text:
Gravy Train (dog food)
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Gravy Train is an American commercial dog food. Originally developed by General Foods, it was the first brand of dog food to have a brown gravy form when warm water is added to the dry kibble, mixing with the kibble's powder coating. The gravy is intended to make the food more palatable.
The advertising catchphrase is "The Gravy Taste Dogs Can't Wait to Finish."
Gravy Train was once a brand of General Foods Corporation as part of its Gaines Division which included Gaines Meal, Gaines-Burgers as well as Prime Choice and Top Choice.[1]
Since 2014, Gravy Train has been owned by Big Heart Pet Brands, which spun off from Del Monte Foods.
References[edit]
Jump up ^ History Project's 1984 ad for Gravy Train
External links[edit]
Official website

This brand-name food or drink product–related article is a stub. You can help Wikipedia by expanding it.
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Chod rig
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This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. Please help to improve this article by introducing more precise citations. (January 2011) (Learn how and when to remove this template message)
The chod rig is a technique for carp fishing, generally regarded as having two main advantages: the way in which it allows a bait to be displayed over soft mud, weed or debris; and the way its distinct shape allows the chosen bait (usually a buoyant substance) to be attached. The latter benefit is also generally utilised in the chod rig's immediate ancestor, the stiff-hinged rig. It revolves around a rig consisting of a rigid or stiff link, an aggressively angled hookpoint and the ability to spring 360 degrees around the axis of the hook.
The chod rig is widely used and developed by large fishing manufacturers. Industry headliners[according to whom?] such as Jim Shelley and Terry Hearn use the chod rig to great effect. Known carp such as Benson and Heather the Leather have been captured by the chod rig.
The two key features of the chod combine to make it very difficult for a carp to avoid the hook or physically dislodge it after being snared. The hookholds that the chod delivers are generally very strong and secure, causing less damage to the fish's mouth. Not only do very few fish fall off with this set-up, but they suffer minimal damage.
Sources[edit]
http://www.bristolangling.com
http://www.korda.co.uk/rigz/?id=10
http://www.fishingmagic.com/
http://www.korda.co.uk
http://www.carp-fishing.org/Carp-Rigs/Chod-Rig-Carp-Fishing.htm
http://www.essex-fishing.co.uk
How to create and use the chod rig to catch fish
Tying the chod right made simple
How to tie a chod rig
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Easter Bunny
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Easter Bunny
A 1907 postcard featuring the Easter Bunny
Grouping
Legendary creature
Sub grouping
Animal
Mythology
Folkloric figure and symbol of Easter
Other name(s)
Easter Rabbit, Easter Hare
Country
Germany
Habitat
Grass
The Easter Bunny (also called the Easter Rabbit or Easter Hare) is a folkloric figure and symbol of Easter, depicted as a rabbit bringing Easter eggs. Originating among German Lutherans, the "Easter Hare" originally played the role of a judge, evaluating whether children were good or disobedient in behavior at the start of the season of Eastertide.[1] The Easter Bunny is sometimes depicted with clothes. In legend, the creature carries colored eggs in his basket, candy, and sometimes also toys to the homes of children, and as such shows similarities to Santa Claus or the Christkind, as they both bring gifts to children on the night before their respective holidays. The custom was first[2][unreliable source?] mentioned in Georg Franck von Franckenau's De ovis paschalibus[3] ('About Easter Eggs') in 1682, referring to a German tradition of an Easter Hare bringing Easter eggs for the children.
Contents
[hide]
1 Symbols
1.1 Rabbits and hares
1.2 Eggs
2 Association with Ēostre
2.1 Transformed bird
3 See also
4 References
5 External links
Symbols
Rabbits and hares
The hare was a popular motif in medieval church art. In ancient times, it was widely believed (as by Pliny, Plutarch, Philostratus, and Aelian) that the hare was a hermaphrodite.[4][5][6] The idea that a hare could reproduce without loss of virginity led to an association with the Virgin Mary, with hares sometimes occurring in illuminated manuscripts and Northern European paintings of the Virgin and Christ Child. It may also have been associated with the Holy Trinity, as in the three hares motif.[4][7] Eggs, like rabbits and hares, are fertility symbols[8] of antiquity. Since birds lay eggs and rabbits and hares give birth to large litters in the early spring, these became symbols of the rising fertility of the earth at the Vernal Equinox.
Rabbits and hares are both prolific breeders. Female hares can conceive a second litter of offspring while still pregnant with the first.[9][10] This phenomenon is known as superfetation. Lagomorphs mature sexually at an early age and can give birth to several litters a year (hence the saying, "to breed like rabbits" or "to breed like bunnies"). It is therefore not surprising that rabbits and hares should become fertility symbols, or that their springtime mating antics should enter into Easter folklore.
