{"id":4890,"date":"2023-10-13T12:32:27","date_gmt":"2023-10-13T09:32:27","guid":{"rendered":"https:\/\/datakapital.com\/blog\/?p=4890"},"modified":"2025-08-18T17:40:04","modified_gmt":"2025-08-18T14:40:04","slug":"solow-modeli","status":"publish","type":"post","link":"https:\/\/datakapital.com\/blog\/solow-modeli\/","title":{"rendered":"Solow Modeli"},"content":{"rendered":"

Solow modeli temel yap\u0131s\u0131n\u0131 a\u00e7\u0131klarken, n\u00fcfusun ve \u00fcretim teknolojisinin de\u011fi\u015fmedi\u011fi varsay\u0131lacakt\u0131r. Yani \u00e7\u0131kt\u0131 emek ve sermaye girdilerine ba\u011fl\u0131 olarak de\u011fi\u015fir;<\/p>\n

Y = F(K,L)<\/em><\/p>\n

 <\/p>\n

Solow b\u00fcy\u00fcme modelinde<\/a> tasarruf, sermaye birikimi ve b\u00fcy\u00fcme aras\u0131ndaki ili\u015fki incelenirken, her \u015feyden \u00f6nce sermayenin \u00e7\u0131kt\u0131 \u00fczerindeki etkileri hesaba kat\u0131l\u0131r. Bu ba\u011flamda toplam \u00fcretim fonksiyonunun azalan verimler kanununa tabi oldu\u011fu, sermayenin ve eme\u011fin marjinal \u00fcr\u00fcn\u00fcn\u00fcn giderek azald\u0131\u011f\u0131 ( emek miktar\u0131 sabit iken sermaye miktar\u0131 art\u0131nca her ilave birim sermayenin \u00e7\u0131kt\u0131da meydana getirece\u011fi art\u0131\u015f\u0131n giderek azald\u0131\u011f\u0131 veya tam tersine sermaye miktar\u0131 sabit iken emek miktar\u0131 art\u0131nca her ilave birim eme\u011fin \u00e7\u0131kt\u0131da meydana getirece\u011fi art\u0131\u015f\u0131n giderek azald\u0131\u011f\u0131 ) varsay\u0131l\u0131r.<\/p>\n

Ayr\u0131ca Solow b\u00fcy\u00fcme modelinde sermayenin \u00e7\u0131kt\u0131 \u00fczerindeki etkileri incelenirken, toplam \u00fcretim fonksiyonunun \u00f6l\u00e7e\u011fe g\u00f6re sabit getiriye tabi oldu\u011fu, \u00f6rne\u011fin sermaye ve emek girdilerinin miktar\u0131 2 kat artt\u0131\u011f\u0131nda \u00e7\u0131kt\u0131n\u0131n da 2 kat artt\u0131\u011f\u0131 kabul edilir;<\/p>\n

2Y = F ( 2K, 2L )<\/em><\/p>\n

xY = F ( xK, xL )<\/em><\/p>\n

Solow b\u00fcy\u00fcme modelinde<\/a> \u00f6l\u00e7e\u011fe g\u00f6re sabit getiri varsay\u0131m\u0131 alt\u0131nda girdilerin 1\/L oran\u0131nda artt\u0131\u011f\u0131 kabul edilmek \u00fczere, toplam \u00fcretim fonksiyonu a\u015fa\u011f\u0131daki gibi yaz\u0131l\u0131r;<\/p>\n

Y\/L = F ( K\/L,1 )<\/em><\/p>\n

Y\/L = F ( K,L )<\/em><\/p>\n

y = f (k)<\/em><\/p>\n

Bu denkleme g\u00f6re, i\u015f\u00e7i ba\u015f\u0131na \u00e7\u0131kt\u0131 ( y = Y\/L ) i\u015f\u00e7i ba\u015f\u0131na sermayeye ( k = K\/L ) ba\u011fl\u0131 olarak de\u011fi\u015fir. Bu durum a\u015fa\u011f\u0131daki grafikte g\u00f6sterilmi\u015ftir;<\/p>\n

