correction list1 eg 2012

8/13/2019 Correction List1 Eg 2012

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Christian Groth, University of Copenhagen

16.02.2012 Economic Growth

Errata to Acemoglus textbookThe list below refers to what looks like typos or logical errors (as far as I can see) in our

textbook, AcemoglusIntroduction to Modern Economic Growth, Princeton 2009.

Symbol glossary: l. means line; f.b. means from below; eq. means equation;

n means footnote. In the third column, in square brackets, occasionally appears a comment.

page reads should read (or my comment)

17, l. 2 f.b. as economies below as economies below or above17, l. 2 f.b. grow toward adjust toward18, title of and average growth of investments to and average investment to

figure GDP ratio GDP ratio29, l. 23-24 diminishing returns to capital distin- [this is misleading. In the Harrod-Domar

guishes the Solow growth model model the production function is Leonti-from its antecedent, the Harrod- ef (iso-quants are of L form, there is noDomar model substitutability between capital and la-

bor). It is in the opposite case the caseofperfect substitutability that dimin-

ishing returns to capital is absent.]33, l. 3 f.b. Moreover,(0) = 0for all [This isimplied,and thus not an additio-and nal assumption, as soon as the other part

of Assumption 2 is assumed togetherwith Assumption1.]

53, l. 12 f.b. In addition, is increasing in [This is true only if((+)) 1]54, l. 1 f.b. min{()();(1 )()()} min{()(); ()()}56,figure ( )() +1

1+ () [since(+ 1) is on the ver-

tical axis, the figure must be about the di-screte time case]

57, l. 2 f.b. This estimate ignores the share of [The estimate 1/3 represents the incomeland; share of physical capital and land; cal-

ling it income share of capital is a kindof shortening of income share of non-human wealth]

78, l. 19 f.b. as total factor productivity as growth in total factor productivity79, l. 4 +1 +181, l. 12 aroundlog () aroundlog

100, l. 3 TFP difference difference in TFP growth303, l. 1 f.b. then consumption would reach zero in then

finite time, and thus [delete the remainder since it is wrong]

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page reads should read (or comment)313, l. 12 () = (1 )(0(() ) [To avoid confusion, note that this ()

is the after-tax interest rate, which in thestandard notation in this course wouldbe written(1 )()]

331, l. 16 Total savings in the economy Total savings by the young336, l. 16 with log preferences with CRRA preferences[that is, the theo-

rem holds not only for log preferences]362, l. 13- Integrating both sides of this equa- [This is wrong since, generally, (10.10)

11 f.b. tion ... is valid only at= not in an intervalaround ; see Lecture Note 6]

366, l. 8 f.b. is always increasing is increasing if (0)

387, l. 10 neoclassical model as well. neoclassical model with = 0as well.394, l. 6-9 there are no constraints on human [wrong; negative gross investment in

and physical capital investments human capital is impossible; (11.25) is.... and physical capital. conditional on aninteriorsolution]

394, l. 23 + (1 )(0() ) + +(1 )(

0() )+401, l. 13-14 (with output reaching infinity in [Delete]

finite time ...transversality condition).402, l. 9 f.b. will not be possible. will not be possible without technical

progress.434, l. 14 though the results are identical with- [Delete]

out this assumption;436, l. 10 f.b. Let us normalize the marginal costs Let us specify the marginal costs437, l. 15 recall that one unit recall that on average one unit439, l. 6 and the transversality condition is and provides scope for satisfaction of

satisfied. the transversality condition.439, l. 16- [See Comment to 13.1.4 below.]

5 f.b.440, l. 5 f.b. Maximization gives In the special case = 1 maximiza-

tion gives

Continued next page.

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page reads should read (or comment)

441, l. 13 f.b. Hamiltonian is strictly concave and [The truth is that the Hamiltonian issatisfies the conditions of Theorem concave in(() ()), which is enough7.14. to ensure that the FOCs together with

the TVC aresufficient conditionsfor optimality; the Hamiltonian isnotstrictly concave; moreover, themaximizedHamiltonian is concave in() but not strictly concave;so the conditions of Theorem 7.14arenot satisfied. ]

442, l. 14- the gap between the decentralized the gap between the decentralized13 f.b. equilibrium and the Pareto optimal equilibrium and the social planners

allocation, optimal allocation,[it is not clearwhatthePareto optimal allocationis there are infinitely many Paretooptimal allocations as soon as thereare more than one household]

444-445 [(1326)and (13.27) presuppose= 1 ]

445, eq. (13.31) See Comment to 13.2 below.445, l. 6 f.b. equilibrium (see Exercise 13.17). equilibrium (see Exercise 13.16).446, l. 20 , and output per capita would reach [Delete]

infinity in finite time (explode)447, eq. (13.38) =

=

448, l. 12-13 It is not clear whether the data sup- [See Afterthoughts as of May 19]ports these types of scale effects either.

448, l. 18-21 semi-endogenous growth models ... [Here semi-endogenous growth isnot respond to taxes or other policies. defined differently than in the lectu-

res and in Lecture Note 7 and 8; seeAfterthoughts as of June 9.]

Comment to 13.1.4 (p. 439) It is true that in general equilibrium with positive R&D, there is

no transitional dynamics. In my view, however, Acemoglu does not provide a valid proof. In

connection with one of the exercise problems on this model we show that the relevant approach

is analogue to that applied for the simple AK model (pp. 390-391).

A related error in Acemoglu is the claim p. 439, l. 6, that the last inequality in (13.21)

ensures that the transversality condition (TVC) is satisfied. The point is that (13.21) only

opens up for the possibility that the TVC can be satisfied. What then ensures satisfaction

of the TVC is that (0) is at a certain level determined by (0) This level in turn ensures

balanced growth from the beginning, i.e., absence of transitional dynamics.

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Comment to 13.2 (p. 445)One might wonder whether the formula (13.31) is valid for 0

(the general case) or only in the special case = 1 ?

The answer is that the formula, fortunately, is valid also in the general case 0 as are

(13.29) and (13.30). This is because cancels out anyway in these formulas. But when stating

(13.26) and (13.27),= 1

is presupposed.

This is another illustration that assuming = 1 may easily lead to confusions.

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correction list1 eg 2012

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