Eggs
Main articles: Easter egg and Egg decorating
In addition, Orthodox churches have a custom of abstaining from eggs during the fast of Lent. The only way to keep them from being wasted was to boil or roast them, and begin eating them to break the fast.[citation needed] As a special dish, they would probably have been decorated as part of the celebrations. Later, German Protestants retained the custom of eating colored eggs for Easter, though they did not continue the tradition of fasting.[11] Eggs boiled with some flowers change their color, bringing the spring into the homes, and some over time added the custom of decorating the eggs.[12] Many Christians of the Eastern Orthodox Church to this day typically dye their Easter eggs red,[13] the color of blood, in recognition of the blood of the sacrificed Christ (and, of the renewal of life in springtime). Some also use the color green, in honor of the new foliage emerging after the long-dead time of winter. The Ukrainian art of decorating eggs for Easter, known as pysanky, dates to ancient, pre-Christian times. Similar variants of this form of artwork are seen amongst other eastern and central European cultures.[14]
The idea of an egg-giving hare went to the U.S. in the 18th century. Protestant German immigrants in the Pennsylvania Dutch area told their children about the "Osterhase" (sometimes spelled "Oschter Haws"[15]). Hase means "hare", not rabbit, and in Northwest European folklore the "Easter Bunny" indeed is a hare. According to the legend, only good children received gifts of colored eggs in the nests that they made in their caps and bonnets before Easter.[16]
Dreihasenfenster (Window of Three Hares) in Paderborn Cathedral in Paderborn, Germany
Marshmallow bunnies and candy eggs in an Easter basket
A bunny and decorated Easter eggs
A chocolate Easter Bunny
Chocolate Easter Bunny molds from Alsace Musée du pain d'épices
Association with Ēostre
In his 1835 Deutsche Mythologie, Jacob Grimm states "The Easter Hare is unintelligible to me, but probably the hare was the sacred animal of Ostara". This proposed association was repeated by other authors including Charles Isaac Elton [17] and Charles J Billson.[18] In 1961 Christina Hole wrote, "The hare was the sacred beast of Eastre (or Eostre), a Saxon goddess of Spring and of the dawn."[19] The belief that Ēostre had a hare companion who became the Easter Bunny was popularized when it was presented as fact in the BBC documentary Shadow of the Hare (1993).[20]
The Oxford Dictionary of English Folklore however states "... there is no shred of evidence" that hares were sacred to Ēostre, noting that Bede does not associate her with any animal.[21]
Transformed bird
Sarah Ben Breathnach in Mrs Sharp's Traditions (1990) provides an origin story for the Easter Bunny: "According to legend, Eostre's favorite animal was a large handsome bird, which in a fit of anger she turned into a hare."[22] Another version of this story, in which Ēostre transforms the bird into a hare in an act of mercy, was written by Jean-Andrew Dickmann and appeared in Cricket magazine.[23] Both Breathnach and Dickmann present their respective 'transformed bird' stories as if they were legend, though no earlier version of either has been attested.
See also
Domestic and pet rabbits
Easter Bilby
Ēostre
Mad as a March hare
Osterfuchs[de] (Easter Fox) (in German)
Rabbits in the arts
Rabbits in culture and literature
The Goose That Laid the Golden Eggs
References
Jump up ^ Cross, Gary (2004). Wondrous Innocence and Modern American Children's Culture. Oxford University Press. ISBN 0195348133.
Jump up ^ Easter Bunny - What Does He Have To Do With Easter?, occultcenter.com
Jump up ^ Franck von Franckenau, Georg (1682). Disputatione ordinaria disquirens de ovis paschalibus / von Oster-Eyern. Satyrae Medicae. XVIII. Heidelberg. p. 6. Retrieved 18 July 2013.
^ Jump up to: a b Chapman, Chris (2004). "What does the Symbol Mean?". Three Hares Project. Retrieved 20 April 2014.
Jump up ^ Marta Powell Harley. "Rosalind, the hare, and the hyena in Shakespeare's As You Like It". Shakespeare Quarterly.
Jump up ^ "Sir Thomas Browne (1646; 6th ed., 1672) Pseudodoxia Epidemica III:xvii (pp. 162-166)".
Jump up ^ "Three Hares as representation of the Trinity". Threehares.blogspot.com. 2006-02-25. Retrieved 2010-06-29.
Jump up ^ Heller, Steven (April 2014). "Seeing Rabbits". Academic Search Complete (Vol. 68 Issue 2). |access-date= requires |url= (help)
Jump up ^ Martinez-Gomez, Margarita (September 2004). "Overlapping litters and reproductive performance in the domestic rabbit". Academic Search Complete (Vol. 82 Issue 4). Physiology & Behavior. |access-date= requires |url= (help)
Jump up ^ Lumpkin, Susan; John Seidensticker (2011). Rabbits: The Animal Answer Guide. JHU Press. ISBN 0-8018-9789-0. p. 122.