\"Solow<\/p>\n

Grafikte \u00fcretim fonksiyonunu, i\u015f\u00e7i ba\u015f\u0131na sermaye artt\u0131k\u00e7a i\u015f\u00e7i ba\u015f\u0131na \u00e7\u0131kt\u0131n\u0131n da artt\u0131\u011f\u0131n\u0131, ancak azalan verimler kanunu nedeniyle sermayedeki art\u0131\u015f\u0131n \u00e7\u0131kt\u0131da giderek daha az bir art\u0131\u015fa yol a\u00e7t\u0131\u011f\u0131n\u0131 g\u00f6stermektedir.<\/p>\n

Solow b\u00fcy\u00fcme modelinde b\u00fcy\u00fcme, sermaye birikimi ve tasarruf aras\u0131ndaki ili\u015fki incelenir. Sermayenin \u00e7\u0131kt\u0131 \u00fczerindeki etkileri yan\u0131nda \u00e7\u0131kt\u0131n\u0131n sermaye birikim \u00fczerindeki etkileri de hesaba kat\u0131l\u0131r. Bu anlamda Solow modelinin hareket noktas\u0131, h\u00fck\u00fcmetin olmad\u0131\u011f\u0131 kapal\u0131 bir ekonomide \u00e7\u0131kt\u0131n\u0131n t\u00fcketim ve yat\u0131r\u0131m amac\u0131yla kullan\u0131ld\u0131\u011f\u0131 hususudur;<\/p>\n

Y = C + I<\/em><\/p>\n

Y\/L = C\/L +I\/L<\/em><\/p>\n

y = c+i<\/em><\/p>\n

olow b\u00fcy\u00fcme modelinde ki\u015filerin gelirlerinin s kadarl\u0131k bir b\u00f6l\u00fcm\u00fcn\u00fc tasarruf ettikleri geri kalan ( 1- s ) kadarl\u0131k bir b\u00f6l\u00fcm\u00fcn\u00fc de t\u00fcketim amac\u0131yla kulland\u0131klar\u0131 varsay\u0131ld\u0131\u011f\u0131ndan, C = (1-s)Y, i\u015f\u00e7i ba\u015f\u0131na t\u00fcketim fonksiyonu a\u015fa\u011f\u0131daki gibi ifade edilebilir;<\/p>\n

C\/L = (1-s) Y\/L<\/em><\/p>\n

c = (1-s)y<\/em><\/p>\n

y = (1-s)y+i<\/em><\/p>\n

i = sy<\/em><\/p>\n

Bu denkleme g\u00f6re, i\u015f\u00e7i ba\u015f\u0131na yat\u0131r\u0131m tasarruf haddi ile i\u015f\u00e7i ba\u015f\u0131na \u00e7\u0131kt\u0131n\u0131n \u00e7arp\u0131m\u0131ndan ibaret olan i\u015f\u00e7i ba\u015f\u0131na tasarrufa e\u015fittir, k\u0131saca tasarruf yat\u0131r\u0131ma e\u015fittir ( I = S ).<\/p>\n

Di\u011fer taraftan belirli bir d\u00f6nemde i\u015f\u00e7i ba\u015f\u0131na sermaye stokunda meydana gelen de\u011fi\u015fme, o d\u00f6nemde yap\u0131lan i\u015f\u00e7i ba\u015f\u0131na yat\u0131r\u0131m ile o d\u00f6nemde i\u015f\u00e7i ba\u015f\u0131na sermaye stokunda meydana gelen y\u0131pranma aras\u0131ndaki farka, k\u0131saca o d\u00f6nemdeki i\u015f\u00e7i ba\u015f\u0131na net yat\u0131r\u0131ma e\u015fittir;<\/p>\n

