Replication and Returns to Scale in Production

2014 ◽  
Vol 14 (1) ◽  
pp. 127-148 ◽  
Author(s):  
Christian Jensen
Keyword(s):  
Public Goods ◽  
Production Process ◽  
Production Function ◽  
Stationary Point ◽  
Returns To Scale ◽  
Profit Maximization ◽  
Scale Production ◽  
Production Processes ◽  
Integer Problem ◽  
Constant Returns To Scale

AbstractReplication alone does not yield a smooth constant-returns-to-scale production function as those usually assumed in the literature. However, such a function arises endogenously with replication, driven by profit-maximization, if the efficiency of the underlying production process varies with the intensity it is operated at, and reaches a maximum at a stationary point. The result applies when the number of production processes must be discrete, thus overcoming the so-called integer problem. When inputs are non-rival, public goods or generated by externalities, replication can lead to increasing or decreasing returns to scale.

scholarly journals AN ENDOGENOUSLY DERIVED AK MODEL OF ECONOMIC GROWTH

2018 ◽  
Vol 22 (8) ◽  
pp. 2182-2200
Author(s):  
Christian Jensen
Keyword(s):  
Economic Growth ◽  
Steady State ◽  
Returns To Scale ◽  
Profit Maximization ◽  
Perfect Competition ◽  
Production Processes ◽  
Input Use ◽  
Integer Problem ◽  
Ak Model ◽  
Constant Returns To Scale

When the returns to scale of a production process vary with the intensity it is operated at, an AK model with constant returns to scale in production arises endogenously due to replication driven by profit maximization. If replication occurs at the efficiency-maximizing scale, as with perfect competition, the result applies also when the number of production processes must be discrete, thus, overcoming the so-called integer problem. When competition is imperfect, there is only convergence toward the AK model for large enough input use, so an economy is more prone to stalling in a steady state without growth, the smaller and less competitive it is.

Production with Constant Returns

2011 ◽  
Author(s):  
Yves Balasko
Keyword(s):  
Returns To Scale ◽  
Profit Maximization ◽  
Maximization Problem ◽  
Scale Production ◽  
Constant Returns To Scale ◽  
Activity Vector ◽  
Inputs And Outputs

This chapter examines the net supply correspondence of a constant returns to scale firms under suitable convexity and smoothness assumptions. These assumptions are comparable to those used in the previous chapters for consumers and production with decreasing returns to scale. The chapter starts by formulating constant returns to scale production by way of production sets with arbitrary numbers of inputs and outputs. It then addresses the profit maximization problem of a constant returns to scale firm. That problem does not always have a solution. More accurately, if some feasible activity yields a strictly positive profit at some given prices, then it suffices to consider an arbitrarily large multiple of that activity vector to get a feasible activity that yields an arbitrarily large profit at the same prices. The firm can then make an arbitrarily large profit.

scholarly journals Variable and Constant Returns-to-Scale Production Technologies with Component Processes

2021 ◽  
Author(s):  
Victor V. Podinovski
Keyword(s):  
Returns To Scale ◽  
Efficiency Analysis ◽  
Scale Production ◽  
Worst Case ◽  
Production Processes ◽  
Component Processes ◽  
Production Technologies ◽  
Constant Returns To Scale ◽  
Shared Inputs ◽  
Inputs And Outputs

Efficiency Analysis for Multicomponent Production Processes Conventional models concerned with efficiency analysis of organizations typically consider a single production process, or technology, in which all inputs are used in the production of all outputs. This approach does not account well for the situations in which the organizations are involved in several component production processes whose inputs and outputs may be shared by different processes. The main difficulty in modeling such technologies is the fact that we often do not know the exact allocation of the shared inputs and outputs to individual processes. In “Variable and Constant Returns-to-Scale Production Technologies with Component Processes,” V. V. Podinovski shows how this problem can be overcome by the consideration of the worst-case scenario for the allocation of the shared inputs and outputs to different components of the technology. This approach leads to the development of multicomponent variants of two well-established nonparametric models. An application involving universities in England demonstrates the usefulness and improved discriminating power of the new models compared with their conventional analogues.

scholarly journals PARETO OPTIMALITY OF THE GOLDEN RULE EQUILIBRIUM IN AN OVERLAPPING GENERATIONS MODEL WITH PRODUCTION AND TRANSFERS

2015 ◽  
Vol 19 (8) ◽  
pp. 1780-1799 ◽  
Author(s):  
Jean-François Mertens ◽  
Anna Rubinchik
Keyword(s):  
Overlapping Generations ◽  
Returns To Scale ◽  
Golden Rule ◽  
Life Time ◽  
Equilibrium Price ◽  
Scale Production ◽  
Present Value ◽  
Overlapping Generations Model ◽  
Aggregate Consumption ◽  
Constant Returns To Scale

