عدم التحدب (اقتصاد) (Arabic Wikipedia)

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Green، Jerry؛ Heller، Walter P. (1981). "1 Mathematical analysis and convexity with applications to economics". في Arrow، Kenneth Joseph؛ Intriligator، Michael D (المحررون). Handbook of mathematical economics, Volume I. Handbooks in economics. Amsterdam: North-Holland Publishing Co. ج. 1. ص. 15–52. DOI:10.1016/S1573-4382(81)01005-9. ISBN:0-444-86126-2. MR:0634800.
Page 1: Guesnerie، Roger (1975). "Pareto optimality in non-convex economies". Econometrica. ج. 43. ص. 1–29. DOI:10.2307/1913410. JSTOR:1913410. MR:0443877. {{استشهاد بخبر}}: الوسيط |ref=harv غير صالح (مساعدة) ("Errata". Econometrica. ج. 43 رقم 5–6. 1975. ص. 1010. DOI:10.2307/1911353. JSTOR:1911353. MR:0443878. {{استشهاد بخبر}}: يحتوي الاستشهاد على وسيط غير معروف وفارغ: |1= (مساعدة))
Samuelson (1950, pp. 359–360):
It will be noted that any point where the indifference curves are convex rather than concave cannot be observed in a competitive market. Such points are shrouded in eternal darkness—unless we make our consumer a monopsonist and let him choose between goods lying on a very convex "budget curve" (along which he is affecting the price of what he buys). In this monopsony case, we could still deduce the slope of the man's indifference curve from the slope of the observed constraint at the equilibrium point.
Samuelson، Paul A. (1950). "The problem of integrability in utility theory". Economica. New Series. ج. 17. ص. 355–385. DOI:10.2307/2549499. JSTOR:2549499. MR:0043436. {{استشهاد بخبر}}: الوسيط |ref=harv غير صالح (مساعدة)For the نقش to their seventh chapter, "Markets with non-convex preferences and production" presenting Starr (1969), Arrow & Hahn (1971, p. 169) quote جون ميلتون's description of the (non-convex) Serbonian Bog in الفردوس المفقود (Book II, lines 592–594):
A gulf profound as that Serbonian Bog
Betwixt Damiata and Mount Casius old,
Where Armies whole have sunk.
Diewert (1982, pp. 552–553): Diewert، W. E. (1982). "12 Duality approaches to microeconomic theory". في Arrow، Kenneth Joseph؛ Intriligator، Michael D (المحررون). Handbook of mathematical economics, Volume II. Handbooks in economics. Amsterdam: North-Holland Publishing Co. ج. 1. ص. 535–599. DOI:10.1016/S1573-4382(82)02007-4. ISBN:978-0-444-86127-6. MR:0648778.
Aumann (1966, pp. 1–2): Aumann، Robert J. (يناير 1966). "Existence of competitive equilibrium in markets with a continuum of traders". Econometrica. ج. 34 ع. 1: 1–17. DOI:10.2307/1909854. JSTOR:1909854. MR:0191623. Aumann (1966) builds on two papers: Aumann (1964, 1965) Aumann، Robert J. (يناير–أبريل 1964). "Markets with a continuum of traders". Econometrica. ج. 32 ع. 1–2: 39–50. DOI:10.2307/1913732. JSTOR:1913732. MR:0172689. Aumann، Robert J. (أغسطس 1965). "Integrals of set-valued functions". Journal of Mathematical Analysis and Applications. ج. 12 ع. 1: 1–12. DOI:10.1016/0022-247X(65)90049-1. MR:0185073.

archive.org

Page 1: Guesnerie، Roger (1975). "Pareto optimality in non-convex economies". Econometrica. ج. 43. ص. 1–29. DOI:10.2307/1913410. JSTOR:1913410. MR:0443877. {{استشهاد بخبر}}: الوسيط |ref=harv غير صالح (مساعدة) ("Errata". Econometrica. ج. 43 رقم 5–6. 1975. ص. 1010. DOI:10.2307/1911353. JSTOR:1911353. MR:0443878. {{استشهاد بخبر}}: يحتوي الاستشهاد على وسيط غير معروف وفارغ: |1= (مساعدة))
Sraffa، Piero (1926). "The Laws of returns under competitive conditions". Economic Journal. ج. 36 رقم 144. ص. 535–550. JSTOR:2959866. {{استشهاد بخبر}}: الوسيط |ref=harv غير صالح (مساعدة)
Hotelling، Harold (يوليو 1938). "The General welfare in relation to problems of taxation and of railway and utility rates". Econometrica. ج. 6 ع. 3: 242–269. DOI:10.2307/1907054. JSTOR:1907054.
Pages 5–7: Quinzii، Martine (1992). Increasing returns and efficiency (ط. Revised translation of (1988) Rendements croissants et efficacité economique. Paris: Editions du Centre National de la Recherche Scientifique). New York: Oxford University Press. ص. viii+165. ISBN:0-19-506553-0.
Aumann (1966, pp. 1–2): Aumann، Robert J. (يناير 1966). "Existence of competitive equilibrium in markets with a continuum of traders". Econometrica. ج. 34 ع. 1: 1–17. DOI:10.2307/1909854. JSTOR:1909854. MR:0191623. Aumann (1966) builds on two papers: Aumann (1964, 1965) Aumann، Robert J. (يناير–أبريل 1964). "Markets with a continuum of traders". Econometrica. ج. 32 ع. 1–2: 39–50. DOI:10.2307/1913732. JSTOR:1913732. MR:0172689. Aumann، Robert J. (أغسطس 1965). "Integrals of set-valued functions". Journal of Mathematical Analysis and Applications. ج. 12 ع. 1: 1–12. DOI:10.1016/0022-247X(65)90049-1. MR:0185073.

