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Supply and demand

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(Redirected fromLaw of supply and demand)
Economic model of price determination in a market
For other uses, seeSupply and demand (disambiguation).
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Supply and demand curves witheconomic equilibrium of price and quantity sold
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Supply chain as connected supply and demand curves

Inmicroeconomics,supply and demand is aneconomic model ofprice determination in amarket. It postulates that,holding all else equal, theunit price for a particulargood or other traded item in aperfectly competitive market, will vary until it settles at themarket-clearing price, where the quantity demanded equals the quantity supplied such that aneconomic equilibrium is achieved for price and quantity transacted. The concept of supply and demand forms the theoretical basis of modern economics.

In situations where a firm hasmarket power, its decision on how much output to bring to market influences the market price, in violation of perfect competition. There, a more complicated model should be used; for example, anoligopoly ordifferentiated-product model. Likewise, where a buyer has market power, models such asmonopsony will be more accurate.

Inmacroeconomics, as well, theaggregate demand-aggregate supply model has been used to depict how the quantity oftotal output and theaggregate price level may be determined in equilibrium.

Graphical representations

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Supply schedule

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Main article:Price elasticity of supply

A supply schedule, depicted graphically as a supply curve, is a table that shows the relationship between the price of a good and the quantity supplied by producers. Under the assumption ofperfect competition, supply is determined bymarginal cost: Firms will produce additional output as long as the cost of extra production is less than the market price.

A rise in the cost of raw materials would decrease supply, shifting the supply curve to the left because at each possible price a smaller quantity would be supplied. This shift may also be thought of as an upwards shift in the supply curve, because the price must rise for producers to supply a given quantity. A fall in production costs would increase supply, shifting the supply curve to the right and down.

Mathematically, a supply curve is represented by a supply function, giving the quantity supplied as a function of its price and as many other variables as desired to better explain quantity supplied. The two most common specifications are:

1) linear supply function, e.g., the slanted line

Q(P)=3P6{\displaystyle Q(P)=3P-6}, and

2) the constant-elasticity[1] supply function (also calledisoelastic or log-log or loglinear supply function), e.g., the smooth curve

Q(P)=5P0.5{\displaystyle Q(P)=5P^{0.5}}

which can be rewritten as

logQ(P)=log5+0.5logP{\displaystyle \log Q(P)=\log 5+0.5\log P}

The concept of a supply curve assumes that firms are perfect competitors, having no influence over the market price. This is because each point on the supply curve answers the question, "If this firm is faced with this potential price, how much output will it sell?" If a firm has market power—in violation of the perfect competitor model—its decision on how much output to bring to market influences the market price. Thus the firm is not "faced with" any given price, and a more complicated model, e.g., amonopoly oroligopoly ordifferentiated-product model, should be used.

Economists distinguish between the supply curve of an individual firm and the market supply curve. The market supply curve shows the total quantity supplied by all firms, so it is the sum of the quantities supplied by all suppliers at each potential price (that is, the individual firms' supply curves are added horizontally).

Economists distinguish between short-run and long-run supply curve.Short run refers to a time period during which one or more inputs are fixed (typicallyphysical capital), and the number of firms in the industry is also fixed (if it is a market supply curve).Long run refers to a time period during which new firms enter or existing firms exit and all inputs can be adjusted fully to any price change. Long-run supply curves are flatter than short-run counterparts (with quantity more sensitive to price, more elastic supply).

Common determinants of supply are:

  1. Prices of inputs, including wages
  2. The technology used,productivity
  3. Firms' expectations about future prices
  4. Number of suppliers (for a market supply curve)

Demand schedule

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Main article:Price elasticity of demand

A demand schedule, depicted graphically as ademand curve, represents the amount of a certaingood that buyers are willing and able to purchase at various prices, assuming all other determinants of demand are held constant, such as income, tastes and preferences, and the prices ofsubstitute andcomplementary goods. Generally, consumers will buy an additional unit as long as the marginal value of the extra unit is more than the market price they pay. According to thelaw of demand, the demand curve is always downward-sloping, meaning that as the price decreases, consumers will buy more of the good.

