ࡱ> Root Entryghj2 FȮ^-,DataOHl g!99WordDocument% *'()c+;41234=8B*F<ObjectPoolCDE&PJIuNLyZ\r+ uf)"#$%&'(A,.@/0123465789;:<=>VBCDEFGHIJKLMNOPQRSTUW\]~ghijvwxyz{| Equation Native ?1TableR SummaryInformation(3CDocumentSummaryInformation8J "%&'(+.147:=@ABDEFGHIKLMNOPQSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz|~CompObj5{X0Table1} ynamics Brad DeLong Brad DeLongstant. This does not meant that there was no technological progress before 1800. There was a great deal of technological progress before 1800. In the Middle East people invented astronomy, irrigation, and the wheel. In what is now Russia people domesticated the horse. In China people domesticated silkworms, created silk manufacture, designed sailing ships--junks--that could sail from China all the way across the IndianAN{61D75200-6C24-11D3-A34F-F60FF0C55E12}`KQ`/@ 8`HtKu` [4@4NormalCJOJPJQJmH <A@<Default Paragraph Font4O4Text ParagraphPOPMemo heading style  CJOJQJL!LThesis Statement$6CJOJPJQJ4Z"ve values of g, did not lead to sustained increases in the efficiency of labor E. Why not? Because at pre-1800 levels of technology natural resources were very, very important and--by our standards--very, very scarce. Improvements in technology allowed civilizations to expand into regions that before had been too poor in resources to support reasonably high population densities. And as civilizations expanded into these new resource-poor regions the fall in labor efficiency produced by the decline in the average amount of natural resources per capita about offset the potential rise in labor efficiency that would have been generated by technological progress. If the rate at which the efficiency of labor grows g is equal to zero, then the level of the efficiency of labor is constant: let's call this constant level E0. And our equation for the steady-state level of output per worker becomes simpler. Instead of steady-state output per worker rising over time at a proportional rate g, and dependent on the balance between the savings rate s and capital requirements (n+g+d):  EMBED Equation.3  Steady-state output per worker is constant.  EMBED Equation.3  Higher savings rates raise it; higher population growth rates lower it. If we know what the values are of the savings rate s, the diminishing-returns-to-investment parameter a, and the depreciation rate d, we can see that there is an inverse relationship between the steady-state level of output per worker: the higher the population growth rate n, the lower the steady-state value of output per worker (Y/L).  Determinants of Population Growth Before 1800 Turn now to the second of Malthus's insights: that back before 1800 the higher the level of output per worker, the higher the rate of population growth. It is easy to see why population would stagnate (or decline) if a economy were desperately poor. One possible road: set g, the growth rate of total factor productivity, to zero--assume that technological progress is offset by other factors (Ricardian limits, et cetera) and that as a result total factor productivity E is constant. Then:  EMBED Equation.3  Combine this with a "Malthusian" demographic equation:  EMBED Equation.3  Combining these two equations:  EMBED Equation.3  Or, graphically: For the case aDH5`/@b8cH8P8aHH5]`/@b8cH8`8aLH51`/@b8cHl8888aPHN`/@b8cH<8h8aTHM`/@b8cHa@Aa=1/2:  EMBED Equation.3   EMBED Equation.3  Making the further approximation:  EMBED Equation.3  We can approximate:  EMBED Equation.3   EMBED Equation.3  And the solution for n is then approximately 4 Plain Text CJOJQJ2O22H5 dh@&5OJPJQJ6O6H4 dh@&6CJOJPJQJ6O6H3 dh@&5CJOJPJQJ8Ob8H2$dh@&5CJ OJPJQJ8O8H1$dh@&5CJ$OJPJQJy@     :y:<=>l{!8F!6!6!!6!6!6!6!6!6!6{@B">vUnknown Brad DeLong?SU,.Rfh.03GIy::::::::::,17<+ 0 e n 5:cl{\aj: N 80={ Brad DeLong;Macintosh_HD:Desktop Folder:Malthusian Dynamics-draft 9/15/@d  GHhxyp@pqp0@q@q2@q @qf@qn@q@qBp2@ppGTimes New Roman5Symbol3 Arial3Times;Helvetica? Courier New"qh99;7$! 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An economy with a relatively high output per worker level Y/L would see fast population growth. An economy with a relatively low output per worker level Y/L would see its population growth rate n fall to zero or below. Population would stagnate of even decline. The Efficiency of Labor Before 1800 It is not a bad approximation to say that before 1800 the growth rate g of the efficiency of labor was effectively zero, so that the level of the efficiency of labor E was approximately constant. This does not meant that there was no technological progress before 1800. There was a great deal of technological progress before 1800. In the Middle East people invented astronomy, irrigation, and the wheel. In what is now Russia people domesticated the horse. In China people domesticated silkworms, created silk manufacture, designed sailing ships--junks--that could sail from China all the way across the IndianRoot Entryghj2 F-+DataOHl 5g!99WordDocument% *'()c+;11234=8BmB<ObjectPoolCDE&PJIuNL4yZ\r u"#$%&'(A./0123465789;:<=>c?