Jump up ^ Shrove Tuesday Pancakes! by Bridget Haggerty - Irish Culture & Customs, World Cultures European, paragraph 5 line 2 refers to the Catholic custom of abstaining from eggs during Lent. Accessed 3/1/08
Jump up ^ Snodgrass, Lucie L. (March 2005). "DYED IN Tradition". Academic Search Complete (Issue 329). Vegetarian Times. |access-date= requires |url= (help)
Jump up ^ How To Dye Red Eggs with Onion Skins for Greek Easter by Nancy Gaifyllia from Your Guide to Greek Food on About.Com Accessed April 9, 2008
Jump up ^ Hallett, Vicky (March 31, 2003). "Egg-cellent art". Academic Search Complete (Vol. 134 Issue 10). U.S. News & World Report. |access-date= requires |url= (help)
Jump up ^ "Gruß vom Osterhasen: Oschter Haws Song : GERMAN WORLD MAGAZINE". Germanworldonline.com. 2011-04-23. Retrieved 2013-03-31.
Jump up ^ Easter Symbols Archived 2008-03-12 at the Wayback Machine. from Lutheran Hour Ministries. Accessed 2/28/08
Jump up ^ Charles Isaac Elton (1890), Origins of English History
Jump up ^ Charles J Billson (1892), Folk-Lore vol 3 issue 4
Jump up ^ Christina Hole (1961) Easter and its Customs
Jump up ^ Attenborough, Sir David (Presenter) (April 12, 1993). Wildlife on One Easter Special Shadow of the Hare (Television). United Kingdom: BBC.
Jump up ^ Jacqueline Simpson and Stephen Roud (2000), A Dictionary of English Folklore
Jump up ^ Sarah Ben Breathnach (1990), Mrs Sharp's Traditions: Reviving Victorian Family Celebrations of Comfort and Joy
Jump up ^ Jean-Andrew Dickmann (2002), The Coming of Eostre, Cricket magazine vol 29 issue 7
External links
Wikimedia Commons has media related to Easter Bunny.
Charles J. Billson. "The Easter Hare". Folk-Lore. Vol. 3, No. 4 (December 1892).
On the Bunny Trail: In Search of the Easter Bunny, Stephen Winick, Folklife Today, March 22, 2016
[show]
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Easter
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GND: 4172936-5
Retrieved from "https://en.wikipedia.org/w/index.php?title=Easter_Bunny&oldid=835456319"
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text:
Elections in the Bahamas
From Wikipedia, the free encyclopedia
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The Bahamas
This article is part of a series on the
politics and government of
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Executive[show]
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Elections in the Bahamas take place in the framework of a parliamentary democracy. Since independence voter turnout has been generally high in national elections, with a low of 87.9% in 1987 and a high of 98.5% in 1997. The current Prime Minister is the Hon Hubert Minnis.
Contents
[hide]
1 Electoral system
1.1 House of Assembly
1.2 Senate
2 Referendums
3 History
4 Latest elections
5 References
Electoral system[edit]
The country's electoral law was passed on 31 December 1979 and was last amended in 1992.[1] Elections are run by the Parliamentary Registration Department, headed by a Parliamentary Commissioner. Appointed by the Governor-General, the Commissioner is responsible for voter registration. There is also an Electoral Broadcasting Council, which is responsible for ensuring that media reports are fair and not biased towards any party.[2]
The country has a bicameral Parliament with a House of Assembly and Senate.
House of Assembly[edit]
The House of Assembly has 39 elected members who are elected in single-member constituencies.[1] Elections for the House are held every five years.[3]
Voters must be aged 18 or over, hold Bahamian citizenship and lived for three months in the constituency.[1] They can disqualified if insane, imprisoned or under a death sentence. Until 1972 British citizens could also vote if they had been resident for six months.
Candidates must be at least 21 years old, citizens of the country, and have lived in the country for at least a year prior to the elections.[1] Those with dual citizenship or an undischarged bankruptry are ineligible, as are those who have a criminal conviction, a history of electoral fraud, or are insane or under a death sentence.[1]
Senate[edit]
The Senate is unelected and consists of 16 members appointed by the Governor-General; nine on the advice of the Prime Minister, four on the advice of the leader of the opposition, and three on the advice of the Prime Minister after consultations with the leader of the opposition.[4]
Referendums[edit]
There have been two national referendums and one opinion poll held within the last twenty years. The first, held in 2002, it asked voters five questions ranging from changes to the constitution to the setting up of a national commission on teaching. The first opinion poll, held in January 2013, asked individuals whether they wanted to legalize online gambling. The second national referendum took place on June 7th, 2016, and asked voters four questions pertaining to equal rights within the Bahamas. All three (3) referendum's/opinion polls were rejected.