Mathematically, a demand curve is represented by a demand function, giving the quantity demanded as a function of its price and as many other variables as desired to better explain quantity demanded. The two most common specifications are linear demand, e.g., the slanted line

Q(P)=322P{\displaystyle Q(P)=32-2P}

and the constant-elasticity demand function (also calledisoelastic or log-log or loglinear demand function), e.g., the smooth curve

Q(P)=3P2{\displaystyle Q(P)=3P^{-2}}

which can be rewritten as

logQ(P)=log32logP{\displaystyle \log Q(P)=\log 3-2\log P}

As a matter of historical convention, a demand curve is drawn with price on the verticaly-axis and demand on the horizontalx-axis. In keeping with modern convention, a demand curve would instead be drawn with price on thex-axis and demand on they-axis, because price is the independent variable and demand is the variable that is dependent upon price.

Just as the supply curve parallels themarginal cost curve, the demand curve parallelsmarginal utility, measured in dollars.[2] Consumers will be willing to buy a given quantity of a good, at a given price, if the marginal utility of additional consumption is equal to theopportunity cost determined by the price, that is, the marginal utility of alternative consumption choices. The demand schedule is defined as thewillingness andability of a consumer to purchase a given product at a certain time.

The demand curve is generally downward-sloping, but for some goods it is upward-sloping. Two such types of goods have been given definitions and names that are in common use:Veblen goods, goods which because of fashion orsignalling are more attractive at higher prices, andGiffen goods, which, by virtue of beinginferior goods that absorb a large part of a consumer's income (e.g.,staples such as the classic example of potatoes in Ireland), may see an increase in quantity demanded when the price rises. The reason the law of demand is violated for Giffen goods is that the rise in the price of the good has a strongincome effect, sharply reducing the purchasing power of the consumer so that he switches away from luxury goods to the Giffen good, e.g., when the price of potatoes rises, the Irish peasant can no longer afford meat and eats more potatoes to cover for the lost calories.

As with the supply curve, the concept of a demand curve requires that the purchaser be a perfect competitor—that is, that the purchaser have no influence over the market price. This is true because each point on the demand curve answers the question, "If buyers arefaced with this potential price, how much of the product will they purchase?" But, if a buyer has market power (that is, the amount he buys influences the price), he is not "faced with" any given price, and we must use a more complicated model, ofmonopsony.

As with supply curves, economists distinguish between the demand curve for an individual and the demand curve for a market. The market demand curve is obtained by adding the quantities from the individual demand curves at each price.

Common determinants of demand are:

  1. Income
  2. Tastes and preferences
  3. Prices of related goods and services
  4. Consumers' expectations about future prices and incomes
  5. Number of potential consumers
  6. Advertising

History of the curves

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Cournot'sRecherches (1838)
Jenkin'sGraphical Representation (1870)
Marshall'sPrinciples (1890)
Figure 2. Early supply and demand curves

Since supply and demand can be considered asfunctions of price they have a natural graphical representation. Demand curves were first drawn byAugustin Cournot in hisRecherches sur les Principes Mathématiques de la Théorie des Richesses (1838) – seeCournot competition. Supply curves were added byFleeming Jenkin inThe Graphical Representation of the Laws of Supply and Demand... of 1870.[3] Both sorts of curve were popularized byAlfred Marshall who, in hisPrinciples of Economics (1890), chose to represent price – normally the independent variable – by the vertical axis; a practice which remains common.[4]

If supply or demand is a function of other variables besides price, it may be represented by a family of curves (with a change in the other variables constituting a shift between curves) or by a surface in a higher dimensional space.[5]

Microeconomics

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Equilibrium

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Generally speaking, an equilibrium is defined to be the price-quantity pair where the quantity demanded is equal to the quantity supplied. It is represented by the intersection of the demand and supply curves. The analysis of various equilibria is a fundamental aspect ofmicroeconomics.

Market equilibrium

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A situation in a market when the price is such that the quantity demanded by consumers is correctly balanced by the quantity that firms wish to supply. In this situation, the market clears.[6]

Changes in market equilibrium

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Practical uses of supply and demand analysis often center on the different variables that change equilibrium price and quantity, represented as shifts in the respective curves.Comparative statics of such a shift traces the effects from the initial equilibrium to the new equilibrium.

Demand curve shifts

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Main article:Demand curve
Right-shift ofdemand curve increases both price and quantity.

When consumers increase the quantity demandedat a given price, it is referred to as anincrease in demand. Increased demand can be represented on the graph as the curve being shifted to the right. At each price point, a greater quantity is demanded, as from the initial curveD1 to the new curveD2. In the diagram, this raises the equilibrium price fromP1 to the higherP2. This raises the equilibrium quantity fromQ1 to the higherQ2. (A movement along the curve is described as a "change in the quantity demanded" to distinguish it from a "change in demand", that is, a shift of the curve.) Theincrease in demand has caused an increase in (equilibrium) quantity. The increase in demand could come from changing tastes and fashions, incomes, price changes in complementary and substitute goods, market expectations, and number of buyers. This would cause the entire demand curve to shift changing the equilibrium price and quantity. Note in the diagram that the shift of the demand curve, by causing a new equilibrium price to emerge, resulted inmovement along the supply curve from the point(Q1,P1) to the point(Q2,P2).