doi.org

Mas-Colell، A. (1987). "Non-convexity" (PDF). في Eatwell، John؛ Milgate، Murray؛ Newman، Peter (المحررون). The New Palgrave: A Dictionary of Economics (ط. first). Palgrave Macmillan. ص. 653–661. DOI:10.1057/9780230226203.3173. ISBN:9780333786765.
Green، Jerry؛ Heller، Walter P. (1981). "1 Mathematical analysis and convexity with applications to economics". في Arrow، Kenneth Joseph؛ Intriligator، Michael D (المحررون). Handbook of mathematical economics, Volume I. Handbooks in economics. Amsterdam: North-Holland Publishing Co. ج. 1. ص. 15–52. DOI:10.1016/S1573-4382(81)01005-9. ISBN:0-444-86126-2. MR:0634800.
Page 1: Guesnerie، Roger (1975). "Pareto optimality in non-convex economies". Econometrica. ج. 43. ص. 1–29. DOI:10.2307/1913410. JSTOR:1913410. MR:0443877. {{استشهاد بخبر}}: الوسيط |ref=harv غير صالح (مساعدة) ("Errata". Econometrica. ج. 43 رقم 5–6. 1975. ص. 1010. DOI:10.2307/1911353. JSTOR:1911353. MR:0443878. {{استشهاد بخبر}}: يحتوي الاستشهاد على وسيط غير معروف وفارغ: |1= (مساعدة))
Hotelling، Harold (يوليو 1938). "The General welfare in relation to problems of taxation and of railway and utility rates". Econometrica. ج. 6 ع. 3: 242–269. DOI:10.2307/1907054. JSTOR:1907054.
Samuelson (1950, pp. 359–360):
It will be noted that any point where the indifference curves are convex rather than concave cannot be observed in a competitive market. Such points are shrouded in eternal darkness—unless we make our consumer a monopsonist and let him choose between goods lying on a very convex "budget curve" (along which he is affecting the price of what he buys). In this monopsony case, we could still deduce the slope of the man's indifference curve from the slope of the observed constraint at the equilibrium point.
Samuelson، Paul A. (1950). "The problem of integrability in utility theory". Economica. New Series. ج. 17. ص. 355–385. DOI:10.2307/2549499. JSTOR:2549499. MR:0043436. {{استشهاد بخبر}}: الوسيط |ref=harv غير صالح (مساعدة)For the نقش to their seventh chapter, "Markets with non-convex preferences and production" presenting Starr (1969), Arrow & Hahn (1971, p. 169) quote جون ميلتون's description of the (non-convex) Serbonian Bog in الفردوس المفقود (Book II, lines 592–594):
A gulf profound as that Serbonian Bog
Betwixt Damiata and Mount Casius old,
Where Armies whole have sunk.
Diewert (1982, pp. 552–553): Diewert، W. E. (1982). "12 Duality approaches to microeconomic theory". في Arrow، Kenneth Joseph؛ Intriligator، Michael D (المحررون). Handbook of mathematical economics, Volume II. Handbooks in economics. Amsterdam: North-Holland Publishing Co. ج. 1. ص. 535–599. DOI:10.1016/S1573-4382(82)02007-4. ISBN:978-0-444-86127-6. MR:0648778.
Aumann (1966, pp. 1–2): Aumann، Robert J. (يناير 1966). "Existence of competitive equilibrium in markets with a continuum of traders". Econometrica. ج. 34 ع. 1: 1–17. DOI:10.2307/1909854. JSTOR:1909854. MR:0191623. Aumann (1966) builds on two papers: Aumann (1964, 1965) Aumann، Robert J. (يناير–أبريل 1964). "Markets with a continuum of traders". Econometrica. ج. 32 ع. 1–2: 39–50. DOI:10.2307/1913732. JSTOR:1913732. MR:0172689. Aumann، Robert J. (أغسطس 1965). "Integrals of set-valued functions". Journal of Mathematical Analysis and Applications. ج. 12 ع. 1: 1–12. DOI:10.1016/0022-247X(65)90049-1. MR:0185073.