History[edit]
Prior to the introduction of universal suffrage in 1961, elections in the Bahamas were dominated by the white oligarchy known as the Bay Street Boys.[5] They were represented by the United Bahamian Party (UBP), which by gerrymandering the constituency boundaries, won the 1962 elections despite receiving fewer votes than the black Progressive Liberal Party (PLP).[5] In the next elections in 1967 the UBP received more votes than the PLP, but they won the same number of seats. With the support of the sole Labour Party MP the PLP was able to form the country's first black-led government.
The PLP dominated national politics until the 1990s, winning every election until 1992 when they were defeated by the Free National Movement (FNM) formed after a split within the PLP in 1971.[5] The FNM won the next elections in 1997 in which voter turnout hit a record 98.5%,[6] but power was ceded back to the PLP in 2002.[7] The FNM returned to power again in 2007. The PLP regained power in 2012, only to lose it in 2017.
Latest elections[edit]
Main article: Bahamian general election, 2012
Template:Bahamian general election, 2017*
References[edit]
^ Jump up to: a b c d e House of Assembly, Electoral System, Inter-Parliamentary Union.
Jump up ^ Nohlen, D. (2005), Elections in the Americas: A data handbook, Volume I, p. 77, ISBN 978-0-19-928357-6
Jump up ^ General information about the parliamentary chamber, Inter-Parliamentary Union.
Jump up ^ Senate, Electoral system Inter-Parliamentary Union.
^ Jump up to: a b c Nohlen, p. 73.
Jump up ^ Nohlen, p. 78.
Jump up ^ Nohlen, p. 82.
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text:
Return address
From Wikipedia, the free encyclopedia
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For other uses, see Return address (disambiguation).
Envelope with return address in top left corner
In postal mail, a return address is an explicit inclusion of the address of the person sending the message. It provides the recipient (and sometimes authorized intermediaries) with a means to determine how to respond to the sender of the message if needed. The return address need not include a sender's name, but should include address or P.O. box details in the same way as the delivery address should. In some countries, the return address is conventionally located in the upper left hand corner of the envelope, card, or label. In the United Kingdom, the return address is usually placed on the reverse of the envelope, near the top.[1]
Businesses often use envelopes preprinted with a return address. Many individuals have sheets of adhesive labels preprinted with their home address to affix to their correspondence. Charities sometimes include such sheets in mailshots. Rolls of Return Address Labels can be purchased from companies that sell personalized labels to provide individuals an easy way to peel and stick return address labels to their envelopes.
The return address is not required on postal mail. However, lack of a return address prevents the postal service from being able to return the item if it proves undeliverable; such as from damage, postage due, or invalid destination. Such mail may otherwise become dead letter mail.[2]
Should the return address be of a different state or country, the mail may be routed through that location for ease of return.
History[edit]
The return address has been used on U. S. postage since the 1880s. As pressure printing became more commonplace during the early 1900s, labels became cheaper and more easily distributed. The profession involved with producing these labels was known as lithography. During the 1950s in the United States, more and more mail was not arriving at intended recipients, and as a result of the lack of a return address, said mail ended up in the dead letter office. With this rise in dead mail, the post office pleaded for people to use a return address. Even after this, the public still tended to neglect adding a return address. This prompted the postmaster to inform the public that mail without a return address would be less of a priority than mail with a return address. Still, the public did not widely use a return address until the 1960s when companies began to offer deals for preprinted return labels such as 2,500 labels for $2.00. They became more popular with the invention of label dispensers. With the invention of the personal computer, software enabled people to print their own labels. As e-mail began to overtake written mail, the return address became automatic in an e-mail.[3]
References[edit]
Jump up ^ Conventional Positioning of Return Address Labels in the UK: http://thelabelroom.co.uk/blogo/wordpress/?p=48
Jump up ^ "Business Mail 101". United States Postal Service Website. Retrieved 23 August 2013.
Jump up ^ "The History of Return Address Labels!". Web page. Retrieved 23 August 2013.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Return_address&oldid=767535802"
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Production function
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Graph of total, average, and marginal product
In economics, a production function relates quantities of physical output of a production process to quantities of physical inputs or factors of production. The production function is one of the key concepts of mainstream neoclassical theories, used to define marginal product and to distinguish allocative efficiency, a key focus of economics. 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, while abstracting away from the technological problems of achieving technical efficiency, as an engineer or professional manager might understand it.
