14.02 –
Principles of Macroeconomics
Quiz 2
Solutions
SECTION I: TRUE or FALSE?
Explain your answer in one or two sentences. (20 points total, 2 points each)
True – Per the Interest
Rate Parity condition, i = i* + (E^{e} – E)/E or E = E^{e} /(1
+ i  i*). If E^{e} and i* are
given, when i®
¯E. This means there will
be a stronger domestic currency (i.e. a currency that buys more in terms of
foreign currency).
False – According to the
JCurve, a depreciation of the US dollar relative to the yen causes the quantities
of imports to and exports from Japan to adjust gradually over the midterm (57
months). Quantities of imports will
fall and quantities of exports will rise, so real Net Exports will gradually
improve. However, in the very short
run, the price effect (change in the nominal exchange rates) dominates, causing
Nominal Net Exports to fall: NX = Xe*Q, so if e rises and X and Q are fixed,
NX worsens. Eventually, if the
MarshallLerner condition holds, the quantity effect will dominate, and nominal
NX will increase as well.
False – APCºY/C. It is the
marginal propensity to consume (MPC) described above.
True – While the
Ricardian Equivalence hypothesis predicts that individuals will undo the
effects of government tax cuts, anticipating the future deficits that may come
from these policies, there is no evidence in the data that people actually
behave this way. Instead, the marginal
propensity to consume is quite stable over time, even in the presence of tax
cuts.
False – The Life Cycle
model states that individuals will try to smooth their consumption, borrowing
and saving over time in order to keep consumption levels constant. However, if they are unable to reach the
optimal C* due to borrowing restrictions in some period (t=1), then they are
forced to currently consume less than they would like. Instead, they consume the maximum they can afford,
C_{1}<C*; therefore, in later periods they have C_{2}>C*. If borrowing restrictions are relaxed,
consumers can set C=C* in every period and improve smoothing.
False – The growth rate
of investment is more volatile than that of consumption – unlike consumers,
firms have no desire to smooth their spending over time. Instead, firms need to adjust the capital
stock in advance in order to accommodate expected future growth.
False – In equilibrium,
the optimal capital (K*) is chosen such that MPK=MCK, i.e. the marginal product
of capital must equal marginal cost of capital. Since MCK= r + d
(where d is the depreciation rate)
and ¶MPK/¶K<0 (by the diminishing return to factor assumption),
if r®¯K*. Intuitively,
the interest rate is the cost of capital – if the cost of something increases,
you consume less of it.
False – The size of the capital stock is
about 100% of GDP. Note that DK* =
I_{N} = 10% GDP_{US}.
True – If DM < DP ® M/P¯ ® LM curve shifts to the left ®
i & Y¯.
False – If U<U_{NAIRU},
then Y is above the natural rate. This
means there will be an increase in the price level. In the conventional ASAD framework, this is equivalent to a
shift left in the AS curve – if Y >Y_{NAIRU}, then prices are higher
than expected prices. This leads to
increases in expected prices, which shifts the AS curve in, moving along the AD
curve, until the economy lands back at the natural rate of Y. When prices rise, this means the LM curve
must be shifting in. You can also see
this outcome by looking at the modified Philips Curve given in Prof. Brinner’s
slides. When Y > Y_{NAIRU},
there is an increase in the inflation rate which shifts the LM curve back until
the economy hits the natural rate of output again.
(b) 100/(1+20%) = 83.33
(c) Consumers look ahead to the future in making current spending decision
in both of these models – in both cases, consumers try to smooth their
consumption from year to year. In order
to do this, they must look ahead and estimate their total wealth/ lifetime
income.
(c) Firms choose their
optimal level of capital by maximizing profits with respect to capital. Profits are equal to revenues minus costs –
here, that means Profits = P*Y – R*K, or P(AK^{B} ) – R*K. Taking the derivative of this expression
with respect to capital, setting your answer equal to zero, and solving for K*
gives you (c). (Note that you have to
rearrange your answer a bit to get this.)
Intuitively, the optimal level of capital (K*) is chosen such that MPK =
MCK, i.e. the marginal product of capital must equal the marginal cost of
capital. This is the condition profit
maximization gives you.
(i) The natural rate of unemployment will decrease.
(ii) Real wages in equilibrium will increase.
(iii)The natural rate of unemployment will increase
a. Just (i).
b. Just (iii).
c. (i) and (ii).
d. (ii) and (iii).
e. None of the above.
(a) The most
straightforward way to answer this question is to use the labor market model
that lies behind the AS curve. Changes
in firm bargaining power affect the “z” term in the wage setting equation. This shifts the WS curve inward, and lowers
the natural rate of unemployment. Since
there is no change in the price setting equation, the real wage will not
change. Equivalently, at every level of
unemployment, wage growth will be lower (workers are not able to bargain for
large raises). But we know that real
wage growth does not depend on bargaining power in the long run (rearrange the
price setting equation to see W/P = K/A).
So long run unemployment must be lower because the rate of change of
wages is negatively correlated with unemployment.
(d) All of the above are true. If
labor supply is procyclical, then L (the labor force) increases when Y increases
– since U tends to fall when Y increases (Okun’s Law gives you an estimated,
negative relationship between U and Y), the growth in L dampens this
effect. If productivity is
procyclical, increases in output are matched by increases in productivity, so
there is less need to increase workers (and thus less change in U.) Finally, labor hoarding means that firms
keep their work force constant across business cycles. Obviously, if companies don’t adjust
employment when output changes, unemployment will be less sensitive to DY.
(a) This question was a
bit tricky. Although the country
described above has fixed exchange rates, their fixed E regime cannot be
credible if they have permanent high inflation. This means E^{e} does not always equal E, i.e. the
country has to devalue occasionally in order to maintain purchasing power
parity (PPP). Therefore, (E^{e}
– E)/E > 0, and using the Interest Rate Parity condition, i = i* + (E^{e}
– E)/E, you can see that i > i*.
(a) See the chart below –
note that Investment is a function of both output and interest rates, so its
change is ambiguous.


