MAKØK 2, blok 1, 2015
Errata to Lecture Notes
(continuously updated)
12/9 2015
Ch. 2, p. 28, line 5-3
from below: Should read:
Indeed, from the mean value theorem <footnote> we know that for any k > 0 there exists a number a ∈(0,1) such that f '(ak) = (f(k) - f(0))/k. For this a we thus have f(k) - f '(ak)k =f(0) < f(k)-f '(k)k, where the inequality follows from f '(ak) > f '(k), by f ' ' < 0. In view of ...
Ch. 3, p. 73, line 1: "By continuity of
U(t), it follows" should read "By
continuity of dU(t)/dt, it follows".
- -
, line 11 from below:
"r_t+1 more units" should read "1
+ r_t +1 more
units".
- - , line
9 from below: "r_t+1 units" should read
"1 + r_t +1 units".
- , p. 76, line 15:
"... as young, and thus saving, happens" should read
"... as young - and thus saving - happens".
- , p. 84, DEF 1, line 3: "and
for all t = 0, 1, 2, ... , (3.27) has" should read
", satisfies (3.27), and for all t = 0, 1, 2, ..., has".
13/9
Ch. 3, p. 82, n. 12, line 2: "will not"
should read "will generally not".
- , p. 96, line 5 from below:
delete the text.
17/9
Ch. 3, p. 90, Lemma 2, line 1: After the comma add:
"For all k_t > 0" should read "For
all k_t > 0 for which dk_t+1/dk_t is defined".
- , p. 99, Proposition 4, line 4: Before
"Oscillations do not occur" add "If k_t does not converge to k*,
k_t converges to another steady state."
- , p. 99, Proof, line 4:
Delete "By Lemma 4 the roof then does the same." (not because it is wrong, but
because it has no role in the proof).
- - - , Proof, line
9: After "stable." add "If k_t does not converge to
k*, k_t converges to one of the other steady states. Indeed,
divergence is ruled out since, by Lemma 5, there exists k_bar > 0 such
that w(k)/(1+n) < k_bar for all k > k_bar (Fig. 3.7 illustrates).
19/9
Ch. 4, p. 130, line 6 from below: Relocate "Assume (1 +
g)/(1 + n) > 1 - d. Then:" to p. 131, line 1, right after "(ii)".
- , p. 136, line 13 from below:
Replace ". That is, given these ...... and so" with ", and that, if
there exist several steady states,".
- , p. 136, line 12 from below:
Replace "in a steady state" with "in one of
them".
24/9
Ch. 6, p. 219, line 3 from below:
"it can not" should read "the tax
revenue aimed at can not".
-
, p. 222, line 10: "because lending"
should read "because borrowing".
- , p. 238, line 13: "(13.68)" should
read "(6.25)".
- -
, line 15: "(13.67)" should read
"(6.24)".
- -
, line 20: "(13.69)" should read
"(6.26)".
1/10
Ch. 9, p. 370, line 7: "takes the form of"
should read "is".
9/10
Ch. 9, p. 364: Replace line 13-16 by "only if their
net debt does not exceed the present value of future primary saving. Denoting by
d_o net debt at time 0, i.e., d_o ≡ - a_o, the solvency requirement as seen from
time 0 is".
Ch. 11, p. 440-442: T should be replaced by a
Calligraphic T.
19/10
Ch. 11, p. 443, line 3: "the future, and ..."
should read "the future. And ...".
- -
, line 4: "the future. The shift ..." should
read "the future, the shift ...".
25/10
Ch. 14, p. 607, line 2: Before "Text not yet available."
should be added "The divergent paths can be shown to violate the transversality
condition of the firm."
Note 2, s. 3, line 5: " , = " should read " = ".