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Unformatted text preview: Mark L.J. Wright Econ 102
Macroeconomic Theory n1 wright©ec0n.ucla.edu
Winter 2007 Bunche 9284
First Midterm Exam
Date: Thursday lst February, 2007
Instructions
1. Answer each part of the exam in a separate blue book. 99°74??? 10. . Write your name, student number, TA section and the part attemptsd on the front page of
each blue book that you use. Write your answers in permanent ink. Answers submitted in pencil, or in erasable ink, are
not eligible for regrade requests. You have 75 minutes to answer this exam. The exam has four (4) pages. Please check that you have all pages. There are seventy ﬁve (75) points worth of questions. Answer all que stions. This is a “closad book” exam. You may not consult your notes or textbooks during the exam.
No calculators are to be used on the exam. You may not talk to any other student while completing the exam. Exam answers are to be
completed, and handed in, individually. Professor Wright will be available to answer questions during the ﬁrst ten minutes of the exam. If you are confused about a question on the exam after the ﬁrst ten 1r inutes, explain why y0u
are confused in your answer, state what you think is necessary to resolve your confusion, and then proceed to answer the question accordingly. Part A (Short Answer Questions)
(24 points total) Evaluate each of the following statements. State whether they are true, False or uncertain, and
give a short explanation of your reasoning. No points will be awarded withc ut an explanation. 1. Suppose that the government legalized the growing of, and use of produ :ts from, the Cannabis
sativa plant (Marijuana). Philip Morris responds by introducing a new line of Marlboro joints.
The level of real GDP rises as a reSult, but living standards fall. (8 p0 nts) 2. If the CPI shows that inﬂation is high, but the GDP deﬂator shows tl at inﬂation is low, the
difference can only be due to substitution bias in the CPI. (8 points) 3. In the Solow—Swan growth model, a decrease in the population growth rate 1:. has no effect on
the long—run level of output per person. (8 points) Part B (Long Answer Question on Growth Accounting) (26 points) Consider a version of the SolowSwan model exactly as described in class Output is produced
using the production function Y = F (K , AL) ,
which has constant returns to scale. Teachnology and Labor grow according to
g = a: and —% = 11, while capital is accumulated according to K=sY5K 1. Assume that this economy is in steady state. That is, capital, output, technology and labor
are all growing at constant (although not necessarily equal) rates. A. what rates do capital
and output grow? At what rate do output per worker grow? (6 poi: 1ts) 2. Imagine you were observing the growth of capital, output and labor p:oduced by this model.
Apply the techniques of growth accounting to these growth rates. What fraction of the
growth in output does growth accounting attribute to technological pr egress? What fraction is attributed to growth in capital? (12 points) 3. In class, I said that the growth rate of output per worker in the long run is determined solely
by the rate of technological progress. How can you reconcile your answer in part 2. with this
statement? (8 points) ECON 102
(Winter Quarter 2007)
Answer Key for the First Midterm 2007 February 8, 2007 Part A
Part A.1. Uncertain. Real GDP increases sincettransactions that used to take place in the in'
formal (underground) economy are now carried out in the m arketplace and
are recorded preperly. Real GDP is an imperfect measure of living standards. Living standard
is a much broader concept. For instance, some people may have ethical
reasons for not supporting the use of drugs and they’ll be worse OH with
everyone around them pufﬁng on Marlboro joints, Others may be happier
because they can smoke a joint whenever they please, without the worry of
being arrested. Part A32.
False. The CPI and GDP deﬂator nee a different basket of goods and services.
For instance, the CPI includes imported goods while GDP only consists
of domestically produced goods. Similarly, the CPI — by dc ﬁnition — only
includes consumer goods, whereas GDP also contains producc :rs‘equipment. Part A._3. False. In the Solow growth model, a. shift in n is associated with a. diﬁ‘erent steady
state. In particular, a lower population growth rate is assmiated with a.
higher steadystate output per capita % (see ﬁgure 711 in Mankiw, p. 207). Part B
Part B.1.
