ECON7021 Tutorial 1 Solutions Introduction to the Macroeconomy

ECON7021

Tutorial 1 Solutions Introduction to the Macroeconomy Question 1 The quantity of coffee demanded (Q D

• depends on the price of coffee (P
• and the price of tea

(P T), while the quantity of coffee supplied (Q S

• depends on the price of coffee (P
• and

the price of electricity (P

E), according to the following equations:

Q D

=17−2P

C+10P T Q S =2+3P

C−5P

T (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.Q D

=17−2P

C+101Q

S =2+3P

C−50.50

Thus, Q D

=27−2P

CQ S

=−0.5+3P

C At equilibrium, Q D =Q S , therefore

27−2P

C =0.5+3Pc5P C =27.5 The equilibrium price is $5.50, and the equilibrium quantity is 16.(b)P C and Q (c)P T and P E 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 sales140 Capital goods purchases40 Manufacturing inputs30 Wages70 Operating surplus (accounting profit) 40 Manufacturing Sales of capital goods 100 Sales of other manufactures260 Capital goods purchases60 Agricultural inputs purchased80 Wages170 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=∑ i VA 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=60C

Mfg =Total Mfg sales−Mfg inputs to Ag ¿260−30=230 I Ag =Purchases of capital goods inAg¿40I Mfg =Purchases of capital goods inMfg

¿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.

20002010

Price of an automobile$50,000 $60,000 Price of a loaf of bread$10$20 Number of automobiles produced100120 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,





2000 2000 2000 2000

2000

2010 2010 2010 2010

2010 Nominal GDP

($50,000 100) ($10 500,000)

$5,000,000 $5,000,000

$10,000,000

Nominal GDP

($60,000 120) ($20 400,

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P Q P Q

P Q P Q

   

   

 



   

   000)

$7,200,000 $8,000,000

$15,200,000

 







2000 2000 2000 2000

2000

2010 2010 2010 2010

2010 Nominal GDP

($50,000 100) ($10 500,000)

$5,000,000 $5,000,000

$10,000,000

Nominal GDP

($60,000 120) ($20 400,

cars cars bread bread cars cars bread bread

P Q P Q

P Q P Q

   

   

 



   

   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



2000 2010 2000 2010

2010 Real GDP

($50,000 120) ($10 400,000)

$6,000,000 $4,000,000

$10,000,000

cars cars bread bread

P Q P Q   

   

 

 Real GDP for 2000 is calculated by multiplying the quantities in 2000 by the prices in

• 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:

2010 2010 2010 Nominal GDP Implicit Price Deflator 100 Real GDP

 

Using the values for nominal GDP2010 and real GDP2010 calculated above:

2010

$15,200,000

Implicit Price Deflator 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

2010 2000 2000 2000 2000

( ) ( )

100

( ) ( )

($60,000 100) ($20 500,000)

100

($50,000 100) ($10 500,000)

$16,000,000

100

$10,000,000

160 cars cars bread bread cars cars bread bread

P Q P Q

CPI

P Q P Q

  

 

  

  

 

  

 

 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