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Lecture

# Introduction to Macroeconomics: Math App - Lecture 003

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University of Toronto Scarborough

Economics for Management Studies

MGEA06H3

Iris Au

Winter

Description

14 January 2013
CHAPTER 19: INFLATION AND UNEMPLOYMENT SUPPLEMENTARY B
Inflation refers to the percentage change in (general) price level (%Δ in price) each year. To get the %Δ
in price level, we:
Collect information on the prices and quantities of goods and services bought (our consumption
basket), what kind of information, goods and services, we include
Compute the cost of bundle (P●Q), we will then know how much it will cost to buy the same
bundle in a different price period
Calculate the %Δ in the cost of bundle (IE: the %Δ in price) will give us the inflation rate, how
fast the price level changes in a given time period
Example #1
Suppose an average household consumes two goods only, using the Period-1 Bundle to calculate the %
Δ in Price.
Period 1 Period 2
(Base Year) (Current Year)
Price Quantity Price Quantity
Food $1 400 $1 800
Clothing $6 100 $12 60
There are 2 ways to approach this question:
Look at how much it will cost to buy the base year bundle in year 1 and year 2 then look at the %
of the base year bundle
Calculate how much it costs to buy the current year bundle in year 1 and year 2 and then look at
the % in price
In a “perfect” world they both result in the same answer, but unfortunately we don’t live in a perfect
world so the choice of the bundle matters in terms of how much price goes up.
Using the Period 1 Bundle
Cost of period-1 bundle in period 1 (P1●Q 1
P Q = $1 x 400 + $6 x 100 = $1000
1 1
Cost of period-1 bundle in period 2 (P2●Q 1 [Quantity is fixed, the prices have changed]
P2Q 1 $1 x 400 + $12 x 100 = $1600
How much have prices risen?
The $ change in price = ($1600 - $1000) / $1000 x 100% = 60%. This means that the price has gone up
60% and it costs more to buy the period 1 bundle in year 2 than in year 1.
Using the Period-2 Bundle
Cost of period-2 bundle in period 1 (P1●Q 2
P1Q 2 $1 x 800 + $6 x 60 = $1160
Cost of period-2 bundle in period 2 (P2●Q 2
P2Q 2 $1 x 800 + $12 x 60 = $1520 How much have prices rise?
% in price = ($1520 - $1160) / $1160 x 100% = 31.03%. This means that the price has gone up 31.03%
and it costs more to buy the period 2 bundle in year 2 than in year 1.
The period 1 bundle gives a bigger increase in price (60% compared to 31%). This is because the way we
enter our calculations matter:
Consumers respond to price changes (the substitution effect). By holding everything constant, if
the price goes up, quantity goes down. From period 1 to period 2 the price of clothing goes up,
so the quantity relatively goes down
The Period 1 bundle (or the initial bundle) tends to give more weight to items that go up in price
a lot. In period 2, we use 60 units of clothing and 800 units of food, we have a higher weight on
the goods that price increased by a smaller amount and a lower weight on the good that price
increased a lot. In the period 1 bundle, however, there is a lower quantity in food and a higher
quantity in clothing compared to period 2
Which measures the rise in prices correctly, using period 1 or period 2 bundle?
Neither is correct. The actual amount of money spent:
In period 1: P Q = $1 x 400 + $6 x 100 = $1000
1 1
In period 2: P2Q 2 $1 x 800 + $12 x 60 = $1520
The percentage change is a 52% increase in amount spent.
Using the period 1 bundle, it went up by 60% and using period 2 bundle, it went up by 31%. None of
these measurements actually captured how the standing went up. Unfortunately we cannot use simple
equation because the bundles in the calculations are different (IE: the quantities of the bundles are
different), similar to saying, 2 apples cost more than 3 oranges, so it is an approximate measure on how
prices have gone up.
Later, we will see that using the Period 1 bundle is the construction of CPI and using Period 2 bundle is
calculating the GDP Deflator.
TWO PRICE INDICES
We will consider two price indices:
GDP Deflator measures how fast the prices of goods and services produced within Canada
change over time. It uses the current year bundle (Nominal GDP /Real GDP ) x 100
t t
Consumer Price Index (CPI) measures how fast the prices of goods and services bought by a
typical Canadian household change over time (what we consume, does not matter what
government or firms do). It does not matter where the good is produced, it uses the base year
bundle
CPI – THE MOST COMMONLY USED PRICE INDEX
It is the most commonly used price index to compute inflation rate. Statistics Canada is responsible for
the computation of the CPI. To construct the CPI, it will:
Choose a base year and determine a bundle purchased by a typical household in that year
Get the cost of the bundle in different time periods (IE: P t Q Base-year
Multiply the cost of that bundle in different time periods by 100/P Baes-year Q Base-yearcost of
bundle in the base year)

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