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From Wikipedia

Production function

In microeconomics and macroeconomics, a production function is a function that specifies the output of a firm, an industry, or an entire economy for all combinations of inputs. This function is an assumed technological relationship, based on the current state of engineering knowledge; it does not represent the result of economic choices, but rather is an externally given entity that influences economic decision-making. Almost all economic theories presuppose a production function, either on the firm level or the aggregate level. In this sense, the production function is one of the key concepts of mainstreamneoclassical theories. Some non-mainstream economists, however, reject the very concept of an aggregate production function.

Concept of production functions

In micro-economics, a production function is a function that specifies the output of a firm for all combinations of inputs. A meta-production function (sometimes metaproduction function) compares the practice of the existing entities converting inputs into output to determine the most efficient practice production function of the existing entities, whether the most efficient feasible practice production or the most efficient actual practice production.clarification needed In either case, the maximum output of a technologically-determined production process is a mathematical function of one or more inputs. Put another way, given the set of all technically feasible combinations of output and inputs, only the combinations encompassing a maximum output for a specified set of inputs would constitute the production function. Alternatively, a production function can be defined as the specification of the minimum input requirements needed to produce designated quantities of output, given available technology. It is usually presumed that unique production functions can be constructed for every production technology.

By assuming that the maximum output technologically possible from a given set of inputs is achieved, economists using a production function in analysis are abstracting from the engineering and managerial problems inherently associated with a particular production process. The engineering and managerial problems of technical efficiency are assumed to be solved, so that analysis can focus on the problems of allocative efficiency. The firm is assumed to be making allocative choices concerning how much of each input factor to use and how much output to produce, given the cost (purchase price) of each factor, the selling price of the output, and the technological determinants represented by the production function. A decision frame in which one or more inputs are held constant may be used; for example, (physical) capital may be assumed to be fixed (constant) in the short run, and labour and possibly other inputs such as raw materials variable, while in the long run, the quantities of both capital and the other factors that may be chosen by the firm are variable. In the long run, the firm may even have a choice of technologies, represented by various possible production functions.

The relationship of output to inputs is non-monetary; that is, a production function relates physical inputs to physical outputs, and prices and costs are not reflected in the function. But the production function is not a full model of the production process: it deliberately abstracts from inherent aspects of physical production processes that some would argue are essential, including error, entropy or waste. Moreover, production functions do not ordinarily model the business processes, either, ignoring the role of management. (For a primer on the fundamental elements of microeconomic production theory, see production theory basics).

The primary purpose of the production function is to address allocative efficiency in the use of factor inputs in production and the resulting distribution of income to those factors. Under certain assumptions, the production function can be used to derive a marginal product for each factor, which implies an ideal division of the income generated from output into an income due to each input factor of production.

Specifying the production function

A production function can be expressed in functional form as the right side of

Q = f(X_1,X_2,X_3,...,X_n)
Q = quantity of output
X_1,X_2,X_3,...,X_n = quantities of factor inputs (such as capital, labour, land or raw materials).

If Q is a scalar, then this form does not encompass joint production, which is a production process that has multiple co-products. On the other hand, if f maps from Rn to Rk then it is a joint production function expressing the determination of k different types of output based on the joint usage of the specified quantities of the n inputs.

One formulation, unlikely to be relevant in practice, is as a linear function:

Q=a+b X_1+c X_2+d X_3+ ...
where a, b, c, and d are parameters that are determined empirically.

Another is as a Cobb-Douglas production function:

Q = aX_1^b X_2^c \cdot \cdot \cdot .

The Leontief production function applies to situations in which inputs must be used in fixed proportions; starting from those proportions, if usage of one input is increased without another being increased, output will not change. This production function is given by

Q = \min (aX_1, \ \ bX_2, \ \ ...).

Other forms include the constant elasticity of substitution production function (CES), which is a generalized form of the Cobb-Douglas function, and the quadratic production function. The best form of the equation to use and the values of the parameters (a, b, c, ...) vary from company to company and industry to industry. In a short run production function at least one of the X's (inputs) is fixed. In the long run all factor inputs are variable at the discretion of management.

Production function as a graph

Any of these equations can be plotted on a graph. A typical (quadratic) production function is shown in the following diagram under the assumption of a sin

From Yahoo Answers

Question:Question for Chemist or doctors, how can i increase or motivate the production of HCL acid, when u have stomach acid deficiency???

Answers:Histidine Botanical Herbal Combinations Bitter herbs are thought to stimulate digestive function by increasing saliva production and promoting both stomach acid and digestive enzyme production. As a result, they are particularly used when there is low stomach acid but not in cases of heartburn or too much stomach acid. These herbs taste bitter, thus the name. Some examples of bitter herbs include greater celandine, wormwood, and gentian. Bitters are generally taken either by mixing 1 3 ml tincture into water and sipping slowly 10 30 minutes before eating, or by making tea, which is also sipped slowly before eating. There are many combination products available from your health food store. A more comprehensive list would include andrographis, artichoke, barberry, bitter melon, bitter orange, blessed thistle, boldo, centaury, dandelion, devil s claw, elecampane, gentian, goldenseal, greater celandine, horehound, juniper, Oregon grape, picrorhiza, prickly ash, vervain, wormwood, yarrow and yellow dock. Cayenne Pepper (Capsicum frutescens) Capsaicin, the active ingredient in cayenne, is believed to assist digestion by stimulating the flow of both salvia and stomach secretions. One or two capsules of cayenne pepper taken before meals stimulates hunger also. Diet Therapeutic Fasting Fasting gives the digestive system a needed break from the nearly constant effort that is required to process what we swallow. Unless we have been eating very healthfully, and sometimes even if we have, fasting will provide a period of rest to allow digestive rejuvenation to occur. Juices / Juicing A juice fast gives the digestive tract a rest from its heavy responsibilities, and strengthens a digestive weakness. Vinegar Apple cider vinegar or lemon juice taken with meals mildly stimulates hydrochloric acid production.