jstor.org

Page 1: Guesnerie، Roger (1975). "Pareto optimality in non-convex economies". Econometrica. ج. 43. ص. 1–29. DOI:10.2307/1913410. JSTOR:1913410. MR:0443877. {{استشهاد بخبر}}: الوسيط |ref=harv غير صالح (مساعدة) ("Errata". Econometrica. ج. 43 رقم 5–6. 1975. ص. 1010. DOI:10.2307/1911353. JSTOR:1911353. MR:0443878. {{استشهاد بخبر}}: يحتوي الاستشهاد على وسيط غير معروف وفارغ: |1= (مساعدة))
Sraffa، Piero (1926). "The Laws of returns under competitive conditions". Economic Journal. ج. 36 رقم 144. ص. 535–550. JSTOR:2959866. {{استشهاد بخبر}}: الوسيط |ref=harv غير صالح (مساعدة)
Hotelling، Harold (يوليو 1938). "The General welfare in relation to problems of taxation and of railway and utility rates". Econometrica. ج. 6 ع. 3: 242–269. DOI:10.2307/1907054. JSTOR:1907054.
Samuelson (1950, pp. 359–360):
It will be noted that any point where the indifference curves are convex rather than concave cannot be observed in a competitive market. Such points are shrouded in eternal darkness—unless we make our consumer a monopsonist and let him choose between goods lying on a very convex "budget curve" (along which he is affecting the price of what he buys). In this monopsony case, we could still deduce the slope of the man's indifference curve from the slope of the observed constraint at the equilibrium point.
Samuelson، Paul A. (1950). "The problem of integrability in utility theory". Economica. New Series. ج. 17. ص. 355–385. DOI:10.2307/2549499. JSTOR:2549499. MR:0043436. {{استشهاد بخبر}}: الوسيط |ref=harv غير صالح (مساعدة)For the نقش to their seventh chapter, "Markets with non-convex preferences and production" presenting Starr (1969), Arrow & Hahn (1971, p. 169) quote جون ميلتون's description of the (non-convex) Serbonian Bog in الفردوس المفقود (Book II, lines 592–594):
A gulf profound as that Serbonian Bog
Betwixt Damiata and Mount Casius old,
Where Armies whole have sunk.
Aumann (1966, pp. 1–2): Aumann، Robert J. (يناير 1966). "Existence of competitive equilibrium in markets with a continuum of traders". Econometrica. ج. 34 ع. 1: 1–17. DOI:10.2307/1909854. JSTOR:1909854. MR:0191623. Aumann (1966) builds on two papers: Aumann (1964, 1965) Aumann، Robert J. (يناير–أبريل 1964). "Markets with a continuum of traders". Econometrica. ج. 32 ع. 1–2: 39–50. DOI:10.2307/1913732. JSTOR:1913732. MR:0172689. Aumann، Robert J. (أغسطس 1965). "Integrals of set-valued functions". Journal of Mathematical Analysis and Applications. ج. 12 ع. 1: 1–12. DOI:10.1016/0022-247X(65)90049-1. MR:0185073.

upf.edu

econ.upf.edu

Mas-Colell، A. (1987). "Non-convexity" (PDF). في Eatwell، John؛ Milgate، Murray؛ Newman، Peter (المحررون). The New Palgrave: A Dictionary of Economics (ط. first). Palgrave Macmillan. ص. 653–661. DOI:10.1057/9780230226203.3173. ISBN:9780333786765.

wikisource.org

en.wikisource.org

Samuelson (1950, pp. 359–360):
It will be noted that any point where the indifference curves are convex rather than concave cannot be observed in a competitive market. Such points are shrouded in eternal darkness—unless we make our consumer a monopsonist and let him choose between goods lying on a very convex "budget curve" (along which he is affecting the price of what he buys). In this monopsony case, we could still deduce the slope of the man's indifference curve from the slope of the observed constraint at the equilibrium point.
Samuelson، Paul A. (1950). "The problem of integrability in utility theory". Economica. New Series. ج. 17. ص. 355–385. DOI:10.2307/2549499. JSTOR:2549499. MR:0043436. {{استشهاد بخبر}}: الوسيط |ref=harv غير صالح (مساعدة)For the نقش to their seventh chapter, "Markets with non-convex preferences and production" presenting Starr (1969), Arrow & Hahn (1971, p. 169) quote جون ميلتون's description of the (non-convex) Serbonian Bog in الفردوس المفقود (Book II, lines 592–594):
A gulf profound as that Serbonian Bog
Betwixt Damiata and Mount Casius old,
Where Armies whole have sunk.