The main result is that the golden rule equilibrium (GRE) is Pareto optimal (in the classical sense) in an overlapping generations (OG) model with constant-returns-to-scale production, transfers, arbitrary life-time productivity and homogeneous instantaneous felicity. In addition, we extend Cass and Yaari's equivalence between efficiency (aggregate consumption dominance) and present value dominance (with evaluation made using a candidate equilibrium price path).

scholarly journals Cotton Farmers' Technical Efficiency: Stochastic and Nonstochastic Production Function Approaches

2002 ◽  
Vol 31 (2) ◽  
pp. 211-220 ◽  
Author(s):  
Kalyan Chakraborty ◽  
Sukant Misra ◽  
Phillip Johnson
Keyword(s):  
Technical Efficiency ◽  
Production Function ◽  
Returns To Scale ◽  
Empirical Application ◽  
West Texas ◽  
Level Data ◽  
The Mean ◽  
Cotton Farmers ◽  
The Individual ◽  
Constant Returns To Scale

Technical efficiency for cotton growers is examined using both stochastic (SFA) and nonstochastic (DEA) production function approaches. The empirical application uses farm-level data from four counties in west Texas. While efficiency scores for the individual farms differed between SFA and DEA, the mean efficiency scores are invariant of the method of estimation under the assumption of constant returns to scale. On average, irrigated farms are 80% and nonirrigated farms are 70% efficient. Findings show that in Texas, the irrigated farms, on average, could reduce their expenditures on other inputs by 10%, and the nonirrigated farms could reduce their expenditures on machinery and labor by 12% and 13%, respectively, while producing the same level of output.

The Rules of Derived Demand when the Firm is a Monopolist

1975 ◽  
Vol 41 (04) ◽  
pp. 379-387
Author(s):  
R.W. Latham ◽  
D.A. Peel
Keyword(s):  
Production Function ◽  
Economies Of Scale ◽  
Scale Parameter ◽  
Returns To Scale ◽  
Elasticity Of Demand ◽  
Competitive Industry ◽  
Competitive Behaviour ◽  
Polar Opposite ◽  
Derived Demand ◽  
Constant Returns To Scale

In a recent paper Andrieu [l] derived the rules of derived demand for a factor in a perfectly competitive industry when the industry’s production function was homogeneous but not necessarily of degree one. In order to achieve compatibility with competitive behaviour economies of scale were assumed to be external to each firm but internal to the industry. Within this framework he showed that Marshall’s third rule concerning relative shares was modified and, further, proposed a ‘ fifth law ’ with respect to the returns to scale parameter : ‘ Other things being equal, an increase in the returns to scale will make the derived demand for a factor more (less) elastic if the demand for output is elastic (inelastic). The purpose of this note is to examine a model which is the polar opposite to that considered by Andrieu. Here the firm is assumed to be the industry i.e. a monopolist. Non-constant returns to scale are introduced by assuming that the production function is homogeneous of an arbitrary degree. The analysis is not completely general since both the price elasticity of demand and the elasticity of supply of the second factor are assumed to be constant. However within this model it is shown that not only are Marshall’s second and third laws modified but also Andrieu’s fifth law.

scholarly journals The Cobb-Douglas function for a continuum model

2017 ◽  
Vol 36 (70) ◽  
pp. 1-18 ◽  
Author(s):  
Javier Humberto Ospina Holguín
Keyword(s):  
Continuum Model ◽  
Returns To Scale ◽  
Profit Maximization ◽  
Functional Derivative ◽  
Maximization Problem ◽  
Constant Elasticity ◽  
Constant Elasticity Of Substitution ◽  
Competitive Firm ◽  
The One ◽  
Constant Returns To Scale

This paper introduces two formal equivalent definitions of the Cobb-Douglas function for a continuum model based on a generalization of the Constant Elasticity of Substitution (CES) function for a continuum under not necessarily constant returns to scale and based on principles of product calculus. New properties are developed, and to illustrate the potential of using the product integral and its functional derivative, it is shown how the profit maximization problem of a single competitive firm using a continuum of factors of production can be solved in a manner that is completely analogous to the one used in the discrete case.

scholarly journals A NOTE ON THE CHARACTERIZATION OF THE NEOCLASSICAL PRODUCTION FUNCTION

2016 ◽  
Vol 21 (7) ◽  
pp. 1827-1835
Author(s):  
Andreas Irmen ◽  
Alfred Maußner
Keyword(s):  
Production Function ◽  
Returns To Scale ◽  
Production Functions ◽  
Alternative Characterization ◽  
Factors Of Production ◽  
Constant Returns To Scale

We study production functions with capital and labor as arguments that exhibit positive, yet diminishing marginal products and constant returns to scale. We show that such functions satisfy the Inada conditions if (i) both inputs are essential and (ii) an unbounded quantity of either input leads to unbounded output. This allows for an alternative characterization of the neoclassical production function that altogether dispenses with the Inada conditions. Although this proposition generalizes to the case of n > 2 factors of production, its converse does not hold: 2n Inada conditions do not imply that each factor is essential.

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