Question:I m a farmer I want to increase my verious crops like cotton, Soyabin,chana, tomato, chilly etc ) agriculture production,

Answers:plant cotton in china, india, pakistan, bangladesh. if not your cotton will not be as competitive as you will have a higher production cost. the effect of globalization is sad but this is modern day reality.

Question:Both capital and labor are required for production, and each factor is subject to diminishing marginal productivity. a. Explain how it is possible for a company to have increasing returns to scale and yet have diminishing marginal productivity for both factors of production. b. If the firm increases its labor force and keeps the capital stock constant, how will this effect the real wage and the real rental price of capital? c. If the firm increases both factors by the same percentage, what will be the effect on the real wage and real rental price?

Answers:Marginal productivity refers to what happens when only one input changes. Returns to scale allows all inputs to increase simultaneously. Suppose you were a baker. Add more people and you can bake more bread, but eventually you will be limited by your ovens. Add more ovens but not more people, and eventually you will have ovens idle. Add both people and ovens and you can keep making more bread. If you really didn't understand part (a), this should be enough help. If you did understand part (a) and didn't bother answering it for yourself, sorry, but I've already wasted too much time on you.

Question:Corn used for ethanol production covered 11 million on acres in 2005, and now covers 23 million acres. To meet the 15 billion gallon mandate passed by the house in June, we will need about 36 million acres of corn. Corn is being planted in lieu of crops like soybeans, and in place of grasslands. Crop rotation is diminishing as corn-on-corn becomes the norm, and water quality could suffer due to increased fertilizer runoff. Farmer participation in the Conservation Reserve Program, a federal program that retires marginal farm land from agricultural production, is diminishing. All of this is not good news for the Henslow's sparrow, whose recovery is dependent on the presence of perennial grasslands created by the CRP. In creating solutions, shouldn't we avoid creating more and new problems?

Answers:Your observation is correct. We are actually destroying natural resources by over exploiting them for every growing demand for energy. Oil, coal and water are not infinite. They have already become "preserving commodities". We are all culprits in misusing costly electricity even during day time when the sun is shining. Burning bulbs contribute CO2. Have a look at my World Bank honored grassroots level initiative. Even burning bulbs contribute to global warming. I was honored by the World Bank for my grassroots initiative U-SEE A grassroot level initiative U-SEE - Unlimited Savings of Electrical Energy which gives to the world how we can stop misuse of electricity during day time when the sun is shining. My idea revolves around "bring home the sunshine" and "get moonlight from sunlight". Have a look at the following World Bank link and let me know if you want more details. The idea is a child's play and is so simple but saves billions of units of costly electricity and also reduces over exploitation of the natural resources like oil, coal, water and also reduces global warming from stopping burning of bulbs. Link: http://dmblog.worldbank.org/mirrors-can-bring-light-rural-homes Please spread this link to all your family members, friends and neighbors. Let them also benefit and save the world before it is too late. vkumar_m@yahoo.com - Vasanthkumar Mysoremath, Bangalore, India

From Youtube

How can agriculture productivity of oilseeds be increased :Brief interaction with Deepak Pental, Vice Chancellor, Delhi University, June 30, 2009, 2 pm (In Indian Institute of Management, Indore)

Integrated Pest Management Can Increase Crop Production :I'm Alex Villarreal with the VOA Special English Agriculture Report, from voaspecialenglish.com | http Farmers know that if you reduce harmful insects and diseases in your crops, you have a chance for a better harvest. Today, many farmers and experts praise Integrated Pest Management, or IPM. IPM is a series of choices and methods to control insects, diseases and fungi. The program provides current information on how pests live and act in the environment. A number of non-governmental and other organizations in many countries provide education in IPM. Farmers can get information meant for the needs of their own land. They can learn to recognize possible problems and how to plan crops to help prevent failures.Paul Jepson heads the Integrated Plant Protection Center at Oregon State University. He says farmers who have attended field schools in Asia and Africa have increased the use of IPM. And he says this has cut pesticide use. James Frederick is an IPM expert with Clemson University's Pee Dee Research and Educational Center in South Carolina. He says one basic IPM method is to plant as early in the season as possible so that most of the crop will be in by the time a disease or pest arrives. Not all insects are pests. Some are helpful. IPM programs help farmers learn to identify different kinds.Another IPM method is rotating crops. Farmers do not plant the same crop season after season in the same soil. Instead, they may plant corn one season, soybeans the next, then corn ...