If thedemand decreases, then the opposite happens: a shift of the curve to the left. If the demand starts atD2, anddecreases toD1, the equilibrium price will decrease, and the equilibrium quantity will also decrease. The quantity supplied at each price is the same as before the demand shift, reflecting the fact that the supply curve has not shifted; but the equilibrium quantity and price are different as a result of the change (shift) in demand.

Supply curve shifts

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Main article:Supply (economics)
Right-shift ofsupply curve decreases price and increases quantity.

When technological progress occurs, the supply curve shifts. For example, assume that someone invents a better way of growing wheat so that the cost of growing a given quantity of wheat decreases. Otherwise stated, producers will be willing to supply more wheat at every price and this shifts the supply curveS1 outward, toS2—anincrease in supply. This increase in supply causes the equilibrium price to decrease fromP1 toP2. The equilibrium quantity increases fromQ1 toQ2 as consumers move along the demand curve to the new lower price. As a result of a supply curve shift, the price and the quantity move in opposite directions. If the quantity supplieddecreases, the opposite happens. If the supply curve starts atS2, and shifts leftward toS1, the equilibrium price will increase and the equilibrium quantity will decrease as consumers move along the demand curve to the new higher price and associated lower quantity demanded. The quantity demanded at each price is the same as before the supply shift, reflecting the fact that the demand curve has not shifted. But due to the change (shift) in supply, the equilibrium quantity and price have changed.

The movement of the supply curve in response to a change in a non-price determinant of supply is caused by a change in the y-intercept, the constant term of the supply equation. The supply curve shifts up and down the y axis as non-price determinants of demand change.

Partial equilibrium

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Main article:Partial equilibrium

Partial equilibrium, as the name suggests, takes into consideration only a part of the market to attain equilibrium.

Jain proposes (attributed toGeorge Stigler): "A partial equilibrium is one which is based on only a restricted range of data, a standard example is price of a single product, the prices of all other products being held fixed during the analysis."[7]

The supply-and-demand model is apartial equilibrium model ofeconomic equilibrium, where the clearance on themarket of some specificgoods is obtained independently from prices and quantities in other markets. In other words, the prices of allsubstitutes andcomplements, as well asincome levels ofconsumers are constant. This makes analysis much simpler than in ageneral equilibrium model which includes an entire economy.

Here the dynamic process is that prices adjust until supply equals demand. It is a powerfully simple technique that allows one to studyequilibrium,efficiency andcomparative statics. The stringency of the simplifying assumptions inherent in this approach makes the model considerably more tractable, but may produce results which, while seemingly precise, do not effectively model real world economicphenomena.

Partial equilibrium analysis examines the effects of policy action in creating equilibrium only in that particular sector or market which is directly affected, ignoring its effect in any other market or industry assuming that they being small will have little impact if any.

Hence this analysis is considered to be useful in constricted markets.

Léon Walras first formalized the idea of a one-period economic equilibrium of the general economic system, but it was French economistAntoine Augustin Cournot and English political economistAlfred Marshall who developed tractable models to analyze an economic system.

Other markets

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The model of supply and demand also applies to various specialty markets.The model is commonly applied towages in the market forlabor. The typical roles of supplier and demander are reversed. The suppliers are individuals, who try to sell their labor for the highest price. The demanders of labor are businesses, which try to buy the type of labor they need at the lowest price. The equilibrium price for a certain type of labor is the wage rate.[8] However, economist Steve Fleetwood revisited the empirical reality of supply and demand curves in labor markets and concluded that the evidence is "at best inconclusive and at worst casts doubt on their existence." For instance, he cites Kaufman and Hotchkiss (2006): "For adult men, nearly all studies find the labour supply curve to be negatively sloped or backward bending."[9] Supply and demand can be used to explainphysician shortages,[10]nursing shortages[11] orteacher shortages.[12]

In bothclassical andKeynesian economics, themoney market is analyzed as a supply-and-demand system withinterest rates being the price. Themoney supply may be a vertical supply curve, if thecentral bank of a country chooses to usemonetary policy to fix its value regardless of the interest rate; in this case the money supply is totally inelastic. On the other hand,[13] the money supply curve is a horizontal line if the central bank is targeting a fixed interest rate and ignoring the value of the money supply; in this case the money supply curve is perfectly elastic. The demand for money intersects with the money supply to determine the interest rate.[14]

According to some studies,[15] the laws of supply and demand are applicable not only to the business relationships of people, but to the behaviour of social animals and to all living things that interact on the biological markets[16] in scarce resource environments.