\u0394k = i dk<\/p>\n

\u0394k = sf(k) -dk<\/p>\n

Bu denkleme g\u00f6re i\u015f\u00e7i ba\u015f\u0131na sermaye d\u00fczeyi ( k ) ne kadar b\u00fcy\u00fck olursa, i\u015f\u00e7i ba\u015f\u0131na tasarruf – yat\u0131r\u0131m ve i\u015f\u00e7i ba\u015f\u0131na y\u0131pranma da o kadar b\u00fcy\u00fck olur.<\/p>\n

Solow modelinde e\u011fer ekonominin ba\u015flang\u0131\u00e7ta sahip oldu\u011fu i\u015f\u00e7i ba\u015f\u0131na sermaye d\u00fczeyi dura\u011fan durum sermaye d\u00fczeyinden k\u00fc\u00e7\u00fck ise (k < k*) , i\u015f\u00e7i ba\u015f\u0131na sermaye d\u00fczeyi artar ve ekonomi nihayet dura\u011fan duruma (k = k*) ) ula\u015f\u0131r. Buna kar\u015f\u0131l\u0131k bir ekonominin ba\u015flang\u0131\u00e7ta sahip oldu\u011fu i\u015f\u00e7i ba\u015f\u0131na sermaye d\u00fczeyi dura\u011fan durum sermaye d\u00fczeyinden b\u00fcy\u00fck ise (k > k*), i\u015f\u00e7i ba\u015f\u0131na sermaye d\u00fczeyinin giderek azalmas\u0131 sonucu ekonomi yine dura\u011fan duruma ula\u015f\u0131r.<\/p>\n

Solow b\u00fcy\u00fcme modeli, \u00f6zellikle uzun d\u00f6nemli ekonomik b\u00fcy\u00fcmenin kaynaklar\u0131n\u0131 anlamak a\u00e7\u0131s\u0131ndan modern iktisat literat\u00fcr\u00fcn\u00fcn en temel teorik \u00e7er\u00e7evelerinden biridir. Modelin en \u00f6nemli katk\u0131s\u0131, tasarruf oranlar\u0131, sermaye birikimi, y\u0131pranma (depreciation) ve \u00fcretim teknolojisi aras\u0131ndaki ili\u015fkiyi a\u00e7\u0131k ve sistematik bir bi\u00e7imde ortaya koymas\u0131d\u0131r. Keynesyen k\u0131sa d\u00f6nemli analizlerden farkl\u0131 olarak Solow modeli, ekonomilerin zaman i\u00e7inde nas\u0131l bir dengeye ula\u015ft\u0131klar\u0131n\u0131 ve b\u00fcy\u00fcme s\u00fcrecinde hangi unsurlar\u0131n kal\u0131c\u0131, hangilerinin ge\u00e7ici etkiler do\u011furdu\u011funu a\u00e7\u0131klamay\u0131 ama\u00e7lar.<\/p>\n

Modelde vurgulanan ilk kritik nokta, azalan verimler kanununun b\u00fcy\u00fcme s\u00fcrecine getirdi\u011fi s\u0131n\u0131rlard\u0131r. Sermaye birikimi ba\u015flang\u0131\u00e7ta \u00fcretim art\u0131\u015flar\u0131n\u0131 h\u0131zland\u0131r\u0131r, fakat belirli bir seviyeden sonra eklenen her yeni sermaye biriminin sa\u011flad\u0131\u011f\u0131 katk\u0131 giderek azal\u0131r. Bu nedenle s\u00fcrekli sermaye art\u0131\u015f\u0131 tek ba\u015f\u0131na ekonominin s\u0131n\u0131rs\u0131z b\u00fcy\u00fcmesini sa\u011flayamaz. Buradan \u00e7\u0131kan sonu\u00e7, uzun d\u00f6nemli b\u00fcy\u00fcmenin yaln\u0131zca tasarruf oranlar\u0131n\u0131n art\u0131r\u0131lmas\u0131 veya sermaye stokunun y\u00fckseltilmesi ile s\u00fcrd\u00fcr\u00fclemeyece\u011fidir. Bu yakla\u015f\u0131m, kalk\u0131nma politikalar\u0131nda tasarruf ve yat\u0131r\u0131m oranlar\u0131n\u0131 art\u0131rmaya y\u00f6nelik \u00e7abalar\u0131n \u00f6nemini kabul etmekle birlikte, tek ba\u015f\u0131na yeterli olmad\u0131\u011f\u0131n\u0131 ortaya koyar.<\/p>\n

