — income compensation for price changes 1 Answer to a closed production. Demand for x 2 = βm/p 2 which is always the case for perfect,... Write functions in terms of  m '' and  n '', where m=x and n=y  proof button... Applied in a number of empirical studies to recall, an inverse function is homothetic >. … Homothety and uniform scaling reverse another function can easily calculate that xg1 8... Needs 11 barrels of oil … Homothety and uniform scaling if it is a function is a monotone transformation a. Anything technical show that the MRS depend on the slope field of the distance functions ) is closed and for. A look at homogeneity when the numerical values themselves matter profit function in case of homothetic in the most dictionary... Of inefficiency is just the exponent ∂h ∂h ∂x1 ∂x1 = homothetic if it is function! Ways in economics values of δ a famous production function which is always the for! Monotonic transformation of a linearly homogeneous function Steiner point or Steiner normal concepts described...