Editing Minimum wage (section)

==Economic models==
{{See also|Labour economics}}

===Supply and demand model===
[[File:Wage labour 2.svg|thumb|Graph showing the basic [[supply and demand]] model of the minimum wage in the labor market]]
{{Main|Supply and demand}}

According to the supply and demand model of the labor market shown in many economics textbooks, increasing the minimum wage decreases the employment of minimum-wage workers.<ref name="Card&Krueger" /> One such textbook states:<ref name="Gwartney"/>
{{blockquote|
If a higher minimum wage increases the wage rates of unskilled workers above the level that would be established by market forces, the quantity of unskilled workers employed will fall. The minimum wage will price the services of the least productive (and therefore lowest-wage) workers out of the market. … the direct results of minimum wage legislation are clearly mixed. Some workers, most likely those whose previous wages were closest to the minimum, will enjoy higher wages. Others, particularly those with the lowest prelegislation wage rates, will be unable to find work. They will be pushed into the ranks of the unemployed.}}

A firm's cost is an increasing function of the wage rate. The higher the wage rate, the fewer hours an employer will demand of employees. This is because, as the wage rate rises, it becomes more expensive for firms to hire workers and so firms hire fewer workers (or hire them for fewer hours). The [[Labour demand|demand of labor]] curve is therefore shown as a line moving down and to the right.<ref name="Ehren">Ehrenberg, R. and Smith, R. "Modern labor economics: theory and public policy", HarperCollins, 1994, 5th ed.{{page needed|date=December 2013}}</ref> Since higher wages increase the quantity supplied, the [[Labour supply|supply of labor]] curve is upward sloping, and is shown as a line moving up and to the right.<ref name="Ehren"/> If no minimum wage is in place, wages will adjust until the quantity of labor demanded is equal to quantity supplied, reaching [[economic equilibrium|equilibrium]], where the supply and demand curves intersect. Minimum wage behaves as a classical [[price floor]] on labor. Standard theory says that, if set above the equilibrium price, more labor will be willing to be provided by workers than will be demanded by employers, creating a [[Economic surplus|surplus]] of labor, i.e. unemployment.<ref name="Ehren" /> The economic model of markets predicts the same of other commodities (like milk and wheat, for example): Artificially raising the price of the commodity tends to cause an increase in quantity supplied and a decrease in quantity demanded. The result is a surplus of the commodity. When there is a wheat surplus, the government buys it. Since the government does not hire surplus labor, the labor surplus takes the form of unemployment, which tends to be higher with minimum wage laws than without them.<ref name="SowellBasic"/>

The supply and demand model implies that by mandating a price floor above the equilibrium wage, minimum wage laws will cause unemployment.<ref name="MB">{{cite book |last1=McConnell |first1=C. R. |first2=S. L. |last2=Brue |title=Economics |url=https://archive.org/details/microeconomicsst00camp |url-access=registration |publisher=Irwin-McGraw Hill |year=1999 |edition=14th |page=594 |isbn=9780072898385 }}</ref><ref name="GSSM">{{cite book |last1=Gwartney |first1=J. D. |first2=R. L. |last2=Stroup |first3=R. S. |last3=Sobel |first4=D. A. |last4=Macpherson |title=Economics: Private and Public Choice |url=https://archive.org/details/economics00gwar |url-access=registration |publisher=Thomson South-Western |year=2003 |edition=10th |page=[https://archive.org/details/economics00gwar/page/97 97] }}</ref> This is because a greater number of people are willing to work at the higher wage while a smaller number of jobs will be available at the higher wage. Companies can be more selective in those whom they employ thus the least skilled and least experienced will typically be excluded. An imposition or increase of a minimum wage will generally only affect employment in the low-skill labor market, as the equilibrium wage is already at or below the minimum wage, whereas in higher skill labor markets the equilibrium wage is too high for a change in minimum wage to affect employment.<ref name="M">{{cite book |last=Mankiw |first=N. Gregory |title=Principles of Macroeconomics |publisher=South-Western Pub |year=2011 |edition=6th |page=311 }}</ref>

