Econ 299 Tutor Questions
Chapter #1 Solutions
L. Priemaza
1a) Fill in the blanks of the following table. Show all computations used.
Year
Nom. GDP GDP
Population
Real GDP
Real GDP/
(millions)
(millions)
(millions)
capita
Deflator
1995
78.2
91.0
2.7
85.9
31.8
1996
45.9
93
2.8
49.4
18
1997
88.3
97
2.6
91.0
35
1998
81.5
95
3.0
85.8
28.6
1999
89.1
100
3.0
89.1
30
2000
97.3
107
3.1
90.9
29
GDP deflator
= (Nominal GDP/RealGDP) * 100
= 78.2/85.9 *100
=91.0
Real GDP/capita = Real GDP/Population
=85.9/2.7
=31.8
Nominal GDP
=Real GDP * GDP Deflator/100
=49.4*93/100
=45.9
Population
=Real GDP/Real GDP per capita
=2.6
Real GDP/capita = Real GDP/Population
=85.8/3.0
=28.6
Real GDP
=Nominal GDP/GDP Deflator/100
=89.1/100/100
=89.1
Or: Real GDP=Nominal GDP in base year (by definition)=89.1
Nominal GDP
=Real GDP*GDP Deflator/100
=90.9*107/100
=97.3
1b) Which year is the base year? 1999, since the GDP deflator = 100 in this
year
1c) Calculate the growth in nominal and real GDP between 1999 and 2000. Use
one formula with logs and one without.
Growth
= [Xt-Xt-1]/Xt * 100
=(97.3-89.1)/97.3 *100
=8.42% growth in nominal terms
Growth
=[ln(Xt)-ln(Xt-1)] * 100
=[ln(97.3)-ln(89.1)] *100
=8.80% growth in nominal terms
Growth
= [Xt-Xt-1]/Xt * 100
=(90.9-89.1)/89.1
=2.02% growth in real terms
Growth
=[ln(Xt)-ln(Xt-1)] * 100
=[ln(90.9)-ln(89.1)] * 100
=2.00% growth in real terms
1d) Calculate inflation between 1997 and 1998. Use one formula with logs and
one without.
Inflation
=[Xt-Xt-1]/Xt-1 * 100
=(95-97)/97 *100
= -2.06%
Inflation
=[ln(Xt)-ln(Xt-1)] * 100
=[ln(95)-ln(97)] * 100
= 2.08%
2) Phillipe has a choice between three investments. One safe investment pays 3% a
year. An escalating GIC pays 1.5% in the first year, 2% in the second, 2.5% in the
third, 3% in the fourth, and 5% in the last year. One risky investment pays 3% in the
first two years, 15% in the third year, 0% in the fourth year, and -15% in the fifth year.
a) Calculate the arithmetic and geometric means of these three investments.
Safe Arithmetic = (i1 + i2 + i3 + i4 + i5)/5
= (3+3+3+3+3)/5
=3%
Safe Geometric =[(1+i1)(1+i2)(1+i3)(1+i4)(1+i5)]1/5
=[(1.03)(1.03)(1.03)(1.03)(1.03)]1/5-1
=3%
GIC Arithmetic =(i1 + i2 + i3 + i4 + i5)/5
=(1.5+2+2.5+3+5)/5
=2.8%
GIC Geometric =[(1+i1)(1+i2)(1+i3)(1+i4)(1+i5)]1/5
=[(1.015)(1.02)(1.025)(1.03)(1.05)]1/5-1
=2.79%
Risky Arithmetic =(i1 + i2 + i3 + i4 + i5)/5
= (3+3+15+0-15)/5
=1.2%
Risky Geometric =[(1+i1)(1+i2)(1+i3)(1+i4)(1+i5)]1/5
=[(1.03)(1.03)(1.15)(1)(0.85)]1/5-1
=0.730%
b) Which is the best investment and why?
-The safe investment is the best
-It has the greatest geometric mean, and geometric means are used for rates
of return
c) Faced with 3% inflation, calculate real return for each of the three
investments.
Real Return
= Nominal Return – inflation
=3–3
=0% (safe return)
Real Return
= Nominal Return – inflation
= 2.8 – 3
= -0.2% (GIC)
Real Return
= Nominal Return – inflation
= 0.73 – 3
= -2.3% (safe return)
3) Indicate whether the following statements are true, false, or uncertain.
Explain.
a) I got a raise from $5.00 to $5.50. Given inflation of 2%, my wage increased
8%.
-True
Nominal Growth =(Xt-Xt-1)/Xt-1 * 100
=(5.50-5)/5 * 100
=10%
Real Growth
=Nominal Growth- Inflation
=10%-2%
=8%
b) In 5 years, I want to buy a 2010 mustang for $30,000. I should save $5,000 a
year at 3% interest to do so.
-False
S=P(1+r)t
-Savings in 5 years = 5,000(1.03)4+5,000(1.03)3+5,000(1.03)2+5,000(1.03)1+5,000
=5627.54 + 5463.64 + 5304.50 + 5151 + 5,000
=$26,546.68
-You won’t have saved enough
c) The amount of weight I’ve gained over Christmas is a stock variable. My
height is a flow variable.
-False
-Stock variables have a set value at a set period in time
-Height is a stock variable
-Flow variables express changes over time
-Weight gained is a flow variable
4) Calculate the effective interest of:
a) 30%, compounded semi-annually
iE = (1+1/m)m -1
= (1+0.30/2)2-1
= (1.15)2 -1
= 32.3 %
b) 28%, compounded monthly
iE = (1+1/m)m -1
= (1+0.28/12)12-1
= (1.023)12 -1
= 31.9 %
c) 26%, compounded weekly
iE = (1+1/m)m -1
= (1+0.26/52)52-1
= (1.005)52 -1
= 29.6 %
d) 20%, compounded daily
iE = (1+1/m)m -1
= (1+0.20/365)365-1
= (1.00056)365 -1
= 22.1 %
5) Dr. Magnanimous wants to start up a scholarship that pays out $20,000 a year.
If he wants his scholarship to pay out over the next 100 years, how much should
he invest now at 5% interest?
PV = a(1-xt)/(1-x)
X=1/1+i
= 1/1.05
=0.952
PV = 20,000(1-0.952100)/(1-0.952)
= 416,806