In macroeconomics, aggregate production functions are estimated to create a framework in which to distinguish how much of economic growth to attribute to changes in factor allocation (e.g. the accumulation of physical capital) and how much to attribute to advancing technology. Some non-mainstream economists, however, reject the very concept of an aggregate production function.[1][2]
Contents
[hide]
1 The theory of production functions
1.1 Specifying the production function
1.2 Production function as a graph
1.3 Stages of production
1.4 Shifting a production function
1.5 Homogeneous and homothetic production functions
1.6 Aggregate production functions
1.7 Criticisms of the production function theory
1.7.1 On the concept of capital
1.7.2 On the empirical relevance
1.7.3 Natural resources
1.8 The practice of production functions
2 See also
3 Footnotes
4 References
5 Further reading
6 External links
The theory of production functions[edit]
In general, economic output is not a (mathematical) function of input, because any given set of inputs can be used to produce a range of outputs. To satisfy the mathematical definition of a function, a production function is customarily assumed to specify the maximum output obtainable from a given set of inputs. The production function, therefore, describes a boundary or frontier representing the limit of output obtainable from each feasible combination of input. (Alternatively, a production function can be defined as the specification of the minimum input requirements needed to produce designated quantities of output.) Assuming that maximum output is obtained from given inputs allows economists to abstract away from technological and managerial problems associated with realizing such a technical maximum, and to focus exclusively on the problem of allocative efficiency, associated with the economic choice of how much of a factor input to use, or the degree to which one factor may be substituted for another. In the production function itself, 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.
In the decision frame of a firm making economic choices regarding production—how much of each factor input to use to produce how much output—and facing market prices for output and inputs, the production function represents the possibilities afforded by an exogenous technology. Under certain assumptions, the production function can be used to derive a marginal product for each factor. The profit-maximizing firm in perfect competition (taking output and input prices as given) will choose to add input right up to the point where the marginal cost of additional input matches the marginal product in additional output. This implies an ideal division of the income generated from output into an income due to each input factor of production, equal to the marginal product of each input.
The inputs to the production function are commonly termed factors of production and may represent primary factors, which are stocks. Classically, the primary factors of production were Land, Labor and Capital. Primary factors do not become part of the output product, nor are the primary factors, themselves, transformed in the production process. The production function, as a theoretical construct, may be abstracting away from the secondary factors and intermediate products consumed in a production process. 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, and the consumption of energy or the co-production of pollution. Moreover, production functions do not ordinarily model the business processes, either, ignoring the role of strategic and operational business management. (For a primer on the fundamental elements of microeconomic production theory, see production theory basics).
The production function is central to the marginalist focus of neoclassical economics, its definition of efficiency as allocative efficiency, its analysis of how market prices can govern the achievement of allocative efficiency in a decentralized economy, and an analysis of the distribution of income, which attributes factor income to the marginal product of factor input.
Specifying the production function[edit]
A production function can be expressed in a functional form as the right side of
Q = f ( X 1 , X 2 , X 3 , … , X n ) {\displaystyle Q=f(X_{1},X_{2},X_{3},\dotsc ,X_{n})}
where Q {\displaystyle Q} is the quantity of output and X 1 , X 2 , X 3 , … , X n {\displaystyle X_{1},X_{2},X_{3},\dotsc ,X_{n}} are the quantities of factor inputs (such as capital, labour, land or raw materials).
If Q {\displaystyle 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 {\displaystyle f} maps from R n {\displaystyle \mathbb {R} ^{n}} to R k {\displaystyle \mathbb {R} ^{k}} then it is a joint production function expressing the determination of k {\displaystyle k} different types of output based on the joint usage of the specified quantities of the n {\displaystyle n} inputs.
One formulation, unlikely to be relevant in practice, is as a linear function:
Q = a 0 + a 1 X 1 + a 2 X 2 + a 3 X 3 + ⋯ + a n X n {\displaystyle Q=a_{0}+a_{1}X_{1}+a_{2}X_{2}+a_{3}X_{3}+\dotsb +a_{n}X_{n}}
where a 0 , … , a n {\displaystyle a_{0},\dots ,a_{n}} are parameters that are determined empirically. Another is as a Cobb-Douglas production function:
Q = a 0 X 1 a 1 X 2 a 2 ⋯ X n a n . {\displaystyle Q=a_{0}X_{1}^{a_{1}}X_{2}^{a_{2}}\cdots X_{n}^{a_{n}}.}
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 ( a 1 X 1 , a 2 X 2 , … , a n X n ) . {\displaystyle Q=\min(a_{1}X_{1},a_{2}X_{2},\dotsc ,a_{n}X_{n}).}
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 0 , … , a n {\displaystyle a_{0},\dots ,a_{n}} ) vary from company to company and industry to industry. In a short run production function at least one of the X {\displaystyle X} 's (inputs) is fixed. In the long run all factor inputs are variable at the discretion of management.