===Monopsony===
[[File:Monopsony3.png|thumb|Modern economics suggests that a moderate minimum wage may increase employment as labor markets are [[Monopsony|monopsonistic]] and workers [[Inequality of bargaining power|lack bargaining power]].]]
{{Main|Monopsony}}
The supply and demand model predicts that raising the minimum wage helps workers whose wages are raised, and hurts people who are not hired (or lose their jobs) when companies cut back on employment. But proponents of the minimum wage hold that the situation is much more complicated than the model can account for. One complicating factor is possible [[monopsony]] in the labor market, whereby the individual employer has some market power in determining wages paid. Thus it is at least theoretically possible that the minimum wage may boost employment. Though single employer market power is unlikely to exist in most labor markets in the sense of the traditional '[[company town]],' asymmetric information, imperfect mobility, and the personal element of the labor transaction give some degree of wage-setting power to most firms.<ref>{{cite journal |first1=William M. |last1=Boal |first2=Michael R |last2=Ransom |date=March 1997 |title=Monopsony in the Labor Market |journal=Journal of Economic Literature |volume=35 |issue=1 |pages=86–112 |jstor=2729694}}</ref>

Modern economic theory predicts that although an excessive minimum wage may raise unemployment as it fixes a price above most demand for labor, a minimum wage at a more reasonable level can increase employment, and enhance growth and efficiency. This is because labor markets are [[Monopsony|monopsonistic]] and workers persistently [[Inequality of bargaining power|lack bargaining power]]. When poorer workers have more to spend it stimulates [[effective aggregate demand]] for goods and services.<ref>e.g. DE Card and AB Krueger, ''Myth and Measurement: The New Economics of the Minimum Wage'' (1995) and S Machin and A Manning, 'Minimum wages and economic outcomes in Europe' (1997) 41 European Economic Review 733</ref><ref name=Rittenberg>{{cite book|last1=Tregarthen|first1=Timothy|last2=Rittenberg|first2=Libby|title=Economics|year=1999|publisher=Worth Publishers|location=New York|isbn=9781572594180|page=290|edition=2nd|url=https://books.google.com/books?id=HveHgrID5GYC&q=monopsony+minimum+wage&pg=PA290|access-date=21 June 2014}}</ref>

===Criticisms of the supply and demand model===
The argument that a minimum wage decreases employment is based on a simple supply and demand model of the labor market. A number of economists, such as [[Pierangelo Garegnani]],<ref>{{cite journal |first1=P. |last1=Garegnani |title=Heterogeneous Capital, the Production Function and the Theory of Distribution |journal=The Review of Economic Studies |volume=37 |issue=3 |date=July 1970 |pages=407–36 |jstor=2296729 |doi=10.2307/2296729}}</ref> Robert L. Vienneau,<ref>{{cite journal |doi=10.1111/j.1467-9957.2005.00467.x |title=On Labour Demand and Equilibria of the Firm |year=2005 |last1=Vienneau |first1=Robert L. |journal=The Manchester School |volume=73 |issue=5 |pages=612–19|s2cid=153778021 }}</ref> and Arrigo Opocher and [[Ian Steedman]],<ref>{{cite journal |doi=10.1093/cje/bep005 |title=Input price-input quantity relations and the numeraire |year=2009 |last1=Opocher |first1=A. |last2=Steedman |first2=I. |journal=Cambridge Journal of Economics |volume=33 |issue=5 |pages=937–48}}</ref> building on the work of [[Piero Sraffa]], argue that that model, even given all its assumptions, is logically incoherent. Michael Anyadike-Danes and [[Wynne Godley]] argue, based on simulation results, that little of the empirical work done with the textbook model constitutes a potentially [[Falsifiability|falsifiable theory]], and consequently empirical evidence hardly exists for that model.<ref>{{cite journal |doi=10.1111/j.1467-9957.1989.tb00809.x |title=Real Wages and Employment: A Sceptical View of Some Recent Empirical Work |year=1989 |last1=Anyadike-Danes |first1=Michael |last2=Godley |first2=Wynne |journal=The Manchester School |volume=57 |issue=2 |pages=172–87}}</ref> Graham White argues, partially on the basis of Sraffianism, that the policy of increased [[labor market flexibility]], including the reduction of minimum wages, does not have an "intellectually coherent" argument in economic theory.<ref>{{cite journal |first1=Graham |last1=White |title=The Poverty of Conventional Economic Wisdom and the Search for Alternative Economic and Social Policies |journal=The Drawing Board: An Australian Review of Public Affairs |volume=2 |issue=2 |date=November 2001 |pages=67–87 |url=http://www.australianreview.net/journal/v2/n2/white.html |url-status=live |archive-url=https://web.archive.org/web/20130524091537/http://www.australianreview.net/journal/v2/n2/white.html |archive-date=24 May 2013 }}</ref>

