Money in the Utility and Production Function: A DSGE Approach

In this paper I use an open economy DSGE model and estimate it for Romanian economy using Bayesian techniques. Based on estimation I derive a smoothed estimation of the output gap. I compare the results with those from standard procedures to estimate the output gap, the Hodrick Prescott ilter, the production function and an unobserved components model. The results show that the DSGE approach can give a better picture of the output gap and it is more consistent with the dynamics of Romanian economy.

Although the representative theory of consumer/firm is widely used in particular forms of utility and production functions, is the optimal growth model adequately supported by a multi-regional microeconomic base in a “general form of utility and production functions”? Is the “optimization of macro-aggregate functions” consistent with the “summation of micro-optimal outcomes”? Economists have explored the problem of summation of macro-variables in a special form of production and utility function setting to find some theoretical foundations of macroeconomics in the case of heterogeneous representative consumers. However, heterogeneous representative producers have not been studied enough, and the conclusions are too dependent on the functional form. This study searches for the conditions for macroeconomics to reach micro-foundations in the framework of heterogeneous producers and general functions. Linking the entire macroeconomy through inter-regional capital flows, we distinguish between using and equity capital, construct a multi-regional dynamic optimal growth model in a homogeneous representative consumer and heterogeneous representative manufacturers, compare the summation of the regional dynamics with the aggregate macro-dynamics, and find that (A) the regional and macro-perspectives are generally inconsistent in their optimization results; (B) if the population growth rate is the same across regions, the macro-steady state is a weighted summation of the steady states; and (C) if the inverse of the absolute risk aversion is linearly additive to consumption, the model is reliable. In particular, CARA and CRRA-type utility functions are eligible. The eligible utility function can only be an exponential utility function or a power function utility function (the logarithmic utility function can be considered a degenerate power function utility).

A simulation of the Heckscher–Ohlin theorem

This paper explores dimensional analysis of production and utility functions in economics. As raised by Barnett, dimensional analysis is important in consistency checks of economics functions. However, unlike Barnett's dismissal of CES and Cobb-Douglas production functions, we will demonstrate that under constant return-to-scale and other assumptions, production function can indeed be justified dimensionally. And then we consider utility functions.

This paper presents sufficient conditions for the existence of a unique and globally stable steady state equilibrium for OLG economies with production. The conditions impose separate requirements on the utility and production functions. Moreover, the conditions do not require assumptions concerning the third order derivatives of the production and utility functions.

In economic analysis, the importance of the homotheticity of production functions (or utility functions), which is due to Shephard (1953), has been well recognized. Its important feature lies in the fact that every expansion path is a ray from the origin and the underlying production (or utility) function is homothetic. Although the proof of the part of this statement is easy, the proof of the only if part, at least as it appears in the literature, is not easy, requiring a few pages for the proof. Lau (1969) proved it by way of partial differential equations (cf. pp. 379-81), and Fare and Shephard (1977a, b) used a set-theoretic approach, whereas Sandler and Swimmer (1978) proved it for the two-input case. F0rsund (1975) provides a simple proof for a closely related proposition (cf. his Proposition 2), and yet his proof requires the use of partial differential equations. It would thus be desirable to obtain an elementary, short alternative proof of the above important proposition. The purpose of this note is to offer such a proof. In this paper we prove both the only if and the part simultaneously. Although our proof is carried out in terms of production theory, the same proof obviously applies to the theory of consumption. Let f(x) be the production function of a firm which produces a single output, where x is an n-dimensional input vector. The firm minimizes its

An entropic framework for modeling economies

INTRODUCTION In any static optimization problem, the objective function and the constraint functions will contain certain parameters and the optimal solution will depend on the values taken by these parameters. Thus, if any particular parameter value is altered, then we should expect the optimal choice of control variables and the maximum value of the objective function to change. The determination of the effects of parameter variations on the optimal choice of control variables and the maximum value of the objective function is referred to in the economics literature as comparative statics analysis . Section 4.2 is devoted to comparative statics analysis. Closely related to comparative statics analysis is the theory of duality . At the heart of duality theory in economics is the notion of ‘equivalent representations’. Following Epstein (1981) we may say that: the theory of duality describes alternative equivalent representations of consumers' preferences (direct or indirect utility function, expenditure function), or of a competitive producer's technology (production, profit or cost function). Thus, in economics, duality refers to the existence of ‘dual functions’ which, under appropriate regularity conditions, embody the same information on preferences or technology as the more familiar ‘primal functions’ such as the utility or production function. Dual functions describe the results of optimizing responses to input and output prices and constraints rather than global responses to input and output quantities as in the corresponding primal functions.

