NOTE TO CHAPTER ix. Substitutability, Complementarity, Transformability, and Antipathy in the case of a Constant- Returns-to-Scale Production Function

2014 ◽  
Vol 14 (1) ◽  
pp. 127-148 ◽  
Author(s):  
Christian Jensen

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.


2015 ◽  
Vol 19 (8) ◽  
pp. 1780-1799 ◽  
Author(s):  
Jean-François Mertens ◽  
Anna Rubinchik

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).


Author(s):  
Yves Balasko

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.


2002 ◽  
Vol 31 (2) ◽  
pp. 211-220 ◽  
Author(s):  
Kalyan Chakraborty ◽  
Sukant Misra ◽  
Phillip Johnson

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.


1975 ◽  
Vol 41 (04) ◽  
pp. 379-387
Author(s):  
R.W. Latham ◽  
D.A. Peel

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.


2016 ◽  
Vol 21 (7) ◽  
pp. 1827-1835
Author(s):  
Andreas Irmen ◽  
Alfred Maußner

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.


2021 ◽  
Author(s):  
Victor V. Podinovski

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.


1972 ◽  
Vol 32 (3) ◽  
pp. 691-705 ◽  
Author(s):  
Jeffrey G. Williamson

As the key conveyance of nineteenth-century American industrialization and early experimentation with tariff policy, the antebellum textile sector has always received extensive attention by economic historians. In the past two decades, we have learned much about industrial financing, investment behavior, productivity growth, the nature of the production function, and the optimality of tariff policy, yet we remain ignorant still on some fundamental issues. One of these involves a better understanding of the equipment replacement decision under conditions of rapid growth, technological improvement, and variable tariff policies. But most importantly, the identification of sources of productivity improvement and their magnitude had remained inadequately understood until very recently with the appearance of Paul David's article in this Journal. David's important contribution applies aggregate production function analysis to textiles in an effort to isolate the determinants of labor productivity growth during the three decades preceding the Civil War. The model is neoclassical with a Cobb-Douglas specification, variable returns to scale, disembodied technical progress and with a learning variable explicitly introduced into the production function. David finds evidence of constant returns to scale, strong learning effects, high rates of disembodied technical progress, and improved labor quality, the latter sufficient to offset the alleged downward pressure on productivity attributable to a long-run decline in input (especially labor) utilization rates.


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