_In steady state: K — Y 6 is constant
K “‘ 3K
z? Yisconstant
K ‘
=> lnYwinKisconstant
2} Y_KM
YK_ Next, differentiate the production function with respect to tine and divide
by Y: AL+AL ; = FK(K,AL)%+§AL(K,AL) Y _ I
= (amenIE); + (FAL(K:AL)£Y£) (“3‘ Jr '
Y K .Rearranging, and setting 9 = 7 = 1,? we get: * (FAL(K,AL)A—%)($+n) _ 3+”
“ W)“ _ Since the function exhibits constant returns to scale in K and AL. What about output per worker? Recall the fundamentai equation of the Solow growth mod:1 after we’ve
divided everything by AL: ic=sf(k)—(:r+n+6) 2 Also, recall that in steady state, t = 0, which implies that k is constant.
This, in turn implies that y = f(k) E 21% is constant . Since { = % = A3; it follows that: dln(Ay) w A _ :6
dt ‘ A ‘
That is, output per worker grows at rate of technological progress 1‘.
Part 13.2. From the previous part we already have an expression for the growth rate
of output and we can use it here: Y K K
r  WWW?) R
EV...“
fraction of output growth attributed to capital growth
AL A it
+ (FMK’ALW) (z + 1‘)
W
fraction of output growth attributed to technological progress
Part B.3. We can reconcile the ﬁndings in parts 1 and 2 by recognizing that is an
endogenous variable. In other words, capital does not grow independently,
but it grows as a result of technological progress. The growth accounting carn'ed out in part 2 does not take the indirect
effect of technological progress through capital accumulation into account,
Instead, it attributes some fraction of the growth contribution to capital,
even though capital only grows because of technological progress (and la
bor force growth, which we need not worry about since we’re interested in
output per Worker only). PartC 1. Let us ﬁrst compute the growth rate of E in the steady state. One
method is as follows. First, take the log of E 2 8R and obtain logE : loge—Hog}? 3 Differentiating with respect to time and noting that e = 0 (as e is a.
constant), I
E _ e R _ R ﬂ —E _ e EeRRR where we used R z —E in the third equality and E = 815 in the fourth
equality. Thus the growth rate of E in the steady state: is —e. Alternatively, by noting that e is a constant, we can directly proceed
from E = 8R to obtain E=eR=—6E which lead to the same result. Now, from
K = 31" 7 6K
we obtain _
K _ Y 6
K “ 3K This implies that in the steady state, since must b: oonstant, Y
and K must grow at the same rate. Let this common late be 9. Now, taking log of the production function, logY = alogK+ﬁ(logA+logL)+(l — a—ﬁ: logE Differentiating with respect to time, Y K A L E
y=af+ﬂ(2+f)+(1—a—5)E which becomes 9=ag+ﬁ($+n)+(lwa—ﬁ)(—8) so that
ﬁ(:1:+n) —(1~*oz—ﬁ)e g: 1+0: To summarize, in the steady state Y and K grow at rate E W,
L grows at rate 11, and E grows at rate —3. 2. Let Y]; E if, or output per person. Taking logs and iifferentiating
with respect to time, YL _ Y L 7; _ ?_f : g—n
ﬁx—(l—auﬁ)(e+n) This tells us that the fact that the stock of non—tens wable energy
sources is declining DOES NOT IMPLY that permanent growth in
output per person is not possible. There will be perm anent growth
in output per person if and only if ﬁr>(1aﬁ)(e+n} This will be true if the rate of technological progress is sufﬁciently
high to offset the rate of decline of energy and the rate 3f population
growth. Economics 102, First Midterm of Winter 2003, Sketch of Answers January 29, 2007 Part A 1) True. Before the marriage the action was registered and counted in GDP as services. Afterwards
not any longer. 2) False. The ﬁrst statement contradicts the second. 3) False. An increase in the savings rate leads to an increase in the 10 [lgrun level of output per
capita. 4) Uncertain. True if the parameters are the same in all countries. Could ﬁnd a counterexample
if different. 5) False. Counterexarnple: in the Solow model capital and output grow at the same rate. Part B (d+n +x)'k 1) There can be three intersections between sf (k) and (6 + n + as) k: as shown in the picture.