Y 
C 



G 
IS 



M 



r 
?I 


¯NX 



¯E 
¯e 
¯X 

By assumption 

=P 



(c) Use the Interest Rate
Parity condition to answer this question.
Since i = i* + (E^{e} – E)/E, (E^{e} – E)/E = i  i* =
5%  7% = 2%. Remember that if E falls
by 2%, this is an appreciation.
SECTION III: LONG
QUESTIONS
PART 1: FUNDAMENTALS OF THE IS CURVE (12 points total)
Define in onetotwo brief sentences each the primary reason or reasons each of the major private final demand components is directly sensitive to interest rates, and the direction of the impact (i.e. the sign of the derivative).
Source of change (3 points):
When the real interest rate is high, then it means that today’s consumption costs consumers more in terms of future consumption.
Direction (1 point): Negatively correlated.
Source of change (3 points):
Residential investment is sensitive to interest rates for the same reason as real consumption.
Direction (1 point): Negatively correlated.
Source of change (3 points):
Real imports
(the quantity of goods imported) are sensitive to the exchange rate – changes
in E change the price of imports for the domestic population. When E rises (a depreciation of the domestic
currency), real imports fall. By the
interest rate parity equation, we know that when E rises, domestic interest
rates fall, so interest rates and real imports move in the same direction.
Direction (1 point): Positively correlated.
PART 2: TAX CUTS IN
THE OPEN ECONOMY (14 points total)
Explain how a fiscal stimulus through a personal tax cut would influence the real and nominal trade balance. Throughout his question, assume no effect on domestic output prices.
A. (2 points) What is the likely short to mediumterm impact on the exchange rate: appreciation or depreciation, and why?
Use the ISLM framework to answer this question – cutting taxes shifts
the IS curve out. This increases output
and interest rates, and leads to an appreciation of the currency because
foreign investors buy domestic currency to purchase domestic bonds.
T¯ ® Y^{d} ® C ® IS
curve shifts to the right ® i ® E¯ (per the Interest Rate Parity condition) ® e¯
(since P & P* are constant).
B. (8 points, 2 each) Briefly describe with one short sentence or phrase each the ultimate longrun impacts (i.e. source of change and direction of change after any possible temporary early J course outcome). Sample answer structure to aid you: “(Real/Nominal) ( exports/imports) would (rise/fall) in response to a (stronger/weaker) domestic currency. An additional (positive/negative) impact would flow from (positive/negative) changes in _________ spending."
i. Real exports
Real exports would fall in response to a stronger domestic currency. An additional positive impact would flow from positive changes in foreign spending (our increased imports boost foreign GDP).
ii.
Real imports
Real imports would rise in response to a stronger domestic currency. An additional positive impact would flow from positive changes in domestic spending.
iii.
Nominal exports
Since exports
are in terms of domestic currency, when its real quantity increases then its
nominal value increases as well.
iv.
Nominal imports
Since the elasticity is greater then one, the percentage change in M is bigger than the percentage change in e. This means that eM, and thus nominal imports, increases, since the rise in M more than offsets the fall in e.
C. (4 points, 1 each) The JCurve effect differentiates between shortrun and longrun effects. Assume the longrun demand elasticities are all greater than one in absolute value. How does this Jcurve phenomenon eventually (after the passage of several years) augment or reduce shortrun impacts? Circle your choice below.
i.
Real exports: augment reduce unchanged
ii. Real imports: augment reduce unchanged
iii. Nominal exports: augment reduce unchanged
iv. Nominal imports: augment reduce unchanged
PART 3: INTEGRATING ISLM WITH A MODERN MODEL OF INFLATION (12 points total)
A. (2 points) With a fixed price level, describe with IS LM curves the impact of a reduction in the money supply on equilibrium output and interest rates.
B. (4 points, 1 each) How would the new output level influence the price level? (Circle your answer.)
i. Impact on labor demand: augment reduce unchanged
When output is low, the firms’ demand for labor force decreases.
ii. Impact on labor supply: augment
reduce unchanged
Because labor supply is procyclical.
iii.Net initial impact on unemployment:
augment
reduce unchanged
Per Okun’s law.
iv.Impact on inflation, hence the price level:
augment reduce unchanged
See graph above.
C. (2 points) Explain the impact of this directional price level shift on the LM curve (assume no impact on the IS curve).
Since DM=0 (since M is fixed at
the new level) and DP<0
Þ M/P¯ ® LM
shifts to the right.
D. (4 points) In what direction does this price shift move income and interest rates relative to the answer given in 3A?
Income and interest rates move in the opposite direction, income rises and interest rates fall.
PART 4: ACCELERATOR MODEL OF INVESTMENT (8 points total, 2 each)
Present the algebraic expressions defining the simple accelerator model of investment. No sentences are to be provided, just the math and the concepts referred to by each symbol you use.
A. Define the relationship between output and the capital stock.
K_{t}=aY_{t } (In the US, ‘a’ is about one.)
B. Define the relationship between net and gross investment.
I_{t}
= I_{Nt }+ D_{t} = I_{Nt }+ d_{1}K_{t}
= I_{Nt }+ dY_{t}
C. Define the relationship between net investment and output.
I_{Nt}
= a(K_{t+1} – K_{t}) = a(Y_{t+1} – Y_{t })
D. Combine your prior answers to define the relationship between gross investment and output.
I_{t}
= a(Y_{t+1} – Y_{t })+ dY_{t}