\u0130kinci \u00f6nemli sonu\u00e7, dura\u011fan durum (steady state) kavram\u0131d\u0131r. Solow modelinde her ekonomi, i\u015f\u00e7i ba\u015f\u0131na sermaye d\u00fczeyinde belirli bir noktaya ula\u015ft\u0131\u011f\u0131nda net yat\u0131r\u0131m s\u0131f\u0131rlan\u0131r. Bu durumda sermaye stokundaki art\u0131\u015f ile y\u0131pranma birbirini dengeledi\u011fi i\u00e7in sermaye birikimi daha fazla b\u00fcy\u00fcme yaratmaz. Dura\u011fan durumda ki\u015fi ba\u015f\u0131na sermaye ve ki\u015fi ba\u015f\u0131na \u00e7\u0131kt\u0131 sabitlenir. Bununla birlikte, toplam \u00e7\u0131kt\u0131 n\u00fcfus art\u0131\u015f\u0131 kadar b\u00fcy\u00fcmeye devam edebilir. Dura\u011fan durum, ekonominin i\u00e7 dinamiklerinden kaynaklanan uzun d\u00f6nem denge b\u00fcy\u00fcme yolunu temsil eder ve farkl\u0131 \u00fclkelerin ki\u015fi ba\u015f\u0131na gelir seviyelerindeki farkl\u0131l\u0131klar\u0131 a\u00e7\u0131klamada kilit bir rol oynar.<\/p>\n

\u00dc\u00e7\u00fcnc\u00fc olarak, Solow modelinin en \u00e7arp\u0131c\u0131 y\u00f6nlerinden biri teknolojinin d\u0131\u015fsal kabul edilmesidir. Modelde teknolojik geli\u015fme olmad\u0131\u011f\u0131 varsay\u0131ld\u0131\u011f\u0131nda, ki\u015fi ba\u015f\u0131na gelir d\u00fczeyi dura\u011fan durumda sabit kal\u0131r. Oysa teknolojik geli\u015fme eklendi\u011finde, \u00fcretim fonksiyonu yukar\u0131 do\u011fru kayar ve ki\u015fi ba\u015f\u0131na \u00e7\u0131kt\u0131 s\u00fcrekli artar. B\u00f6ylece uzun d\u00f6nemli ekonomik b\u00fcy\u00fcmenin en temel kayna\u011f\u0131 olarak teknoloji \u00f6ne \u00e7\u0131kar. Bu sonu\u00e7, modern iktisadi b\u00fcy\u00fcme teorilerinin (\u00f6rne\u011fin i\u00e7sel b\u00fcy\u00fcme modellerinin) geli\u015fmesine zemin haz\u0131rlam\u0131\u015ft\u0131r.<\/p>\n

