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This paper provides a detailed description of the current version of the Ecofin Council approved production function (PF) methodology which is used for assessing both the productive capacity (i.e. potential output) and cyclical position (i.e. output gaps) of EU economies. Compared with the previous 2010 paper on the same topic, there have been two significant changes to the PF methodology, namely an overhaul of the NAWRU methodology & the introduction of a new T+10 methodology.

A sequel to his frequently cited Cost and Production Functions (1953), this book offers a unified, comprehensive treatment of these functions which underlie the economic theory of production.The approach is axiomatic for a definition of technology, by mappings of input vectors into subsets of output vectors that represent the unconstrained technical possibilities of production. To provide a completely general means of characterizing a technology, an alternative to the production function, called the Distance Function, is introduced.The duality between cost function and production function is developed by introducing a cost correspondence, showing that these two functions are given in terms of each other by dual minimum problems.The special class of production structures called Homothetic is given more general definition and extended to technologies with multiple outputs.Originally published in 1971.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

InVEST is a suite of free, open-source software models used to map and value the goods and services from nature that sustain and fulfill human life. If properly managed, ecosystems yield a flow of services that are vital to humanity, including the production of goods (e.g., food), life-support processes (e.g., water purification), and life-fulfilling conditions (e.g., beauty, opportunities for recreation), and the conservation of options (e.g., genetic diversity for future use). Despite its importance, this natural capital is poorly understood, scarcely monitored, and, in many cases, undergoing rapid degradation and depletion.

A short-run production function refers to that period of time, in which the installation of new plant and machinery to increase the production level is not possible. On the other hand, the Long-run production function is one in which the firm has got sufficient time to instal new machinery or capital equipment, instead of increasing the labour units.

The production function can be described as the operational relationship between the inputs and outputs, in the sense that the maximum amount of finished goods that can be produced with the given factors of production, under a particular state of technical knowledge. There are two kinds of the production function, short run production function and long run production function.

Basis for ComparionShort-run Production FunctionLong-run Production FunctionMeaningShort run production function alludes to the time period, in which at least one factor of production is fixed.Long run production function connotes the time period, in which all the factors of production are variable.LawLaw of variable proportionLaw of returns to scaleScale of productionNo change in scale of production.Change in scale of production.Factor-ratioChangesDoes not change.Entry and ExitThere are barriers to entry and the firms can shut down but cannot fully exit.Firms are free to enter and exit.

The short run production function is one in which at least is one factor of production is thought to be fixed in supply, i.e. it cannot be increased or decreased, and the rest of the factors are variable in nature.

Long run production function refers to that time period in which all the inputs of the firm are variable. It can operate at various activity levels because the firm can change and adjust all the factors of production and level of output produced according to the business environment. So, the firm has the flexibility of switching between two scales.

For any production function, short run simply means a shorter time period than the long run. So, for different processes, the definition of the long run and short run varies, and so one cannot indicate the two time periods in days, months or years. These can only be understood by looking whether all the inputs are variable or not.

What if a castaway - we'll call him Carl - wanted to see if he was being efficient in his production? Carl is stranded on an island alone, so it makes for a simple economy: one producer and one consumer -- him. His product, in this case, is coconuts that he collects. One thing he can do is calculate a production function.

A production function is a mathematical and sometimes graphical way to measure the efficiency of production by considering the relationships between two or more variables, meaning two or more factors that are relevant when producing a good or service, such as raw materials and labor. Once a business has determined the factors for production, it can begin building the production function. For our castaway Carl, his factors of production would be his labor compared to the number of coconuts he collects.

Carl's production function would be Q = L (number of coconuts collected = amount of time Carl labors to collect them). This is a pretty simple example; let's look at some other possible scenarios.

If one employee can make 500 snow cones in eight hours, the production function would be Q = 500 L. Using a linear production function, where we assume that each employee will produce at the same rate, we get this:

What's more likely to happen than a linear output is diminishing returns to labor, where each additional employee may not result in a straight production increase. The production function would be Q = 500L^a, where a represents some fraction of the output from one employee.

The castaway Carl production function we've been looking at throughout this lesson, where the number of coconuts the stranded traveler can collect is proportionate to the number of hours he spends collecting coconuts, can be graphed like this:

The production function of this graph shows that at some point, there are diminishing returns of coconuts as the amount of labor increases. As Carl spends more time collecting coconuts, he is able to spend less time on other activities, such as relaxing or building a shelter.

In this lesson, we learned that the production function calculates how efficiently a business is producing its goods or services in light of the inputs to the production. We discovered the basic function is:

The production function is a mathematical equation determining the relationship between the factors and quantity of input for production and the number of goods it produces most efficiently. It answers the queries related to marginal productivity, level of production, and cheapest mode of production of goods.

Production function means a mathematical equation/representation of the relationship between tangible inputs and the tangible output of a firm during the production of goods. A single factor in the absence of the other three cannot help production. In simple words, it describes the method that will enable the maximum production of goods by technically combining the four major factors of production- land, enterprise, labor and capital at a certain timeframe using a specific technology most efficiently. It changes with development in technology. J H Von was the first person to develop the proportions of the first variable of this function in the 1840s.

This function depends on the price factor and output levels that producers can easily observe. Moreover, every manufacturing plant converts inputs into outputs. Hence the factors necessarily determine the production level of goods to maximize profits and minimize cost. Therefore, the production function is essential to know the quantity of output the firms require to produce at the said price of goods. It determines the output and the combination inputs at a certain capital and labor cost.

The Leontief production function is a type of function that determines the ratio of input required for producing in a unit of the output quantity. Also, producers and analysts use the Cobb-Douglas function to calculate the aggregate production function.

The firm cannot vary its input quantities in the short-run production function. The law of variable proportion gets applicable here. There is no change in the level of activity in the short-run function. The ratio of factors keeps changing because only one input changes concerning all the other variables, which remain fixed. The manufacturing firms face exit barriers. As a result, they can be shut down permanently but cannot exit from production.

For any production company, only the nature of the input variable determines the type of productivity function one uses. If one uses variable input, it is a short-run productivity function; otherwise, it is a long-run function.

Bell, F.W. 1967. The relation of the productionfunction to the yield on capital for the fishing industry. In F.W. Belland J.E. Hazleton, eds. Recent developments and research in fisheries.New York, USA, Oceana Publications.

Coelli, T. 1996a. A guide to FRONTIER version 4.1: acomputer programme for frontier production function estimation. CEPA WorkingPaper 96/08, Department of Econometrics, University of New England, Armidale,Australia. 2b1af7f3a8