In this case there are three steadystate levels: 0, k* and k“. The equilibi ium in the middle (k‘) is
unstable. The other two are stable. When capital is above 16* then is = stc) — (6 + n + 1:) k > 0,
hence, capital tends to increase. When capital is below k“ then ll: = s_’(k) ~— (6 + n + as) k < 0,
capital tends to decrease. 2) If the capital is ﬁrst equal to k" and then the production curve mov as down due to a decrease
in the savings rate, it can move so far as to leave only one equilibrium corresponding to a zero level
of capital. This will be the eventual state of the economy. 3) If Worldbank provides the country with a loan, which is enough to buy K = 19* a: (LA) units
of capital, then the economy will eventually converge to k“ as a steady—s tate. Part C 1a) Output per capita increases in the short run: % = L—ﬂA = (ﬁ)0 A == kaA. K does not change,
L goes down 10%, A does not change. Hence output per capita increases (jumps up) by a * 10%. 1b) The steady state does not change, so since the economy is temporarily above the steady
state, it slows down in the short run. Growth of ouput per capita decree ses. 1c) In the long run the steadystate does not change. Neither does t: 1e growth rate.
1d) Those who survive are temporarily better off, because they are endowed with more capital. “T 7 JONWLNI) kl!) mi 2a) None of the variables jumps, so ouput per capita does not change: in the short run. 2b) There are three possible situations, depending on the magnitudes of the changes in the
parameters n and s. If the steadystate value of k goes down, then the growth rate temporarily
decreases. If the longrun value of k goes up, then the growth rate temp< rarily increases. 2c) The longrun growth rate of output per capita is determined by the growth rate of technology,
which does not change. 2d) If the change in the savings rate dominates, people are worse of. Otherwise, people are
better off. ECON 102
(Winter Quarter 2007)
Sketch of Answers*for First Midterm 2004 January 29, 2007 Part A 1. True; before the marriage counted in GDP as consumption. of services,
after the marriage no longer so. 2. False; can tell the change in welfare with certainty only when Laspeyeres index is less than one, or (ii) Paasche index is greater than
one (see lecture note Part I). 3. False; reduces the long—run level of output per capita.
4. False; it’s the growth rate of A that matters here, not the level ‘5. False; capital should grow at the same rate as output, wlich is 5% Part B
1. “GDPyearl = = 40
nGDPyW2 = (5)(4) + (4)(5) = 40 "This is a rough sketch of how you shoulrgapproacilkegzh question, rather than a.
complete solution key. In actual exam, more explanations will be required for full credit. k
2. Note: superscripts denote the base year. 3’
Cpgearl 2 N.
earl 1 ‘ _ seesaw WW W2 _ (4)(5)+(5)(4)
QUE Q‘?\ Hence the rate of inﬂation is (g — 1) x 100 = 2.5(%) *3. Paasche price index in year 2 is Q ? a r
M = O 976
[email protected][email protected] 
so the rate of inﬂation 131' I Q1 ' (“ii ~— 1) x 100 = —2.4(%) ,4. The differences in rates of inﬂation are driven by the fact that the
weights (quantities) are different in the two cases. 5. Note: superscripts denote the base year.
earl
CPIZearl 2 10? Q P Cplzearl = W2 (some)? Pi “ﬁx 1 1 = 1.025 Hence the rate of inﬂation is (“1'3 — 1) x 100 = 2.5(%) 6‘ Paasche price index in year 2 is given as (15531 4033+ gig?
(wem+mw V G P
so that the rate of inﬂatioi’ﬁ is‘ 7 ‘ (1'91? ~ 1) x 100 z 3.2(%) = 1.032 The differences in growth rates are driven by the fact that the weights
(quantities) are different. Part C .1. No effect 2. Short run growth rate will be larger than the long run g1 owth rate. 3. Discrete drop, as K / L falls. 4. Y/L; discrete drop, shortrun growth rate larger than the long—run
growth rate (which is the growth rate of technological pr agress)
Y/AL; discrete drop, shortrun growth rate larger than the longrun t growth rate (which is zero) Worse off, as Y/L falls.
5. No effect on the long run growth rates of Y/L. If the size of the aid is smaller than the capital destroyed, s ame analysis
as in 4. If the size of the aid equals the capital destroyed, no affect to the
economy. If the size of the aid is larger than the capital destroyed, a: :act opposite
effects as in 4. ...
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