`BCDEFGHIJKLMNOPQRSTUYZ[l+bXadghijkfnopqrstvwxyz{|}CompObj{X0Table} Microsoft Word 8.0@f`@62k@B,7!a8` H`8a8K8bT ՜.+,D՜.+,D hp  'selfsi$$: Malthusian Dynamics Title 6> _PID_GUID'AN{61D75200-6C24-11D3-A34F-F60FF0C55E12}`KQ`/@ 8`HtKu` [4@4NormalCJOJPJQJmH <A@<Default Paragraph Font4O4Text ParagraphPOPMemo heading style  CJOJQJL!LThesis Statement$6CJOJPJQJ4Z"0 Y/L()*-d[]-sE 0 Y/L()*() 2 ()xAL/AHd888ahK  Oh+'0h  $ 0 <HPX`'Malthusian Dynamicsalt Brad DeLongradNormalL Brad DeLong18d "%&'(+.147:=@ABDEFGHIKLMNOPQSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz|~agraphPOPMemo heading style  CJOJQJL!LThesis Statement$6CJOJPJQJ4Z"4 Plain Text CJOJQJ2O22H5 dh@&5OJPJQJ6O6H4 dh@&6CJOJPJQJ6O6H3 dh@&5CJOJPJQJ8Ob8H2$dh@&5CJ OJPJQJ8O8H1$dh@&5CJ$OJPJQJx@     :x:<=>lz!8F!6!6!!6!6!6!6!6!6!6z@>vUnknown Brad DeLong?SU+-Qeg-/2FHx::::::::::,17<+ 0 e n 5:bkz\aj: N 8h/<z Brad DeLong;Macintosh_HD:Desktop Folder:Malthusian Dynamics-draft 9/15/@d  @GHhwxp@pqp0@q@q2@q @qf@qn@q@p2@ppGTimes New Roman5Symbol3 Arial3Times;Helvetica? Courier New"1h9o917$!0$UMalthusian Dynamics Brad DeLong Brad DeLongb8cK`/@ 8`HЀ88b8cK/@ 8 b8cH>}`8`HP8 b8cH>a`88aHA`|fx88<``czbPH(A8`8!}N }!a048<@D!HALb9ka9@A9 !988UMalthusian Dynamics Brad DeLong Brad DeLongd<`8\4X0Ta,aPa(aLA$AH FMicrosoft Word DocumentNB6WWord.Document.8K8\88aK9/@b\ [4@4NormalCJOJPJQJmH <A@<Default Paragraph Font4O4Text Parc jbjbSS B11x]2<<<<Pffffffff,9 - |.fffff.jff.jjjfff,,fjjl!F<jMalthusian Dynamics After the year 1800 the Solow model of steady-state growth covered in the last chapter does a fairly good job of capturing the most important features of the long-run gorwth experience. But before the year 1800 it does not. Human history between the dawn of civilization and 1800 sees next to no growth in average material standards of living. It sees very slow--glacial by our standards--growth in human populations up until 1500 or so, and then an acceleration of population growth. This pattern is very different from the steady-state growth--with steadily rising levels of both population and output per worker as the first increases at a constant proportional rate n and the second increases at a constant proportional rate g--that was the prediction of the workhorse Solow model of economic growth covered at such length last chapter. So what has gone wrong? Why doesn't it seem to work? Do we need to throw out the entire theoretical apparatus of the past chapter whenever we look back before 1800? No. We do not. We do, however, need to augment the Solow model of economic growth. We need to augment it in two ways, both of which were outlined at the very end of the eighteenth century by the British economist Thomas Robert Malthus--the first professor of political economy (Adam Smith was a professor of moral philosophy). To understand economic history before 1800, we need to recognize that there was effectively no increase in the efficiency of labor E, so that the parameter g was zero. And we need to recognize that the population growth rate n was not constant, but depended on how prosperous the economy was. An economy with a relatively high output per worker level Y/L would see fast population growth. An economy with a relatively low output per worker level Y/L would see its population growth rate n fall to zero or below. Population would stagnate of even decline. The Efficiency of Labor Before 1800 It is not a bad approximation to say that before 1800 the growth rate g of the efficiency of labor was effectively zero, so that the level of the efficiency of labor E was approximately constant. This does not meant that there was no technological progress before 1800. There was a great deal of technological progress before 1800. In the Middle East people invented astronomy, irrigation, and the wheel. In what is now Russia people domesticated the horse. In China people domesticated silkworms, created silk manufacture, designed sailing ships--junks--that could sail from China all the way across the Indian Ocean to Zanzibar, and invented gunpowder, the compass, and printing. In Europe people invented the watermill, the deep-cutting plough, systematic crop rotation, the mechanical clock, spectacles, hand-carried firearms, movable type, perspective, and steam engines. In the Americas people selectively bred the most efficient and productive agricultural plant ever: corn. In India people invented the zero--without which mathematics is almost unusable. 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