cc15--索洛經(jīng)濟(jì)增長(zhǎng)模型(編輯修改稿)
2024-08-31 10:38 本頁(yè)面
【文章內(nèi)容簡(jiǎn)介】 quantities of capital and effective labor (for example, by doubling K and L with A hild fixed) doubles the amount produced. ? More generally, multipling both arguments by any nonnegative constant causes output to change by the same factor. ? F(cK,cAL)=cF(K,AL) ? The assumption of constant returns allows up to work with the production function in intensive form. Setting c=1/AL in equation yields ? Y/AL = F(K/AL,1) ? y = f(k) ? 狀態(tài) ? 這些假定都與凱恩斯主義的論點(diǎn)相反，而與傳統(tǒng)經(jīng)濟(jì)學(xué)的觀點(diǎn)相近。這也就是他們的模型被稱(chēng)作新古典的由來(lái)。 ? ：勞動(dòng) L和資本 K，且二者可以完全替換 ? 資本 ―― 產(chǎn)出比率或其倒數(shù)資本生產(chǎn)率都是可變的，這個(gè)假定又和哈羅德－多馬的假定相反。哈羅德－多馬模型認(rèn)為實(shí)現(xiàn)均衡增長(zhǎng)的決定因素在需求方面，而新古典模型認(rèn)為實(shí)現(xiàn)均衡增長(zhǎng)的決定因素在供給方面，即由勞動(dòng)力的增長(zhǎng)所決定的。 ? The evolution of the unputs into production ? The initial levels of capital, labor, and knowledge are taken as given. Labor and knowledge grow at constant rates: ? The growth rate of labor is exogenous and constant ? A dot over a variable denotes a derivative with respect to time (that is ,X(t) ish shorthand for dx/dt) ntLtL??)()(? The growth rate of knowledge is exogenous and constant gtAtA??)()(? A key fact about growth rates isthat the growth rate of a variable iquals the rate of change of its natural log. That is ntLtLdttdLtdLtLddttLd ????)()()()()(ln)(ln? So rewrite ? Intergral with both side ndt tLd ?)(lnttL ??)(ln? 或者： ? 這里是的初始值（ value of L at time 0），為一常數(shù)。對(duì)上式兩邊取以 為底的 指數(shù)得(exponentiating both sides of these equations gives us) )0(ln)(ln LnttL ??nteLtL )0()( ?? 在一個(gè)封閉的經(jīng)濟(jì)中 (in a close economy)，產(chǎn)出可以分割為消費(fèi)和儲(chǔ)蓄。儲(chǔ)蓄的產(chǎn)出份額 s是外生的常數(shù)，假定儲(chǔ)蓄完全轉(zhuǎn)化為投資，并假定資本以速率折舊 (existing capital depreciates at rate)。 so新增資本： )()()()( tKtsYtKItK ?? ?????conclusion ? 如果考慮勞動(dòng)力增長(zhǎng)因素，新增資本可以表示為： )()()()( tnKtKtsYtK ?????? 如果再考慮到技術(shù)進(jìn)步需要占用的資本，新增資本可以表示為： )()()()(
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