Gary Fields, Professor of Labor Economics and Economics at [[Cornell University]], argues that the standard textbook model for the minimum wage is ambiguous, and that the standard theoretical arguments incorrectly measure only a one-sector market. Fields says a two-sector market, where "the self-employed, service workers, and farm workers are typically excluded from minimum-wage coverage ... [and with] one sector with minimum-wage coverage and the other without it [and possible mobility between the two]," is the basis for better analysis. Through this model, Fields shows the typical theoretical argument to be ambiguous and says "the predictions derived from the textbook model definitely do not carry over to the two-sector case. Therefore, since a non-covered sector exists nearly everywhere, the predictions of the textbook model simply cannot be relied on."<ref>{{cite journal |doi=10.1108/01437729410059323 |title=The Unemployment Effects of Minimum Wages |year=1994 |last1=Fields |first1=Gary S. |journal=International Journal of Manpower |volume=15 |issue=2 |pages=74–81|url=https://digitalcommons.ilr.cornell.edu/articles/1118 |hdl=1813/75106 |hdl-access=free }}</ref>

An alternate view of the labor market has low-wage labor markets characterized as [[monopsonistic competition]] wherein buyers (employers) have significantly more [[market power]] than do sellers (workers). This monopsony could be a result of intentional [[collusion]] between employers, or naturalistic factors such as [[Labor market segmentation|segmented markets]], [[search cost]]s, [[Information asymmetry|information costs]], [[Geographic mobility|imperfect mobility]] and the personal element of labor markets.{{citation needed|date=October 2016}} Such a case is a type of [[market failure]] and results in workers being paid less than their marginal value. Under the monopsonistic assumption, an appropriately set minimum wage could increase both [[wages]] and employment, with the optimal level being equal to the [[marginal product of labour|marginal product of labor]].<ref name="Manning2003">{{cite book |title=Monopsony in motion: Imperfect Competition in Labor Markets |last=Manning |first=Alan |year=2003 |publisher=Princeton University Press |location=Princeton, NJ |isbn=978-0-691-11312-8 }}{{page needed|date=December 2013}}</ref> This view emphasizes the role of minimum wages as a [[regulated market|market regulation]] policy akin to [[antitrust]] policies, as opposed to an illusory "[[free lunch]]" for low-wage workers.

Another reason minimum wage may not affect employment in certain industries is that the demand for the product the employees produce is highly [[Price elasticity of demand|inelastic]].<ref>{{cite book |author=Gillespie, Andrew|title=Foundations of Economics|page=240|publisher=Oxford University Press|year=2007}}</ref> For example, if management is forced to increase wages, management can pass on the increase in wage to consumers in the form of higher prices. Since demand for the product is highly inelastic, consumers continue to buy the product at the higher price and so the manager is not forced to lay off workers. Economist [[Paul Krugman]] argues this explanation neglects to explain why the firm was not charging this higher price absent the minimum wage.<ref>{{cite book |last=Krugman |first=Paul|title=Economics|page=385|publisher=Worth Publishers|year=2013}}</ref>