The model of supply and demand accurately describes the characteristic of metabolic systems: specifically, it explains howfeedback inhibition allows metabolic pathways to respond to the demand for a metabolic intermediates while minimizing effects due to variation in the supply.[17]

Empirical estimation

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Demand and supply relations in a market can be statistically estimated from price, quantity, and otherdata with sufficient information in the model. This can be done withsimultaneous-equation methods of estimation ineconometrics. Such methods allow solving for the model-relevant "structural coefficients," the estimated algebraic counterparts of the theory. TheParameter identification problem is a common issue in "structural estimation." Typically, data onexogenous variables (that is, variables other than price and quantity, both of which areendogenous variables) are needed to perform such an estimation. An alternative to "structural estimation" isreduced-form estimation, which regresses each of the endogenous variables on the respective exogenous variables.

Macroeconomic uses

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Human-hours worked per week in the United States.Labor is supply, money isdemand.

Demand and supply have also been generalized to explainmacroeconomic variables in amarket economy, including thequantity of total output and theaggregate price level. Theaggregate demand-aggregate supply model may be the most direct application of supply and demand to macroeconomics, but other macroeconomic models also use supply and demand. Compared tomicroeconomic uses of demand and supply, different (and more controversial) theoretical considerations apply to suchmacroeconomic counterparts asaggregate demand andaggregate supply. Demand and supply are also used in macroeconomic theory to relatemoney supply and money demand tointerest rates, and to relate labor supply and labor demand to wage rates.

History

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The 256th couplet ofTirukkural, which was composed at least 2000 years ago, says: "If the world desireth not meat for eating, there will be none to offer it for sale."[18] This statement can be restated to mean: "If people do not consume a product or service, then there will not be anybody to supply that product or service for the sake of price."[19]

According to Hamid S. Hosseini, the power of supply and demand was understood to some extent by several early Muslim scholars, such as fourteenth-century Syrian scholarIbn Taymiyyah, who wrote: "If desire for goods increases while its availability decreases, its price rises. On the other hand, if availability of the good increases and the desire for it decreases, the price comes down."[20]

If desire for goods increases while its availability decreases, its price rises. On the other hand, if availability of the good increases and the desire for it decreases, the price comes down.

— Ibn Taymiyyah,[20]

Shifting focus to the English etymology of the expression, it has been confirmed that the phrase 'supply and demand' was not used by English economics writers until after the end of the 17th century.[21] InJohn Locke's 1691 workSome Considerations on the Consequences of the Lowering of Interest and the Raising of the Value of Money,[22] Locke alluded to the idea of supply and demand, however, he failed to accurately label it as such and thus, he fell short in coining the phrase and conveying its true significance.[23] Locke wrote: “The price of any commodity rises or falls by the proportion of the number of buyer and sellers” and “that which regulates the price... [of goods] is nothing else but their quantity in proportion to [the] Vent.”[23] Locke's terminology drew criticism from John Law. Law argued that,"The Prices of Goods are not according to the quantity in proportion to the Vent, but in proportion to the Demand."[24] From Law the demand part of the phrase was given its proper title and it began to circulate among "prominent authorities" in the 1730s.[23] In 1755,Francis Hutcheson, in hisA System of Moral Philosophy, furthered development toward the phrase by stipulating that, "the prices of goods depend on these two jointly, the Demand... and the Difficulty of acquiring."[23]

