Eco exam
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Econ3_ps2_sol.pdf
Problem Set 2 Solutions
ECON 3 − Principles of Macroeconomics
University of California San Diego
Christopher Gibson
Monday, April 13th
1. If the following table describes consumption and prices for a small economy, with year 1
as the base year,
Apples Bananas
Quantity Price Quantity Price
1 qA1 p A 1 q
B 1 p
B 1
2 qA2 p A 2 q
B 2 p
B 2
3 qA3 p A 3 q
B 3 p
B 3
(a) Quantities qA2 , q A 3 , q
B 2 , and q
B 3 are irrelevant for the calculation of CPI in years 1-3.
(b) All quantities and prices are needed to calculate nominal GDP in years 1-3.
(c) Prices pA2 , p A 3 , p
B 2 , and p
B 3 are irrelevant for the calculation of real GDP in years 1-3.
(d) All quantities and prices are needed to calculate GDP deflator in years 1-3.
2. Consider a small economy in which the representative consumer eats only cheese and
drinks only wine.
Cheese (pounds) Wine (bottles)
Quantity Price Quantity Price
2000 1,200 $1.00 40 $10
2001 1,300 $1.20 60 $12
2002 700 $2.00 120 $4
1
(a)
CPI2000 =
( Qc2000 · Pc2000 + Qw2000 · Pw2000 Qc2000 · Pc2000 + Qw2000 · Pw2000
) · 100 =
( $1, 600
$1, 600
) · 100
= 100
CPI2001 =
( Qc2000 · Pc2001 + Qw2000 · Pw2001 Qc2000 · Pc2000 + Qw2000 · Pw2000
) · 100 =
( $1, 920
$1, 600
) · 100
= 120
CPI2002 =
( Qc2000 · Pc2002 + Qw2000 · Pw2002 Qc2000 · Pc2000 + Qw2000 · Pw2000
) · 100 =
( $2, 560
$1, 600
) · 100
= 160
(b) CPI in 2001 suffers from no substitution bias. Given that the prices both increased
by 20%, the consumer has no incentive to substitute toward one good over the other.
(c) CPI in 2002 suffers from substitution bias. Since wine becomes relatively less ex-
pensive, the consumer would substitute away from consuming cheese and toward
consuming wine. This is exactly what we see in the consumption pattern.
Given that CPI does not account for substitution away from the relatively more
expensive good, it exaggerates the burden of the price change on the consumer and
hence overestimates inflation.
(d) With utility u(qc,qw) = q 2 c · qw, in 2000 the consumer enjoys utility
u(1200, 40) = 12002 · 40 = 57, 600, 000
while in 2002 utility is
u(700, 120) = 7002 · 120 = 58, 800, 000
so it is clear that utility is higher in 2002. Moreover, expenditure on 2000 quantities
would be
Qc2000 · P c 2002 + Q
w 2000 · P
w 2002 = $2 · 1200 + $4 · 40
= $2, 560
while actual expenditure is
Qc2002 · P c 2002 + Q
w 2002 · P
w 2002 = $2 · 700 + $4 · 120
= $1, 880
so the consumer spends less than they would have on the base year basket.
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(e) GDP deflator is
GDPd2002 =
( Qc2002 · Pc2002 + Qw2002 · Pw2002 Qc2002 · Pc2000 + Qw2002 · Pw2000
) · 100 =
( $1, 880
$1, 900
) · 100
= 98.95
Since 2000 is the base year, GDP deflator is 100, so inflation according to GDP
deflator is
π =
( 98.95 − 100
100
) · 100% = −1.05%
while according to CPI
π =
( 160 − 100
100
) · 100% = 60%
GDP deflator indicates deflation, consistent with the price burden of the consumer
as shown above, while CPI indicates large inflation. This discrepancy shows that
GDP deflator seems to be a better representative for 2002 price level than CPI.
3. Beginning with a wage of $10 per hour and increasing 10% per year in real terms, we
know that in 2000 dollars, Esmerelda should make $11 per hour in 2001 and $12.10 in
2002. From (2), inflation in 2001 is
π =
( 120 − 100
100
) · 100% = 20%
while inflation from 2000 to 2002 is
π =
( 160 − 100
100
) · 100% = 60%
Inflating real wage to compensate for price changes gives a nominal wage of $11 · (1.2) = $13.20 in 2001 and f $12.10 · (1.6) = $19.36 in 2002.
Note that you could also have grown nominal wage in 2001 by 10% and applied inflation
from 2001 to 2002, which is
π =
( 160 − 120
120
) · 100% =
100
3 % ≈ 33.33%
Then wage in 2002 is
w2002 = $11 · (1.2) · (1.1) · (
1 + 1
3
) = $11 · (1.1)
( 6
5
) · (
4
3
) = $12.10 ·
( 8
5
) = $19.36.
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4. The exact real interest rate is given by
r = i − π 1 + π
(a) If the nominal interest rate is 6% and inflation is 1%.
i. The exact real interest rate (as a percent) is
r =
( 0.06 − 0.01
1 + 0.01
) · 100% ≈ 4.95%
ii. The real interest rate implied by the approximation rule (as a percent) is
r = (0.06 − 0.01) · 100% = 5%
(b) If the nominal interest rate is 10% and inflation is 5%.
i. The exact real interest rate (as a percent) is
r =
( 0.1 − 0.05 1 + 0.05
) · 100% ≈ 4.76%
ii. The real interest rate implied by the approximation rule (as a percent) is
r = (0.1 − 0.05) · 100% = 5%
(c) If the nominal interest rate is 15% and inflation is 10%.
i. The exact real interest rate (as a percent) is
r =
( 0.15 − 0.1
1 + 0.1
) · 100% ≈ 4.55%
ii. The real interest rate implied by the approximation rule (as a percent) is
r = (0.15 − 0.1) · 100% = 5%
(d) The approximations all indicate the real interest rate is 5%, while the exact real
interest rates are all lower than this. As inflation increases, the real interest rate
decreases, so the approximations become more inaccurate.
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