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 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 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.

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 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 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.

scholarly journals INDIVISIBLE LABOR SUPPLY AND INVOLUNTARY UNEMPLOYMENT: MONOPOLISTIC COMPETITION MODEL

2020 ◽  
pp. 1-14
Author(s):  
YASUHITO TANAKA
Keyword(s):  
Labor Supply ◽  
Utility Maximization ◽  
Overlapping Generations ◽  
Monopolistic Competition ◽  
Returns To Scale ◽  
Profit Maximization ◽  
Wage Rigidity ◽  
Overlapping Generations Model ◽  
Involuntary Unemployment ◽  
Constant Returns To Scale

This paper is an attempt to provide a micro-theoretical basis for Keynesian economics while maintaining as much of the neoclassical framework as possible, such as utility maximization for consumers and profit maximization for firms. We show the existence of involuntary unemployment without assuming wage rigidity when labor supplies of individuals are indivisible. We derive involuntary unemployment using an overlapping generations model under monopolistic competition with constant returns to scale technology and indivisible labor supply.

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