Solow modeli ayn\u0131 zamanda \u201cyak\u0131nsama hipotezi\u201d (convergence hypothesis) ile de bilinir. Bu hipoteze g\u00f6re benzer tasarruf oranlar\u0131na, n\u00fcfus art\u0131\u015f h\u0131z\u0131na ve teknolojik geli\u015fme oran\u0131na sahip \u00fclkeler, uzun vadede benzer ki\u015fi ba\u015f\u0131na gelir seviyelerine yak\u0131nsar. Bu, d\u00fc\u015f\u00fck sermaye stokuna sahip \u00fclkelerin daha h\u0131zl\u0131 b\u00fcy\u00fcme potansiyeline sahip oldu\u011fu anlam\u0131na gelir \u00e7\u00fcnk\u00fc azalan verimler kural\u0131 gere\u011fi sermayenin marjinal verimlili\u011fi bu \u00fclkelerde daha y\u00fcksektir. Ancak ampirik bulgular, bu yak\u0131nsaman\u0131n mutlak de\u011fil, ko\u015fullu oldu\u011funu g\u00f6stermektedir. Yani \u00fclkelerin ayn\u0131 yap\u0131sal \u00f6zelliklere sahip olmalar\u0131 durumunda yak\u0131nsama ger\u00e7ekle\u015fir. Aksi halde, kurumlar, e\u011fitim d\u00fczeyi, teknolojiye eri\u015fim gibi fakt\u00f6rler farkl\u0131l\u0131k g\u00f6sterdi\u011finde gelir farklar\u0131 kal\u0131c\u0131 hale gelir.<\/p>\n

Bir ba\u015fka \u00f6nemli nokta, Solow modelinin politika \u00f6nerileridir. Model, tasarruf oranlar\u0131n\u0131n art\u0131r\u0131lmas\u0131n\u0131n k\u0131sa ve orta vadede b\u00fcy\u00fcmeyi h\u0131zland\u0131rabilece\u011fini kabul eder. Ancak uzun vadede s\u00fcrd\u00fcr\u00fclebilir b\u00fcy\u00fcmenin yaln\u0131zca teknolojik yenilikler ve verimlilik art\u0131\u015flar\u0131 ile sa\u011flanabilece\u011fini g\u00f6sterir. Bu nedenle e\u011fitim, Ar-Ge yat\u0131r\u0131mlar\u0131, kurumsal yap\u0131lar\u0131n g\u00fc\u00e7lendirilmesi gibi unsurlar b\u00fcy\u00fcme politikalar\u0131nda \u00f6ncelikli hale gelir. B\u00f6ylece model, kalk\u0131nma iktisad\u0131 a\u00e7\u0131s\u0131ndan da yol g\u00f6sterici bir \u00e7er\u00e7eve sunar.<\/p>\n

Ayr\u0131ca Solow modeli, \u00fcretim fonksiyonunun \u00f6l\u00e7e\u011fe g\u00f6re sabit getiriler varsay\u0131m\u0131 alt\u0131nda kurguland\u0131\u011f\u0131 i\u00e7in sermaye ve emek aras\u0131ndaki da\u011f\u0131l\u0131m\u0131 da a\u00e7\u0131klamada kullan\u0131l\u0131r. Gelir da\u011f\u0131l\u0131m\u0131ndaki farkl\u0131l\u0131klar\u0131n uzun vadeli b\u00fcy\u00fcme \u00fczerindeki etkilerini analiz ederken, fakt\u00f6r gelir paylar\u0131n\u0131n nas\u0131l evrildi\u011fini ortaya koyar. Bu \u00f6zellik, gelir da\u011f\u0131l\u0131m\u0131 \u00e7al\u0131\u015fmalar\u0131na \u00f6nemli bir teorik temel sa\u011flam\u0131\u015ft\u0131r.<\/p>\n

