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The production function explains the relationship between the inputs and quantities of output. It is one of the key concept of neoclassical theories that is used to determine marginal output which allows us to use our resources more effeciently.

It states that, other factors remaining constant, if more resources such as capital, land, labor etc are introduced, after acheiving optimal output, marginal output will start diminishing. However, marginal output may increase if there are techinical improvements in the process.

This function helps us in effecient allocation of resources.

 Let us apply this function on the actual data of  of Pakistan. The production function is calculated on the ndustrial labor and industrial output in terms of value addition.
 

As you can see there are many occasions when marginal output decreased. That was the time when although labor was added, but that did not add enough output.

YearOutputLabor_PercentLabor_Total
199110289013464.9429019.7999931842658.00000
199210820483848.1871019.3999932679165.00000
199311373613642.6828018.7999933243847.00000
199411299610067.1163017.3999934423342.00000
199512929596230.4005018.7000034623002.00000
199613926871225.7417018.7000036057138.00000
199713458920927.1234019.3999937577329.00000
199813715204147.2824017.5000038653989.00000
199913919220407.9271017.3999940043375.00000
200016059241362.6480018.0000041617498.00000
200116184524218.4816017.8999942713495.00000
200216066076648.2624021.2000043991117.00000
200318506300153.6623021.1000045816310.00000
200424613270800.7643020.6000047704359.00000
200527954044637.9234020.5000050083414.00000
200627000481149.9484020.7000052552027.00000
200730448443287.7815020.8999953655090.00000
200836970493952.4993020.0000054888164.00000
200932271030073.2627019.0000056949646.00000
201034983717514.0838019.1000056124889.00000
201143789238847.2915019.5000057507973.00000
201247791041668.7654019.8999959383085.00000
201346745310692.4475019.5000061333350.00000
201448933664082.4866019.6000062717054.00000
201551651857058.7754019.7000065423214.00000
201650899955818.7476019.7000068396210.00000
201754715290233.9427023.7350069957925.00000
2018 23.9009971517889.00000

YearTotalLaborTotalOutputMarginalOutput
19916304843.099734210289013464.942910289013464.94290
199212644597.841817721109497313.1310820483848.18710
199318894437.75343332483110955.812811373613642.68280
199424884095.819098843782721022.929111299610067.11630
199531358597.193098856712317253.329612929596230.40050
199638101281.999098870639188479.071313926871225.74170
199745391280.067365984098109406.194713458920927.12340
199852155728.142365997813313553.477113715204147.28240
199959123271.3880284111732533961.40413919220407.92710
200066614421.0280284127791775324.05216059241362.64800
200174260132.3616789143976299542.53416184524218.48160
200283586249.1656789160042376190.79616066076648.26240
200393253490.5756789178548676344.45818506300153.66230
2004103080588.529679203161947145.22324613270800.76430
2005113347688.399679231115991783.14627954044637.92340
2006124225957.988679258116472933.09527000481149.94840
2007135439866.43317288564916220.87630448443287.78150
2008146417499.23317325535410173.37536970493952.49930
2009157237931.97317357806440246.63832271030073.26270
2010167957785.77217392790157760.72234983717514.08380
2011179171840.50717436579396608.01343789238847.29150
2012190989068.483861484370438276.77947791041668.76540
2013202949071.733861531115748969.22646745310692.44750
2014215241614.317861580049413051.71348933664082.48660
2015228129987.475861631701270110.48851651857058.77540
2016241604040.845861682601225929.23650899955818.74760
2017258208554.344611737316516163.17954715290233.94270
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