This paper examines the short‐run effects upon several variables of an increase in the variability of an input. The measure of an increase in the variability is the “mean preserving spread” suggested by Rothschild and Stiglitz (1970). The variables examined are real income (utility), expected profits, expected output, the quantity used of the controllable input, and the shadow price of the stochastic input. Four striking features of the results follow: (1) The concepts that have been useful in summarizing deterministic comparative static results are nearly absent when an input is stochastic. (2) Most of the signs of the partial derivatives depend upon more than concavity of the utility and production functions. (3) If the utility function is not “too” risk averse, then the risk‐neutral results hold for the risk‐aversion case. (4) If the production function is Cobb‐Douglas, then definite results are achieved if the utility function is linear or if the “degree of risk‐aversion” is “small.”

A quantitative model of regulator’s preference factor (RPF) in electricity–environment coordinated regulation system

Focuses on the measurement of production functions and marginal productivities by the political economist, Paul Douglas. Presentation of the econometric measurements on the supply of factors of production; Illustration of econometric techniques; Successors of the works of Douglas. (From Ebsco)

Introduction Mathematical applications to economics are rarely introduced in Calculus II or III. This is a missed opportunity since so many important concepts in second and third semester calculus courses can be discussed in terms of production, profit, utility, and social welfare functions, which are central to microeconomics. In this paper, we focus on mathematical techniques for optimizing profit functions with and without constraints. We illustrate these techniques with examples, and provide additional problems at the end of each section for student use. Section 2 (Production Functions) introduces production functions and discusses several of their key properties. Section 3 (Unconstrained Optimization) looks at profit maximization problems and shows how a function's matrix of second-derivatives can be used to determine the function's concavity. In Section 4 (Constrained Optimization), we use the method of Lagrangian multipliers to solve optimization problems with one or more constraints, and explain how to modify the second-derivative test for a constrained maximization problem. We also discuss the significance of the Lagrange multiplier as a shadow price, and how it measures the amount of increase in the objective function as the constraint increases (for instance, the increase in maximal production resulting from an increase in the total budget). Section 5 (Optimization with Inequality Constraints) provides a brief introduction to optimizing production when the constraints are expressed as inequalities as, for example, when a firm can use some, but not all, of its resources.

The study demonstrates the possibility to use the notions and tools of physical potential theory in development of a general theory of economic potential. Production functions and functional of consumer or managerial preferences are treated as microeconomic potential functions. The gradients of these functions i.e. marginal utilities and products can be regarded as power functions. A degree of returns to scale is considered as an indicator of magnitude of microeconomic potential. The study outlines general approaches to equilibrium analysis under increasing returns to scale. The hypothesis of profit maximization for a competitive firm proves to be inadequate and must be replaced by more simple objectives such as output and revenue maximization or cost minimization subject to correspondingly financial or capacity utilization constraints. The study develops the existing concepts of general competitive equilibrium under various types of returns to scale typical to potential (production and utility) functions of economic agents.

Following Lancaster, preferences are defined over a set of characteristics, while commodities vectors are transformed into characteristics by a production function. We assume that both the preferences over the characteristics and the production functions are “neoclassical” and we characterize the set utility functions over the consumption space derived as the composition of preferences over characteristics and production functions. We prove that, under regularity conditions, any function can be derived by such a composition. Thus, the theories of characteristics does not impose any restrictions on derived utility functions.

We show a range of complexity results for the Ricardo and Heckscher-Ohlin models of international trade (as Arrow-Debreu production markets). For both models, we show three types of results: 1 When utility functions are Leontief and production functions are linear, it is NP-hard to decide if a market has an equilibrium. 1 When utility functions and production functions are linear, equilibria are efficiently computable (which was already known for Ricardo). 1 When utility functions are Leontief, equilibria are still efficiently computable when the diversity of producers and inputs is limited. Our proofs are based on a general reduction between production and exchange equilibria. One interesting byproduct of our work is a generalization of Ricardo’s Law of Comparative Advantage to more than two countries, a fact that does not seem to have been observed in the Economics literature.KeywordsUtility FunctionProduction FunctionInternational TradeComparative AdvantageExchange EconomyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.