ECON7021
Tutorial 1 Solutions
Introduction to the Macroeconomy
Question 1
The quantity of coffee demanded ( QD ) depends on the price of coffee ( PC ) and the price of tea
( PT ), while the quantity of coffee supplied ( QS ) depends on the price of coffee ( PC ) and
the price of electricity ( PE ), according to the following equations:
D
Q =17−2 PC +10 PT
QS =2+3 P C −5 PT
(a) If the price of tea is $1.00 and the price of electricity is $0.50, what are the equilibrium price
and quantity of coffee?
(b) What is/are the endogenous variable(s) in this model?
(c) What is/are the exogenous variable(s) in this model?
Answer:
(a) We calculate the equilibrium price and quantity of coffee, given the current prices of tea and
electricity.
QD =17−2 PC +10 1 QS =2+3 P C −5 0.50
Thus,
D S
Q =27−2 PC Q =−0.5+3 PC
At equilibrium, QD =QS , therefore
27−2 PC =0.5+3 P c 5 P C =27.5
The equilibrium price is $5.50, and the equilibrium quantity is 16.
(b) PC and Q
(c) PT and PE
Question 2
A farmer grows a bushel of wheat and sells it to a miller for $1.00. The miller turns the wheat into
flour and then sells the flour to a baker for $3.00. The baker uses the flour to make bread and sells
the bread to an engineer for $6.00. What is the value added by each person? What is GDP?
Answer:
1
,Value added by each person is the value of the good produced minus the amount the person paid for
the materials needed to make the good. Therefore, the value added by the farmer is $1.00 ($1 – 0 =
$1). The value added by the miller is $2: she sells the flour to the baker for $3 but has paid $1 for the
flour. The value added by the baker is $3: she sells the bread to the engineer for $6 but has paid the
miller $3 for the flour. GDP is the total value added, or $1 + $2 + $3 = $6. Note that GDP equals the
value of the final good (the bread).
Question 3
Consider the following economy:
Sector $ billion
Agriculture
Total sales 140
Capital goods purchases 40
Manufacturing inputs 30
Wages 70
Operating surplus (accounting profit) 40
Manufacturing
Sales of capital goods 100
Sales of other manufactures 260
Capital goods purchases 60
Agricultural inputs purchased 80
Wages 170
Operating surplus (accounting profit) 110
Use the data provided to calculate GDP using the income, production (value-added), and expenditure
methods.
Answer:
(a) Income approach:
Y =W + =W Ag +W Mfg+ Ag + Mfg ¿ 70+170+40+ 110=390
(b) Production approach:
Y =∑ V Ai
i
VA Ag =Total sales in agriculture (Ag)−expendable inputs in Ag ¿ 140−30=110
VA Mfg=Total sales in agriculture ( Mfg )−expendable inputs in Mfg ¿ ( 260+100 )−80=280
Y =VA Ag +VA Mfg =110+ 280=390
(c) Expenditure approach:
Y =C +I =C Ag +C Mfg +I Ag + I Mfg
Recall that C is purchases for final consumption only.
C Ag=Total sales of Ag−Mfg sector purchases of Ag products as expendable inputs
2
, ¿ 140−80=60 C Mfg =Total Mfg sales−Mfg inputs to Ag ¿ 260−30=230
I Ag=Purchases of capital goods in Ag ¿ 40 I Mfg=Purchases of capital goods in Mfg
¿ 60 Y =60+230+ 40+60=390
Question 4
Consider a closed economy producing and consuming only bread and automobiles (i.e., the CPI
market basket has two goods, and only these two goods are produced domestically). Below are data
for two different years.
2000 2010
Price of an automobile $50,000 $60,000
Price of a loaf of bread $10 $20
Number of automobiles produced 100 120
Number of loaves of bread produced 500,000 400,000
(a) Using 2000 as the base year, compute the following for each year: nominal GDP, real GDP,
the implicit price deflator for GDP, and the CPI. Compare the CPI with the GDP deflator and
explain the difference.
(b) Suppose a politician is writing a bill to index pensions. The bill would ensure that pension
payments are adjusted for changes in the cost of living. Explain whether he should use the
GDP deflator or the CPI.
Answer:
(a)
(i) Nominal GDP is the total value of goods and services measured at current prices.
