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The Solow Growth Model

The Solow Growth Model. Model lanjutan yang mengikutsertakan pertumbuhan penduduk dan kemajuan teknologi. Model sebelumnya.

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The Solow Growth Model

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  1. The Solow Growth Model Model lanjutan yang mengikutsertakanpertumbuhanpendudukdankemajuanteknologi

  2. Model sebelumnya • Pada model pertumbuhanekonomi Solow sebelumnya, kitabisamelihatsecaradinamisbagaimana savings (S) mempengaruhiperekonomiandariwaktukewaktu. Kita belajarbagaimanakeseimbangankapitaldanbagaimana golden rule keseimbangankapitaldapatdicapaidenganmembuattingkattabunganuntukmemaksimalkankonsumsi per TK. Kita sekarangakanmengembangkan model untukmelihatefekpertumbuhanpendudukdankemajuanteknologi.

  3. Steady State Equilibrium • Untukmelihatbagaimanapertumbuhanpendudukmempengaruhikeseimbangan, kitaharusmengetahuibagaimanapertumbuhanpendudukinimempengaruhiakumulasi modal per TK. Jikakitatambahkanpertumbuhanpenduduk (n) pada model kita, makaperubahandalamstokkapital per TK adalah…Δk = i – (δ+n)k • Kita lihatbahwapertumbuhanpendudukmemilikiefeknegatifpadaakumulasistokkapital. Kita bisakatakan(δ+n)ksebagai break-even investment ataujumlahinvestasi yang dibutuhkanuntukmencapaistokkapital per TK konstan. • Untukmelihatdampakinvestasi, depresiasi, danpertumbuhanpendudukpadapadakapitalkitagunakanrumus (perubahandalamkapital) daripersamaandiatas,Δk = i – (δ+n)k…jikakitagantiimaka,Δk = s*f(k) – (δ+n)k

  4. Steady State Equilibrium with population growth Break-even investment(δ+n)k s*f(k)Investment • At the point where both (k) and (y) are constant it must be the case that,Δk = s*f(k) – (δ+n)k = 0 …or,s*f(k) = (δ+n)k…this occurs at our equilibrium point k*. Like depreciation, population growth is one reason why the capital stock per worker shrinks. InvestmentBreak-even Investment s*f(k*)=(δ+n)k* k k* At k* break-even investment equals investment.

  5. The impact of population growth • Anggappendudukbertambahdari n1menjadi n2. • Inimenggesergaris population growth dan depreciation keatas. An increase in “n” InvestmentBreak-even Investment (δ+n2)k (δ+n1)k • Padatingkatkeseimbanganmapank2* capital per worker dan output per worker semakinturun • Model tersebutmenyatakanbahwaperekonomiandenganpertumbuhanpenduduk yang lebihtinggiakanmemilikitingkatkapital per TK dantingkatpendapatan yang lebihrendah. s*f(k) k k2* k1* …reduces k*

  6. The efficiency of labour • Jikakitatulisulangfungsiproduksisbb…Y=F(K,L*E)dimana “E” adalahefisiensi TK. “L*E” adalahjumlahpekerjaefisien. Pertumbuhanefisiensi TK adalah “g”. • Fungsiproduksikita y=f(k) menjadi output per TK efektifkarena …y=Y/(L*E) and k=K/(L*E) • Pengembangan model “δk” dibutuhkanuntukmenggantidepresiasikapital, “nk” dibutuhkanuntukpenyediaankapitalpadatiap TK, dan “gk” dibutuhkanuntukpenyediaankapitalpadaTK efektifbaru yang terciptaakibatkemajuanteknologi.

  7. Steady State Equilibrium with population growth and technological progress • At the point where both (k) and (y) are constant it must be the case that,Δk = s*f(k) – (δ+n+g)k = 0 …or,s*f(k) = (δ+n)k…this occurs at our equilibrium point k*. Like depreciation and population growth, the labour augmenting technological progress rate causes the capital stock per worker to shrink. Break-even investment(δ+n+g)k InvestmentBreak-even Investment s*f(k)Investment s*f(k*)=(δ+n+g)k* At k* break-even investment equals investment. k k*

  8. The impact of technological progress • Anggappertumbuhanefisiensi TK berubahdari g1to g2. • Iniakanmenggesergaris population growth, depreciation, and worker efficiency growth keatas. An increase in “g” InvestmentBreak-even Investment (δ+n+g2)k (δ+n+g1)k s*f(k) • Padatingkatkeseimbanganbaru k2* capital per worker and output per worker semakinrendah. • model tersebutmengatakanbahwaperekonomiandengantingkatpertumbuhanefisiensiTK yang lebihtinggiakanmemilikicapital per worker dan lower levels of income yang lebihrendah. k k2* k1* …reduces k*

  9. Effects of technological progress on the golden rule • With technological progress the golden rule level of capital is defined as the steady state that maximizes consumption per effective worker. Following our previous analysis steady state consumption per worker is…c* = f(k*) – (δ+ n + g)k* • To maximize this…MPK = δ+ n + gorMPK – δ= n + g • That is, at the Golden Rule level of capital, the net marginal product of capital MPK – δ, equals the rate of growth of total output, n+g.

  10. Steady State Growth Rates in the Solow Model with Technological Progress

  11. Conclusion • Padababinikitatelahmembahasbagaimanaefekdua variables eksogen (population and technological growth) terhadap model pertumbuhan Solow. Kita bisalihatbahwadalamkeseimbangan output per effective TK tetapkonstan, output per TK tergantunghanyakepada technological growth, danbahwa Total output tergantungpada population and technological growth.

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