Question

In: Economics

Using the following data, the Consumer Price Index for 2011 and 2015 using the base 1982...

  1. Using the following data, the Consumer Price Index for 2011 and 2015 using the base 1982 = 100 ($1,210,000) are __________ and ________________.
  2. In reality, the CPI is based on a larger basket of good. Assuming the following prices, the average annual inflation rate for the 33 years (1982-2015) is_______________
  3. The core inflation rate is similar except that it excludes ___________ and ____________ prices because ___________________. The core rate is __________________
  4. If the average rate of inflation is the expected to be the rate in the future and the nominal interest rate is 8% per year, the real rate of interest is______.

Column1

Column2

Column3

Column4

price

Price

Quantity in a typical basket

Price

1982

in 2011

in 1982

in 2015

Item

Button-down shirts

35

$55

12

$85

Loafers

45

65

10

85

Sneakers

35

70

30

75

Textbooks

60

100

25

120

Jeans

30

42

10

50

Restaurant meals

18

25

33

32

cars

12000

17000

30

25000

tractors

14000

35000

50

32000

computers

2300

1800

100

1500

gas

0.9

2.5

1500

4

food

400

800

1000

1400

Solutions

Expert Solution

Answer a

Total Consumption in 2011 = Sum of Price * Quantity of basket = 55*12+65*10+70*30+100*25+42*10+25*33+17000*30+35000*50+1800*100+2.5*1500+800*1000 = 660+650+2100+2500+420+825+510000+1750000+180000+3750+800000 = $3250905

Hence CPI 2011 = New Consumption/ Old Consumption *Base = 3250905/1210000 *100 = 2.687*100 = 268.7

Total Consumption in 2015 = Sum of Price * Quantity of basket =

85*12+85*10+75*30+120*25+50*10+32*33+25000*30+32000*50+1500*100+4*1500+1400*1000 1020+850+2250+3000+500+1056+750000+1600000+150000+6000+1400000 = $3914676

Hence CPI 2015 = New Consumption/ Old Consumption *Base = 3914676/1210000 *100 = 3.235*100 = 323.5

Hence CPI for 2011 is 268.7 and for 2015 is 323.5

Answer b

Inflation 1982-2015 = (323.5-100)/100 = 223.5/100=2.235 or, 223.5%

No. of years =2015-1982 = 33 years

Hence Annual Average = 223.5%/33 = 6.77%

Answer c

Core Inflation Rate excludes Food and Energy sector items because the prices are volatile for these items.

So, following items will be removed:

Restaurant meals, Gas and Food

Consumption in these items in 1982= 18*33+0.9*1500+400*1000 = 594+1350+400000 = 401944

Hence consumption 1982= 1210000-401944 = 808056

Consumption in these items in 2011= 25*33+2.5*1500+800*1000 = 825+3750+800000 = 804575

Hence consumption 2011= 3250905-804575 = 2446330

Hence CPI Index 2011= 2446330/808056 *100= 302.74

Consumption in these items in 2015= 32*33+4*1500+1400*1000 = 1056+6000+1400000 = 1407056

Hence consumption 2015= 3914676-1407056 = 2507620

Hence CPI Index 2015= 2507620/808056 *100= 310.3

Hence Core Inflation = (310.3-100)/100= 210.3%

Hence Annual Average Core Inflation = 210.3%/33 = 6.37%

Answer d

Real Rate = nominal rate- Inflation = 8-6.77= 1.33%

Hence Real Interest rate = 1.33%


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