Therefore,
Nominal GDP2000 Pcars
2000 2000
Qcars Pbread
2000 2000
Qbread
($50, 000 100) ($10 500, 000)
$5, 000, 000 $5, 000, 000
$10, 000, 000
Nominal GDP2010 Pcars
2010 2010
Qcars Pbread
2010 2010
Qbread
($60, 000 120) ($20 400, 000)
$7, 200, 000 $8, 000, 000
$15, 200, 000
Nominal GDP2000 Pcars
2000 2000
Qcars Pbread
2000 2000
Qbread
($50, 000 100) ($10 500, 000)
$5, 000, 000 $5, 000, 000
$10, 000, 000
Nominal GDP2010 Pcars
2010 2010
Qcars Pbread
2010 2010
Qbread
($60, 000 120) ($20 400, 000)
$7, 200, 000 $8, 000, 000
$15, 200, 000
(ii) Real GDP is the total value of goods and services measured at constant prices. Therefore,
to calculate real GDP in 2010 (with base year 2000), multiply the quantities purchased in
the year 2010 by the 2000 prices:
3
, Real GDP2010 Pcars
2000 2010
Qcars Pbread
2000 2010
Qbread
($50, 000 120) ($10 400, 000)
$6, 000, 000 $4, 000, 000
$10, 000, 000
Real GDP for 2000 is calculated by multiplying the quantities in 2000 by the prices in
2000. Since the base year is 2000, real GDP2000 equals nominal GDP2000, which is
$10,000,000. Hence, real GDP stayed the same between 2000 and 2010.
(iii) The implicit price deflator for GDP compares the current prices of all goods and services
produced to the prices of the same goods and services in a base year. It is calculated as
follows:
Nominal GDP2010
Implicit Price Deflator2010 100
Real GDP2010
Using the values for nominal GDP2010 and real GDP2010 calculated above:
$15, 200, 000
Implicit Price Deflator2010 100
$10, 000, 000
152
This calculation reveals that prices of goods produced in 2010 increased by 52 per cent,
compared to prices that the goods sold for in 2000. (Because 2000 is the base year, the
value for the implicit price deflator for the year 2000 is 100 because nominal and real
GDP are the same for the base year.)
(iv) The consumer price index (CPI) measures the level of prices in the economy. The CPI is
called a fixed-weight index because it uses a fixed basket of goods over time to weigh
prices. If the base year is 2000, the CPI in 2010 is an average of prices in 2010 but
weighted by the composition of goods produced in 2000. The CPI2010 is calculated as
follows:
2010 2000 2010 2000
( Pcars Qcars ) ( Pbread Qbread )
CPI 2010 2000 2000 2000 2000
100
( Pcars Qcars ) ( Pbread Qbread )
($60, 000 100) ($20 500, 000)
100
($50, 000 100) ($10 500, 000)
$16, 000, 000
100
$10, 000, 000
160
This calculation shows that the price of goods purchased in 2010 increased by 60 per cent
compared to the prices these goods would have sold for in 2000. The CPI for 2000, the
base year, equals 100.
4
Tutorial 1 Solutions
Introduction to the Macroeconomy
Question 1
The quantity of coffee demanded ( QD ) depends on the price of coffee ( PC ) and the price of tea
( PT ), while the quantity of coffee supplied ( QS ) depends on the price of coffee ( PC ) and
the price of electricity ( PE ), according to the following equations:
D
Q =17−2 PC +10 PT
QS =2+3 P C −5 PT
(a) If the price of tea is $1.00 and the price of electricity is $0.50, what are the equilibrium price
and quantity of coffee?
(b) What is/are the endogenous variable(s) in this model?
(c) What is/are the exogenous variable(s) in this model?
Answer:
(a) We calculate the equilibrium price and quantity of coffee, given the current prices of tea and
electricity.
QD =17−2 PC +10 1 QS =2+3 P C −5 0.50
Thus,
D S
Q =27−2 PC Q =−0.5+3 PC
At equilibrium, QD =QS , therefore
27−2 PC =0.5+3 P c 5 P C =27.5
The equilibrium price is $5.50, and the equilibrium quantity is 16.
(b) PC and Q
(c) PT and PE
Question 2
A farmer grows a bushel of wheat and sells it to a miller for $1.00. The miller turns the wheat into
flour and then sells the flour to a baker for $3.00. The baker uses the flour to make bread and sells
the bread to an engineer for $6.00. What is the value added by each person? What is GDP?
Answer:
1
,Value added by each person is the value of the good produced minus the amount the person paid for
the materials needed to make the good. Therefore, the value added by the farmer is $1.00 ($1 – 0 =
$1). The value added by the miller is $2: she sells the flour to the baker for $3 but has paid $1 for the
flour. The value added by the baker is $3: she sells the bread to the engineer for $6 but has paid the
miller $3 for the flour. GDP is the total value added, or $1 + $2 + $3 = $6. Note that GDP equals the
value of the final good (the bread).
Question 3
Consider the following economy:
Sector $ billion
Agriculture
Total sales 140
Capital goods purchases 40
Manufacturing inputs 30
Wages 70
Operating surplus (accounting profit) 40
Manufacturing
Sales of capital goods 100
Sales of other manufactures 260
Capital goods purchases 60
Agricultural inputs purchased 80
Wages 170
Operating surplus (accounting profit) 110
Use the data provided to calculate GDP using the income, production (value-added), and expenditure
methods.