Adam Smith

It was not until 1767 that the phrase "supply and demand" was first used by Scottish writerJames Denham-Steuart in hisInquiry into the Principles of Political Economy. He originated the use of this phrase by effectively combining "supply" and "demand" together in a number of different occasions such asprice determination andcompetitive analysis. In Steuart's chapter entitled "Of Demand", he argues that "The nature of Demand is to encourage industry; and when it is regularly made, the effect of it is, that the supply for the most part is found to be in proportion to it, and then the demand is simple". It is presumably from this chapter that the idea spread to other authors and economic thinkers.Adam Smith used the phrase after Steuart in his 1776 bookThe Wealth of Nations. InThe Wealth of Nations, Smith asserted that the supply price was fixed but that its "merit" (value) would decrease as its "scarcity" increased, this idea by Smith was later named the law of demand. In 1803, Thomas Robert Malthus used the phrase "supply and demand" twenty times in the second edition of theEssay on Population.[23] AndDavid Ricardo in his 1817 work,Principles of Political Economy and Taxation, titled one chapter, "On the Influence of Demand and Supply on Price".[25] InPrinciples of Political Economy and Taxation, Ricardo more rigorously laid down the idea of the assumptions that were used to build his ideas of supply and demand. In 1838,Antoine Augustin Cournot developed a mathematical model of supply and demand in hisResearches into the Mathematical Principles of Wealth, it included diagrams. It is important to note that the use of the phrase was still rare and only a few examples of more than 20 uses in a single work have been identified by the end of the second decade of the 19th century.[23]

English economistAlfred Marshall pictured c. the release ofPrinciples of Economics (1890)

During the late 19th century the marginalist school of thought emerged. The main innovators of this approach wereStanley Jevons,Carl Menger, andLéon Walras. The key idea was that the price was set by the subjective value of a good at the margin. This was a substantial change from Adam Smith's thoughts on determining the supply price.

In his 1870 essay "On the Graphical Representation of Supply and Demand",Fleeming Jenkin in the course of "introduc[ing] the diagrammatic method into the English economic literature" published the first drawing of supply and demand curves in English,[26] includingcomparative statics from a shift of supply or demand and application to the labor market.[27] The model was further developed and popularized byAlfred Marshall in the 1890 textbookPrinciples of Economics.[25]

Criticism

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Piero Sraffa's critique focused on the inconsistency (except in implausible circumstances) of partial equilibrium analysis and the rationale for the upward slope of the supply curve in a market for a produced consumption good.[28] The notability of Sraffa's critique is also demonstrated byPaul Samuelson's comments and engagements with it over many years, for example:

What a cleaned-up version of Sraffa (1926) establishes is hownearly empty areall of Marshall's partial equilibrium boxes. To a logical purist of Wittgenstein and Sraffa class, theMarshallian partial equilibrium box ofconstant cost is even more empty than the box ofincreasing cost.[29]

ModernPost-Keynesians criticize the supply and demand model for failing to explain the prevalence ofadministered prices, in which retail prices are set by firms, primarily based on a mark-up over normal average unit costs, and are not responsive to changes in demand up to capacity.[30]

