Question

Chapter 11, Problem 1
Suppose that the residents of Vegopia spend all of their income on Cauliflower, broccoli, and carrots. In 2008, they buy 100 heads of cauliflower for $200, 50 bunchesof broccoli for $75, and 500 carrots for $50. In 2009, they buy 75 heads of cauliflower for $225, 80 bunches of broccoli for $120, and 500 carrots for $100.
a. Calculate the price of each vegetable in each year.
b. Using 2008 as the base year, calculate the CPI for each year.
c. What was the inflation rate in 2009?

Answer 1

a) Cauliflower: $200/100 heads = $2/head and $225/75 heads = $3/head
Broccoli: $75/50 bunches = $1.50/bunch and $120/80 bunches = $1.50/bunch
Carrots: $50/500 carrots = $0.10/carrot and $100/500 carrots = $0.20/carrot
b) The CPI for the first year is the sum of what they paid for those goods, or
$200+$75+$50=$325
The CPI for the second year is how much the same number of goods would cost at the second year's prices, or
100 heads*$3 + 50 bunches*$1.50 + 500 carrots*$0.20 = $475
c) The inflation rate is (CPI2 - CPI1)/CPI1 = (475-325)/325 = .4615 = 46.15%

Answer 2

Since the base year is 2010, the CPI is 100. To calculate the CPI for 2011, you need to calculate the total basket of goods in both years.

2010: $200+$75+$50=$325
2011: $225+$120+$100=$445

CPI: [(Total Dollar Purchases Year 1)/(Total Dollar Purchases Year 0)]*100

($445/$325)*100=136.92

Therefore your CPI is 136.92 for 2011.

c) Inflation is the rate of change of the prices after some period. You need to calculate the prices per unit in one year, find their total and compare them to the second year. In this case:

2010: $2/Head of Cauliflower, $1.5/Bunch of Broccoli $.10/Carrot - Total of prices per unit = $3.60
2011: $3/Head of Cauliflower, $1.5/Bunch of Broccoli $.50/Carrot - Total of prices per unit = $5.00

Inflation calculation= [(Prices in Year 1 - Prices in Year 0)/Prices in Year 0]*100

[($5.00-$3.60)/$3.60]*100=38.8888%

Therefore the rate of inflation is 38.89% for 2011.

Answer 3

a)in 2008 1 head of cauliflower is 200/100 = $2 per head
for broccli 100/50= $2 per bunch
for carrots 50/500 =$ 0.1

in 2009 1 head of cauliflower is 240/75 = $3.2 per head
for broccli 180/80= $2.25 per bunch
for carrots 100/500 =$ 0.2

b) Since the base year is 2008, the CPI is 1.
CPI for 2009, you need to calculate the total basket of goods in both years.

2008: $200+$100+$50=$350
2009: $240+$180+$100=$520

CPI: [(Total Dollar Purchases Year (t+1)/(Total Dollar Purchases Year (t)]

($520/$350)=1.5

Therefore your CPI is 1.5 for 2009.

c) Inflation is the rate of change of the prices after some period. You need to calculate the prices per unit in one year, find their total and compare them to the second year. In this case:

2008: $2/Head of Cauliflower, $2/Bunch of Broccoli $.10/Carrot - Total of prices per unit = $4.10
2009: $3.2/Head of Cauliflower, $2.25/Bunch of Broccoli $.20/Carrot - Total of prices per unit = $5.60

Inflation calculation= [(Prices in Year (t+1) - Prices in Year t)/Prices in Year t]*100

[($5.60-$4.10)/$4.10]*100=36.58%

Therefore the rate of inflation is 36.6% for 2009.