Answer:
(a) Income approach:
Y =W + =W Ag +W Mfg+ Ag + Mfg ¿ 70+170+40+ 110=390
(b) Production approach:
Y =∑ V Ai
i
VA Ag =Total sales in agriculture (Ag)−expendable inputs in Ag ¿ 140−30=110
VA Mfg=Total sales in agriculture ( Mfg )−expendable inputs in Mfg ¿ ( 260+100 )−80=280
Y =VA Ag +VA Mfg =110+ 280=390
(c) Expenditure approach:
Y =C +I =C Ag +C Mfg +I Ag + I Mfg
Recall that C is purchases for final consumption only.
C Ag=Total sales of Ag−Mfg sector purchases of Ag products as expendable inputs
2
, ¿ 140−80=60 C Mfg =Total Mfg sales−Mfg inputs to Ag ¿ 260−30=230
I Ag=Purchases of capital goods in Ag ¿ 40 I Mfg=Purchases of capital goods in Mfg
¿ 60 Y =60+230+ 40+60=390
Question 4
Consider a closed economy producing and consuming only bread and automobiles (i.e., the CPI
market basket has two goods, and only these two goods are produced domestically). Below are data
for two different years.
2000 2010
Price of an automobile $50,000 $60,000
Price of a loaf of bread $10 $20
Number of automobiles produced 100 120
Number of loaves of bread produced 500,000 400,000
(a) Using 2000 as the base year, compute the following for each year: nominal GDP, real GDP,
the implicit price deflator for GDP, and the CPI. Compare the CPI with the GDP deflator and
explain the difference.
(b) Suppose a politician is writing a bill to index pensions. The bill would ensure that pension
payments are adjusted for changes in the cost of living. Explain whether he should use the
GDP deflator or the CPI.
Answer:
(a)
(i) Nominal GDP is the total value of goods and services measured at current prices.
Therefore,
Nominal GDP2000 Pcars
2000 2000
Qcars Pbread
2000 2000
Qbread
($50, 000 100) ($10 500, 000)
$5, 000, 000 $5, 000, 000
$10, 000, 000
Nominal GDP2010 Pcars
2010 2010
Qcars Pbread
2010 2010
Qbread
($60, 000 120) ($20 400, 000)
$7, 200, 000 $8, 000, 000
$15, 200, 000
Nominal GDP2000 Pcars
2000 2000
Qcars Pbread
2000 2000
Qbread
($50, 000 100) ($10 500, 000)
$5, 000, 000 $5, 000, 000
$10, 000, 000
Nominal GDP2010 Pcars
2010 2010
Qcars Pbread
2010 2010
Qbread
($60, 000 120) ($20 400, 000)
$7, 200, 000 $8, 000, 000
$15, 200, 000
(ii) Real GDP is the total value of goods and services measured at constant prices. Therefore,
to calculate real GDP in 2010 (with base year 2000), multiply the quantities purchased in
the year 2010 by the 2000 prices:
3
, Real GDP2010 Pcars
2000 2010
Qcars Pbread
2000 2010
Qbread
($50, 000 120) ($10 400, 000)
$6, 000, 000 $4, 000, 000
$10, 000, 000
Real GDP for 2000 is calculated by multiplying the quantities in 2000 by the prices in
2000. Since the base year is 2000, real GDP2000 equals nominal GDP2000, which is
$10,000,000. Hence, real GDP stayed the same between 2000 and 2010.
(iii) The implicit price deflator for GDP compares the current prices of all goods and services
produced to the prices of the same goods and services in a base year. It is calculated as
follows:
Nominal GDP2010
Implicit Price Deflator2010 100
Real GDP2010
Using the values for nominal GDP2010 and real GDP2010 calculated above:
$15, 200, 000
Implicit Price Deflator2010 100
$10, 000, 000
152
This calculation reveals that prices of goods produced in 2010 increased by 52 per cent,
compared to prices that the goods sold for in 2000. (Because 2000 is the base year, the
value for the implicit price deflator for the year 2000 is 100 because nominal and real
GDP are the same for the base year.)
(iv) The consumer price index (CPI) measures the level of prices in the economy. The CPI is
called a fixed-weight index because it uses a fixed basket of goods over time to weigh
prices. If the base year is 2000, the CPI in 2010 is an average of prices in 2010 but
weighted by the composition of goods produced in 2000. The CPI2010 is calculated as
follows:
2010 2000 2010 2000
( Pcars Qcars ) ( Pbread Qbread )
CPI 2010 2000 2000 2000 2000
100
( Pcars Qcars ) ( Pbread Qbread )
($60, 000 100) ($20 500, 000)
100
($50, 000 100) ($10 500, 000)
$16, 000, 000
100
$10, 000, 000
160
This calculation shows that the price of goods purchased in 2010 increased by 60 per cent
compared to the prices these goods would have sold for in 2000. The CPI for 2000, the
base year, equals 100.
4