Moysan and Senouci (2016) provide an analytical formula for all 2-input, neoclassical production functions.[3]
Production function as a graph[edit]
Quadratic production function
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 single variable input (or fixed ratios of inputs so they can be treated as a single variable). All points above the production function are unobtainable with current technology, all points below are technically feasible, and all points on the function show the maximum quantity of output obtainable at the specified level of usage of the input. From point A to point C, the firm is experiencing positive but decreasing marginal returns to the variable input. As additional units of the input are employed, output increases but at a decreasing rate. Point B is the point beyond which there are diminishing average returns, as shown by the declining slope of the average physical product curve (APP) beyond point Y. Point B is just tangent to the steepest ray from the origin hence the average physical product is at a maximum. Beyond point B, mathematical necessity requires that the marginal curve must be below the average curve (See production theory basics for further explanation.).
Stages of production[edit]
To simplify the interpretation of a production function, it is common to divide its range into 3 stages. In Stage 1 (from the origin to point B) the variable input is being used with increasing output per unit, the latter reaching a maximum at point B (since the average physical product is at its maximum at that point). Because the output per unit of the variable input is improving throughout stage 1, a price-taking firm will always operate beyond this stage.
In Stage 2, output increases at a decreasing rate, and the average and marginal physical product both decline. However, the average product of fixed inputs (not shown) is still rising, because output is rising while fixed input usage is constant. In this stage, the employment of additional variable inputs increases the output per unit of fixed input but decreases the output per unit of the variable input. The optimum input/output combination for the price-taking firm will be in stage 2, although a firm facing a downward-sloped demand curve might find it most profitable to operate in Stage 1. In Stage 3, too much variable input is being used relative to the available fixed inputs: variable inputs are over-utilized in the sense that their presence on the margin obstructs the production process rather than enhancing it. The output per unit of both the fixed and the variable input declines throughout this stage. At the boundary between stage 2 and stage 3, the highest possible output is being obtained from the fixed input.
Shifting a production function[edit]
By definition, in the long run the firm can change its scale of operations by adjusting the level of inputs that are fixed in the short run, thereby shifting the production function upward as plotted against the variable input. If fixed inputs are lumpy, adjustments to the scale of operations may be more significant than what is required to merely balance production capacity with demand. For example, you may only need to increase production by million units per year to keep up with demand, but the production equipment upgrades that are available may involve increasing productive capacity by 2 million units per year.
Shifting a production function
If a firm is operating at a profit-maximizing level in stage one, it might, in the long run, choose to reduce its scale of operations (by selling capital equipment). By reducing the amount of fixed capital inputs, the production function will shift down. The beginning of stage 2 shifts from B1 to B2. The (unchanged) profit-maximizing output level will now be in stage 2.
Homogeneous and homothetic production functions[edit]
There are two special classes of production functions that are often analyzed. The production function Q = f ( X 1 , X 2 , … , X n ) {\displaystyle Q=f(X_{1},X_{2},\dotsc ,X_{n})} is said to be homogeneous of degree m {\displaystyle m} , if given any positive constant k {\displaystyle k} , f ( k X 1 , k X 2 , … , k X n ) = k m f ( X 1 , X 2 , … , X n ) {\displaystyle f(kX_{1},kX_{2},\dotsc ,kX_{n})=k^{m}f(X_{1},X_{2},\dotsc ,X_{n})} . If m > 1 {\displaystyle m>1} , the function exhibits increasing returns to scale, and it exhibits decreasing returns to scale if m < 1 {\displaystyle m<1} . If it is homogeneous of degree 1 {\displaystyle 1} , it exhibits constant returns to scale. The presence of increasing returns means that a one percent increase in the usage levels of all inputs would result in a greater than one percent increase in output; the presence of decreasing returns means that it would result in a less than one percent increase in output. Constant returns to scale is the in-between case. In the Cobb-Douglas production function referred to above, returns to scale are increasing if a 1 + a 2 + ⋯ + a n > 1 {\displaystyle a_{1}+a_{2}+\dotsb +a_{n}>1} , decreasing if a 1 + a 2 + ⋯ + a n < 1 {\displaystyle a_{1}+a_{2}+\dotsb +a_{n}<1} , and constant if a 1 + a 2 + ⋯ + a n = 1 {\displaystyle a_{1}+a_{2}+\dotsb +a_{n}=1} .