See also

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References

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  1. ^Theelasticity coefficient, or often justelasticity, is an important parameter inmetabolic control analysis, used to express the local response of an enzyme or other chemical reaction to changes in its environment.
  2. ^"Marginal Utility and Demand". Retrieved2007-02-09.
  3. ^A.D. Brownlie and M. F. Lloyd Prichard, 1963. "Professor Fleeming Jenkin, 1833–1885 Pioneer in Engineering and Political Economy",Oxford Economic Papers, NS, 15(3), p. 211.
  4. ^Schumpeter, Joseph (2003).Ten Great Economists. Simon Publications. p. 271.ISBN 1932512098.
  5. ^"Shifts in Demand and Supply for Goods and Services | OpenStax Macroeconomics 2e".courses.lumenlearning.com. Retrieved2025-09-04.
  6. ^Mankiw, N.G.; Taylor, M.P. (2011).Economics (2nd ed., revised ed.). Andover: Cengage Learning.
  7. ^Jain, T.R. (2006–2007).Microeconomics and Basic Mathematics. New Delhi: VK Publications. p. 28.ISBN 978-81-87140-89-4.[permanent dead link]
  8. ^Kibbe, Matthew B."The Minimum Wage: Washington's Perennial Myth".Cato Institute. Retrieved2007-02-09.
  9. ^Fleetwood, Steve (August 2014)."Do labour supply and demand curves exist?".Cambridge Journal of Economics.38 (5):1087–113.doi:10.1093/cje/beu003.
  10. ^Cole, A. (9 July 2008). "BMA meeting: Doctors vote to limit number of medical students".BMJ.337 (jul09 1): a748.doi:10.1136/bmj.a748.ISSN 0959-8138.
  11. ^Ariste, Ruolz; Béjaoui, Ali; Dauphin, Anyck (October 10, 2019). "Critical analysis of nurses' labour market effectiveness in Canada: The hidden aspects of the shortage".The International Journal of Health Planning and Management.34 (4):1144–1154.doi:10.1002/hpm.2772.ISSN 1099-1751.PMID 30945352.S2CID 92997538.
  12. ^Sutcher, Leib; Darling-Hammond, Linda; Carver-Thomas, Desiree (September 2016).A Coming Crisis in Teaching? Teacher Supply, Demand, and Shortages in the U.S. (Report). Learning Policy Institute. Retrieved20 July 2024.[page needed]
  13. ^Basij J. Moore,Horizontalists and Verticalists: The Macroeconomics of Credit Money, Cambridge University Press, 1988
  14. ^Ritter, Lawrence S.;Silber, William L.; Udell, Gregory F. (2000).Principles of Money, Banking, and Financial Markets (10th ed.). Addison-Wesley, Menlo Park C. pp. 431–38,465–76.ISBN 978-0-321-37557-5.
  15. ^Velev, Milen V. Entropy and free-energy based interpretation of the laws of supply and demand. SN Bus Econ 1, 1 (2021).https://doi.org/10.1007/s43546-020-00009-6
  16. ^Noë, R., Hammerstein, P. Biological markets: supply and demand determine the effect of partner choice in cooperation, mutualism and mating. Behav Ecol Sociobiol 35, 1–11 (1994).https://doi.org/10.1007/BF00167053
  17. ^Hofmeyr, J.-H.S.; Cornish-Bowden, A. (2000). "Regulating the cellular economy of supply and demand".FEBS Lett.476 (1):47–51.doi:10.1111/j.1432-1033.1991.tb21071.x.PMID 1879427.
  18. ^Thiruvalluvar (1916)."26. Abjuring of Flesh-Meat".The Kural. Translated by Aiyar, V. V. S. Retrieved2025-10-08.
  19. ^Chendroyaperumal, Chendrayan (2010-01-29)."The First Laws in Economics and Indian Economic Thought – Thirukkural". Retrieved2025-10-08.
  20. ^abHosseini, Hamid S. (2003). "Contributions of Medieval Muslim Scholars to the History of Economics and their Impact: A Refutation of the Schumpeterian Great Gap". In Biddle, Jeff E.; Davis, Jon B.; Samuels, Warren J. (eds.).A Companion to the History of Economic Thought. Malden, MA: Blackwell. pp. 28–45 [28 & 38].doi:10.1002/9780470999059.ch3.ISBN 978-0-631-22573-7. (citing Hamid S. Hosseini, 1995. "Understanding the Market Mechanism Before Adam Smith: Economic Thought in Medieval Islam,"History of Political Economy, Vol. 27, No. 3, 539–61).
  21. ^Thweatt, W.O. (1983). "Origins of the terminology, supply and demand".Scottish Journal of Political Economy.30 (3):287–294.doi:10.1111/j.1467-9485.1983.tb01020.x.
  22. ^John Locke (1691)Some Considerations on the consequences of the Lowering of Interest and the Raising of the Value of Money
  23. ^abcdefGroenewegen P. (2008) ‘Supply and Demand’. In: Palgrave Macmillan (eds) The New Palgrave Dictionary of Economics. Palgrave Macmillan, London
  24. ^Law, J. (1705).Money and Trade Considered with a Proposal for Supplying the Nation with Money. Edinburgh: Anderson.
  25. ^abHumphrey, Thomas M. (1992)."Marshallian Cross Diagrams and their Uses before Alfred Marshall"(PDF).Economic Review (Mar/Apr):3–23. Retrieved2019-07-27.
  26. ^A.D. Brownlie and M. F. Lloyd Prichard, 1963. "Professor Fleeming Jenkin, 1833–1885 Pioneer in Engineering and Political Economy,"Oxford Economic Papers, NS, 15(3), p. 211.
  27. ^Fleeming Jenkin, 1870. "The Graphical Representation of the Laws of Supply and Demand, and their Application to Labour," in Alexander Grant, ed., (Scroll to chapter)Recess Studies, ch. VI, pp. 151–85. Edinburgh: Edmonston and Douglas
  28. ^Avi J. Cohen, "'The Laws of Returns Under Competitive Conditions': Progress in Microeconomics Since Sraffa (1926)?",Eastern Economic Journal, V. 9, N. 3 (Jul.-Sep.): 1983)
  29. ^Paul A. Samuelson, "Reply" inCritical Essays on Piero Sraffa's Legacy in Economics (edited by H. D. Kurz) Cambridge University Press, 2000
  30. ^Lee, F. S. (1999). Post Keynesian price theory. Cambridge University Press.

Further reading

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External links

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