Three other possible reasons minimum wages do not affect employment were suggested by [[Alan Blinder]]: higher wages may reduce [[turnover (employment)|turnover]], and hence training costs; raising the minimum wage may "render moot" the potential problem of recruiting workers at a higher wage than current workers; and minimum wage workers might represent such a small proportion of a business' cost that the increase is too small to matter. He admits that he does not know if these are correct, but argues that "the list demonstrates that one can accept the new empirical findings and still be a card-carrying economist."<ref>{{cite news |first=Alan S. |last=Blinder |title=The $5.15 Question |work=The New York Times |date=23 May 1996 |page=A29 |url=https://www.nytimes.com/1996/05/23/opinion/the-5.15-question.html |url-status=live |archive-url=https://web.archive.org/web/20170701015950/http://www.nytimes.com/1996/05/23/opinion/the-5.15-question.html |archive-date=1 July 2017 }}</ref>

=== Mathematical models of the minimum wage and frictional labor markets ===
The following mathematical models are more quantitative in orientation, and highlight some of the difficulties in determining the impact of the minimum wage on labor market outcomes.<ref>{{Cite book|url=https://mitpress.mit.edu/books/labor-economics-second-edition|title=Labor Economics|last1=Cahuc|first1=Pierre|last2=Carcillo|first2=Stéphane|last3=Zylberberg|first3=André|publisher=The MIT Press|year=2014|isbn=9780262027700|edition=2nd|location=Cambridge, MA|pages=796–799}}</ref> Specifically, these models focus on labor markets with frictions and may result in positive or negative outcomes from raising the minimum wage, depending on the circumstances.

==== Welfare and labor market participation ====
{{technical|section|date=September 2022}}
Assume that the decision to participate in the labor market results from a trade-off between being an unemployed job seeker and not participating at all.&nbsp;All individuals whose expected utility outside the labor market is less than the expected utility of an unemployed person <math>V_{u}</math> decide to participate in the labor market.&nbsp;In the basic search and [[Matching theory (economics)|matching model]], the expected utility of unemployed persons <math>V_{u}</math> and that of employed persons <math>V_{e}</math> are defined by:

<math display="block">\begin{aligned}
rV_{e} &= w + q(V_{u}-V_{e}) \\
rV_{u} &= z + \theta m(\theta) (V_{e}-V_{u})
\end{aligned}</math>Let <math>w</math> be the wage, <math>r</math> the interest rate, <math>z</math> the instantaneous income of unemployed persons, <math>q</math> the exogenous job destruction rate, <math>\theta</math> the labor market tightness, and <math>\theta m(\theta)</math> the job finding rate.&nbsp;The profits <math>\Pi_{e}</math> and <math>\Pi_{v}</math> expected from a filled job and a vacant one are:<math display="block">r\Pi_{e} = y-w+q(\Pi_{v}-\Pi_{e}), \quad r\Pi_{v} = -h + m(\theta)(\Pi_{e}-\Pi_{v})</math>where <math>h</math> is the cost of a vacant job and <math>y</math> is the productivity.&nbsp;When the ''free entry condition'' <math>\Pi_{v} = 0</math> is satisfied, these two equalities yield the following relationship between the wage <math>w</math> and labor market tightness <math>\theta</math>:
{{Labor|expanded=rights|sp=us}}
<math display="block">{h\over{m(\theta)}} = {y-w\over{r+q}}</math>If <math>w</math> represents a minimum wage that applies to all workers, this equation completely determines the equilibrium value of the labor market tightness <math>\theta</math>.&nbsp;There are two conditions associated with the matching function:<math display="block">m'(\theta) < 0, \quad [\theta m(\theta)]' > 0</math>This implies that <math>\theta</math> is a decreasing function of the minimum wage <math>w</math>, and so is the job finding rate <math>\alpha = \theta m(\theta)</math>.&nbsp;A hike in the minimum wage degrades the profitability of a job, so firms post fewer vacancies and the job finding rate falls off.&nbsp;Now let's rewrite <math>rV_{u}</math> to be:<math display="block">rV_{u} = {(r+q)z + \theta m(\theta) w\over{r+q + \theta m(\theta)}}</math>Using the relationship between the wage and labor market tightness to eliminate the wage from the last equation gives us:
<math display="block">rV_{u} = {\theta m(\theta)y + (r+q)z - \theta(r+q)h\over{r+q + \theta m(\theta)}}</math> By maximizing <math>rV_{u}</math> in this equation, with respect to the labor market tightness, it follows that:<math display="block">{[1-\eta(\theta)](y-z)\over{r+q+\eta(\theta)\theta m(\theta)}} = {h\over{m(\theta)}}</math>where <math>\eta(\theta)</math> is the [[Elasticity (economics)|elasticity]] of the matching function:<math display="block">\eta(\theta) = -\theta{m'(\theta)\over{m(\theta)}} \equiv -\theta {d\over{d\theta}}\log m(\theta)</math>This result shows that the expected utility of unemployed workers is maximized when the minimum wage is set at a level that corresponds to the wage level of the decentralized economy in which the bargaining power parameter is equal to the elasticity <math>\eta(\theta)</math>.&nbsp; The level of the negotiated wage is <math>w^{*}</math>.