If a production function is homogeneous of degree one, it is sometimes called "linearly homogeneous". A linearly homogeneous production function with inputs capital and labour has the properties that the marginal and average physical products of both capital and labour can be expressed as functions of the capital-labour ratio alone. Moreover, in this case if each input is paid at a rate equal to its marginal product, the firm's revenues will be exactly exhausted and there will be no excess economic profit.[4]:pp.412–414
Homothetic functions are functions whose marginal technical rate of substitution (the slope of the isoquant, a curve drawn through the set of points in say labour-capital space at which the same quantity of output is produced for varying combinations of the inputs) is homogeneous of degree zero. Due to this, along rays coming from the origin, the slopes of the isoquants will be the same. Homothetic functions are of the form F ( h ( X 1 , X 2 ) ) {\displaystyle F(h(X_{1},X_{2}))} where F ( y ) {\displaystyle F(y)} is a monotonically increasing function (the derivative of F ( y ) {\displaystyle F(y)} is positive ( d F / d y > 0 {\displaystyle \mathrm {d} F/\mathrm {d} y>0} )), and the function h ( X 1 , X 2 ) {\displaystyle h(X_{1},X_{2})} is a homogeneous function of any degree.
Aggregate production functions[edit]
See also: Cambridge capital controversy
In macroeconomics, aggregate production functions for whole nations are sometimes constructed. In theory they are the summation of all the production functions of individual producers; however there are methodological problems associated with aggregate production functions, and economists have debated extensively whether the concept is valid.[2]
Criticisms of the production function theory[edit]
There are two major criticisms[which?] of the standard form of the production function.[5]
On the concept of capital[edit]
During the 1950s, '60s, and '70s there was a lively debate about the theoretical soundness of production functions (see the Capital controversy). Although the criticism was directed primarily at aggregate production functions, microeconomic production functions were also put under scrutiny. The debate began in 1953 when Joan Robinson criticized the way the factor input capital was measured and how the notion of factor proportions had distracted economists. She wrote:
"The production function has been a powerful instrument of miseducation. The student of economic theory is taught to write Q = f (L, K ) where L is a quantity of labor, K a quantity of capital and Q a rate of output of commodities. [They] are instructed to assume all workers alike, and to measure L in man-hours of labor; [they] are told something about the index-number problem in choosing a unit of output; and then [they] are hurried on to the next question, in the hope that [they] will forget to ask in what units K is measured. Before [they] ever do ask, [they] have become a professor, and so sloppy habits of thought are handed on from one generation to the next".[6]
According to the argument, it is impossible to conceive of capital in such a way that its quantity is independent of the rates of interest and wages. The problem is that this independence is a precondition of constructing an isoquant. Further, the slope of the isoquant helps determine relative factor prices, but the curve cannot be constructed (and its slope measured) unless the prices are known beforehand.
On the empirical relevance[edit]
As a result of the criticism on their weak theoretical grounds, it has been claimed that empirical results firmly support the use of neoclassical well behaved aggregate production functions. Nevertheless, Anwar Shaikh has demonstrated that they also have no empirical relevance, as long as alleged good fit outcomes from an accounting identity, not from any underlying laws of production/distribution.[7]
Natural resources[edit]
See also: Nicholas Georgescu-Roegen § Criticising neoclassical economics (weak versus strong sustainability)
Natural resources are usually absent in production functions. When Robert Solow and Joseph Stiglitz attempted to develop a more realistic production function by including natural resources, they did it in a manner economist Nicholas Georgescu-Roegen criticized as a "conjuring trick": Solow and Stiglitz had failed to take into account the laws of thermodynamics, since their variant allowed man-made capital to be a complete substitute for natural resources. Neither Solow nor Stiglitz reacted to Georgescu-Roegen's criticism, despite an invitation to do so in the September 1997 issue of the journal Ecological Economics.[1] [8]:127-136 [2] [9]
The practice of production functions[edit]
Main article: Production (economics)
The theory of production function depicts the relation between physical outputs of a production process and physical inputs, i.e. factors of production. The practical application of production function is obtained by valuing the physical outputs and inputs by their prices. The economic value of physical outputs minus the economic value of physical inputs is the income generated by the production process. By keeping the prices fixed between two periods under review we get the income change generated by the change of production function. This is the principle how the production function is made a practical concept, i.e. measureable and understandable in practical situations.
See also[edit]
Assembly line
Computer-aided manufacturing
Distribution (economics)
Division of labour
Industrial Revolution
Mass production
Production
Production theory basics
Production, costs, and pricing
Production possibility frontier
Productive forces
Productive and unproductive labour
Productivity
Productivity improving technologies (historical)
Productivity model
Second Industrial Revolution
Footnotes[edit]
^ Jump up to: a b Daly, H (1997). "Forum on Georgescu-Roegen versus Solow/Stiglitz". Ecological Economics. 22 (3): 261–306. doi:10.1016/S0921-8009(97)00080-3.