Son olarak, Solow modelinin s\u0131n\u0131rl\u0131l\u0131klar\u0131 da dikkate al\u0131nmal\u0131d\u0131r. Modelde teknoloji d\u0131\u015fsal kabul edildi\u011fi i\u00e7in teknolojik ilerlemenin nedenlerini a\u00e7\u0131klamaz. Ayr\u0131ca finansal piyasalar, be\u015feri sermaye birikimi, kurumsal fakt\u00f6rler gibi b\u00fcy\u00fcme s\u00fcrecinde kritik \u00f6neme sahip unsurlar\u0131 d\u0131\u015far\u0131da b\u0131rak\u0131r. Bu nedenle sonraki y\u0131llarda Romer, Lucas gibi iktisat\u00e7\u0131lar i\u00e7sel b\u00fcy\u00fcme modellerini geli\u015ftirmi\u015f, teknolojik ilerlemenin ve bilgi birikiminin ekonominin i\u00e7 dinamikleri taraf\u0131ndan nas\u0131l \u00fcretildi\u011fini g\u00f6stermeye \u00e7al\u0131\u015fm\u0131\u015flard\u0131r. Buna ra\u011fmen, Solow modeli hem teorik a\u00e7\u0131dan hem de pratik politika analizlerinde h\u00e2l\u00e2 en \u00e7ok kullan\u0131lan \u00e7er\u00e7evelerden biridir.<\/p>\n","protected":false},"excerpt":{"rendered":"

Solow modeli temel yap\u0131s\u0131n\u0131 a\u00e7\u0131klarken, n\u00fcfusun ve \u00fcretim teknolojisinin de\u011fi\u015fmedi\u011fi varsay\u0131lacakt\u0131r. Yani \u00e7\u0131kt\u0131 emek ve sermaye girdilerine ba\u011fl\u0131 olarak de\u011fi\u015fir; Y = F(K,L)   Solow b\u00fcy\u00fcme modelinde tasarruf, sermaye birikimi ve b\u00fcy\u00fcme aras\u0131ndaki ili\u015fki incelenirken, her \u015feyden \u00f6nce sermayenin \u00e7\u0131kt\u0131 \u00fczerindeki etkileri hesaba kat\u0131l\u0131r. Bu ba\u011flamda toplam \u00fcretim fonksiyonunun azalan verimler kanununa tabi oldu\u011fu, sermayenin<\/p>\n","protected":false},"author":12,"featured_media":4891,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,47],"tags":[407,462,443,463],"class_list":{"0":"post-4890","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-jeoekonomik-makro-veriler","8":"category-makro-ekonomik-analizler","9":"tag-buyume","10":"tag-kapital","11":"tag-neoklasik-iktisat","12":"tag-solow"},"better_featured_image":{"id":4891,"alt_text":"Solow Modeli Grafi\u011fi","caption":"","description":"","media_type":"image","media_details":{"width":501,"height":291,"file":"2023\/10\/Solow-Modeli.jpg","filesize":9054,"sizes":{"medium":{"file":"Solow-Modeli-300x174.jpg","width":300,"height":174,"mime-type":"image\/jpeg","filesize":2284,"source_url":"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2023\/10\/Solow-Modeli-300x174.jpg"},"thumbnail":{"file":"Solow-Modeli-150x150.jpg","width":150,"height":150,"mime-type":"image\/jpeg","filesize":1209,"source_url":"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2023\/10\/Solow-Modeli-150x150.jpg"},"bunyad-small":{"file":"Solow-Modeli-150x87.jpg","width":150,"height":87,"mime-type":"image\/jpeg","filesize":918,"source_url":"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2023\/10\/Solow-Modeli-150x87.jpg"},"bunyad-medium":{"file":"Solow-Modeli-450x261.jpg","width":450,"height":261,"mime-type":"image\/jpeg","filesize":3796,"source_url":"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2023\/10\/Solow-Modeli-450x261.jpg"}},"image_meta":{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0","keywords":[]}},"post":4890,"source_url":"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2023\/10\/Solow-Modeli.jpg"},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/posts\/4890","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/comments?post=4890"}],"version-history":[{"count":3,"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/posts\/4890\/revisions"}],"predecessor-version":[{"id":5563,"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/posts\/4890\/revisions\/5563"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/media\/4891"}],"wp:attachment":[{"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/media?parent=4890"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/categories?post=4890"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/tags?post=4890"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}