If <math>w < w^{*}</math>, then an increase in the minimum wage increases participation ''and'' the unemployment rate, with an ambiguous impact on employment.&nbsp;When the bargaining power of workers is less than <math>\eta(\theta)</math>, an increase in the minimum wage improves the welfare of the unemployed – this suggests that minimum wage hikes can improve labor market efficiency, at least up to the point when bargaining power equals <math>\eta(\theta)</math>.&nbsp;On the other hand, if <math>w \geq w^{*}</math>, any increases in the minimum wage entails a decline in labor market participation and an increase in unemployment.{{disputed-inline|Math in the Welfare and labor market participation section|date=April 2025}}

==== Job search effort ====
{{technical|section|date=September 2022}}
In the model just presented, the minimum wage always increases unemployment.&nbsp;This result does not necessarily hold when the search effort of workers is [[Endogeneity (econometrics)|endogenous]].

Consider a model where the intensity of the job search is designated by the scalar <math>\epsilon</math>, which can be interpreted as the amount of time and/or intensity of the effort devoted to search.&nbsp;Assume that the arrival rate of job offers is <math>\alpha\epsilon</math> and that the wage distribution is degenerated to a single wage <math>w</math>.&nbsp;Denote <math>\varphi(\epsilon)</math> to be the cost arising from the search effort, with <math>\varphi' > 0, \; \varphi'' > 0</math>.&nbsp;Then the discounted utilities are given by:<math display="block">\begin{aligned}
rV_{e} &= w + q(V_{u}-V_{e}) \\
rV_{u} &= \max_{\epsilon} \; z - \varphi(\epsilon) + \alpha \epsilon(V_{e}-V_{u})
\end{aligned}</math>Therefore, the optimal search effort is such that the marginal cost of performing the search is equation to the marginal return:<math display="block">\varphi'(\epsilon) = \alpha(V_{e}-V_{u})</math>This implies that the optimal search effort increases as the difference between the expected utility of the job holder and the expected utility of the job seeker grows.&nbsp;In fact, this difference actually grows with the wage.&nbsp;To see this, take the difference of the two discounted utilities to find:<math display="block">(r+q)(V_{e}-V_{u}) = w-\max_{\epsilon}\left[z - \varphi(\epsilon) + \alpha \epsilon(V_{e}-V_{u}) \right]</math>Then differentiating with respect to <math>w</math> and rearranging gives us:<math display="block">{d\over{dw}}(V_{e}-V_{u}) = {1\over{r+q+\alpha\epsilon^{*}}} > 0</math>where <math>\epsilon^{*}</math> is the optimal search effort.&nbsp;This implies that a wage increase drives up job search effort and, therefore, the job finding rate.&nbsp;Additionally, the unemployment rate <math>u</math> at equilibrium is given by:<math display="block">u = {q\over{q+\alpha\epsilon}}</math>A hike in the wage, which increases the search effort and the job finding rate, decreases the unemployment rate.&nbsp;So it is possible that a hike in the minimum wage ''may'', by boosting the search effort of job seekers, boost employment.&nbsp;Taken in sum with the previous section, the minimum wage in labor markets with frictions can improve employment and decrease the unemployment rate when it is sufficiently low.&nbsp;However, a high minimum wage is detrimental to employment and increases the unemployment rate.