^ Jump up to: a b c Cohen, A. J.; Harcourt, G. C. (2003). "Retrospectives: Whatever Happened to the Cambridge Capital Theory Controversies?". Journal of Economic Perspectives. 17 (1): 199–214. doi:10.1257/089533003321165010.
Jump up ^ see Moysan and, G.; Senouci, M. (2016). "A note on 2-input neoclassical production functions". Journal of Mathematical Economics. doi:10.1016/j.jmateco.2016.09.011.
Jump up ^ Chiang, Alpha C. (1984) Fundamental Methods of Mathematical Economics, third edition, McGraw-Hill.
Jump up ^ On the history of production functions, see Mishra, S. K. (2007). "A Brief History of Production Functions". Working Paper. SSRN 1020577  .
Jump up ^ Robinson, Joan (1953). "The Production Function and the Theory of Capital". Review of Economic Studies. 21: [p. 81].
Jump up ^ Shaikh, A. (1974). "Laws of Production and Laws of Algebra: The Humbug Production Function". Review of Economics and Statistics. 56 (1): 115–120. doi:10.2307/1927538. JSTOR 1927538.
Jump up ^ Daly, Herman E. (1999). "How long can neoclassical economists ignore the contributions of Georgescu-Roegen?". In Daly, Herman E. (2007). Ecological Economics and Sustainable Development. Selected Essays of Herman Daly (PDF contains full book). Cheltenham: Edward Elgar. ISBN 9781847201010.
Jump up ^ Ayres, Robert U.; Warr, Benjamin (2009). The Economic Growth Engine: How Useful Work Creates Material Prosperity. ISBN 978-1-84844-182-8.
References[edit]
Jorgenson, D.W.; Ho, M.S.; Samuels, J.D. (2014). Long-term Estimates of U.S. Productivity and Growth (PDF). Tokyo: Third World KLEMS Conference.
Riistama, K.; Jyrkkiö E. (1971). Operatiivinen laskentatoimi (Operative accounting). Weilin + Göös. p. 335.
Saari, S. (2006). Productivity. Theory and Measurement in Business (PDF). Espoo, Finland: European Productivity Conference.
Saari, S. (2011). Production and Productivity as Sources of Well-being. MIDO OY. p. 25.
Further reading[edit]
Brems, Hans (1968). "The Production Function". Quantitative Economic Theory. New York: Wiley. pp. 62–74.
Craig, C.; Harris, R. (1973). "Total Productivity Measurement at the Firm Level". Sloan Management Review (Spring 1973): 13–28.
Guerrien B. and O. Gun (2015) "Putting an end to the aggregate function of production... forever?", Real World Economic Review N°73
Hulten, C. R. (January 2000). "Total Factor Productivity: A Short Biography". NBER Working Paper No. 7471. doi:10.3386/w7471.
Heathfield, D. F. (1971). Production Functions. Macmillan Studies in Economics. New York: Macmillan Press.
Intriligator, Michael D. (1971). Mathematical Optimalization and Economic Theory. Englewood Cliffs: Prentice-Hall. pp. 178–189. ISBN 0-13-561753-7.
Laidler, David (1981). Introduction to Microeconomics (Second ed.). Oxford: Philip Allan. pp. 124–137. ISBN 0-86003-131-4.
Maurice, S. Charles; Phillips, Owen R.; Ferguson, C. E. (1982). Economic Analysis: Theory and Application (Fourth ed.). Homewood: Irwin. pp. 169–222. ISBN 0-256-02614-9.
Moroney, J. R. (1967). "Cobb-Douglass production functions and returns to scale in US manufacturing industry". Western Economic Journal. 6 (1): 39–51. doi:10.1111/j.1465-7295.1967.tb01174.x.
Pearl, D.; Enos, J. (1975). "Engineering Production Functions and Technological Progress". Journal of Industrial Economics. 24: 55–72. doi:10.2307/2098099. JSTOR 2098099.
Shephard, R. (1970). Theory of Cost and Production Functions. Princeton, NJ: Princeton University Press.
Thompson, A. (1981). Economics of the Firm: Theory and Practice (3rd ed.). Englewood Cliffs: Prentice Hall. ISBN 0-13-231423-1.
External links[edit]
A further description of production functions
Anatomy of Cobb-Douglas Type Production Functions in 3D
Anatomy of CES Type Production Functions in 3D
Authority control
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values:
interlanguage-link interwiki-uk
display: none;

values:
interlanguage-link interwiki-vi
display: none;

values: All languages (initial selection from common choices by you and others)

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Production_function rootpage-Production_function skin-vector action-view