Question

SHOW YOUR WORK PLEASE

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

Answer 1

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%