Problem Set 1
Jorge F. Chavez
October 27, 2014
Nominal GDP, Real GDP and Price Indices
Let PtB and PtC denote the price of bread and cars in year t, respectively. Then, we can calculate the
following price indices:
Implicit price deflators:
The formulas we need to apply are:
2000
IP D2000
=
B QB
C
C
NGDP2000
P2000
2000 + P2000 Q2000
×
100
=
× 100 = 100
B QB
C
C
P2000
RGDP2000
2000
2000 + P2000 Q2000
2000
IP D2010
=
B QB
C
C
P2010
NGDP2010
2010 + P2010 Q2010
×
100
=
× 100 = 152
B QB
C
C
P2000
RGDP2000
2010
2010 + P2000 Q2010
2000
IP D2012
=
B QB
C
C
NGDP2012
P2012
2012 + P2012 Q2012
×
100
=
× 100 =???
B QB
C
C
P2000
RGDP2000
2012
2012 + P2000 Q2012
where N GDPt denotes the nominal GDP of year t and RGDPtτ denotes real GDP of year t in base
year τ . Note that we don’t have information for year 2012, but if we did we could calculate it as it is
shown above. Can you note which measures are used as weights in the numerator and denominator of
the expressions above?
Example 1 Show the formula required to calculate the inflation of 2010 according to the IPD.
(
IP D
π2010
)
2000
IP D2010
=
2000 − 1 × 100%
IP D2009
[( B
)( B
)
]
C
C
C
C
P2010 QB
P2000 QB
2010 + P2010 Q2010
2009 + P2000 Q2009
=
− 1 × 100%
B QB
C
C
B QB
C
C
P2000
P2009
2010 + P2000 Q2010
2009 + P2009 Q2009
)( B
)
]
[( B
C
C
C
C
P2000 QB
P2010 QB
2009 + P2000 Q2009
2010 + P2010 Q2010
− 1 × 100%
=
B QB
C
C
B QB
C
C
P2009
P2000
2009 + P2009 Q2009
2010 + P2000 Q2010
1
Consumer price indices:
Using the year 2000 as base year to construct the CPI implies using the basket of goods consumed in
that year as hour weights in all years.
2000
CP I2000
=
C
C
B QB
P2000
2000 + P2000 Q2000
× 100 = 100
B QB
C
C
P2000
2000 + P2000 Q2000
2000
CP I2010
=
B QB
C
C
P2010
2000 + P2010 Q2000
× 100 = 160
B QB
C
C
P2000
2000 + P2000 Q2000
2000
CP I2012
=
B QB
C
C
P2012
2000 + P2012 Q2000
× 100 =???
B QB
C
C
P2000
2000 + P2000 Q2000
Example 2 Show the formula required to calculate the inflation of 2010 according to the CPI. How
does it differ with the variation in prices according to the IPD?
(
π2010 =
)
2000
CP I2010
2000 − 1 × 100%
CP I2009
[(
=
[(
=
B QB
C
C
P2010
2000 + P2010 Q2000
B QB
C
C
P2000
2000 + P2000 Q2000
B QB
C
C
P2010
2000 + P2010 Q2000
B QB
C
C
P2009
2000 + P2009 Q2000
)(
)
B QB
C
C
P2000
2000 + P2000 Q2000
B QB
C
C
P2009
2000 + P2009 Q2000
)
]
− 1 × 100%
]
− 1 × 100%
Example 3 Show that the accumulated inflation between the base year (2000) and the year (2010) is
2000 − 100
CP I2010
2