Using Percentage Change in Economics
Economists use percent change to understand how much a variable has increased or decreased.
For example:
Paula and Mandy both got raises:
- Paula earned $100,000 per year and now earns $102,000.
- Mandy earned $20,000 per year and now earns $21,000.
Who got a bigger raise?
Paula's raise was $2000; Mandy's raise was $1000. But as a percentage change Mandy had the larger raise.
The change in Mandy's wage is:
`\$21","000 - \$20","000 = \$1","000`
The change in Paula's wage is:
`\$102","000 - \$100","000 = \$2","000`
The percentage change in Mandy's wage is:
`"Change"/("Starting Value") xx 100 = ((\$21","000 - \$20","000)/(\$20","000)) xx 100 = (\$1","000)/(\$20","000) = 0.05 xx 100 = 5"%"`
The percentage change in Paula's wage is:
`"Change"/("Starting Value") xx 100 = ((\$102","000 - \$100","000)/(\$100,000)) xx 100 = (\$2","000)/(\$100","000) = 0.02 xx 100 = 2"%"`
So, while the change in wages was larger for Paula ($2,000 vs. $1,000), the percentage change (or relative change) in wages was larger for Mandy (5% vs. 2%) because Mandy's initial wage was so much lower than Paula's that even a larger absolute change in Paula's wages represented a smaller percentage change, compared to Mandy's.
How do I calculate percentage change?
The percentage change between two numbers (or values, as numbers are often referred to in economics) can be calculated in two steps:
Step 1: Subtract the starting value (number) from the ending value (number). This is the change.
`"Ending Value" - "Starting Value" = "Change"`
Step 2: Divide the change from step 1 by the starting value and multiply by 100. This is the percentage change.
`"Change"/"Starting Value" xx 100 = "Percentage Change"`
That's all there is to it! It doesn't matter whether you're comparing changes in wages, prices, sales, stock prices, or output, the process of calculating percentage change is the same.
Suppose the quantity of items sold by a business rises from 5,000 to 6,000 from one year to the next, what is the percentage change in sales?
Step 1: The change in sales is 6,000 - 5,000 = 1000.
Step 2: Using the formula, the percentage change in sales is 1,000/5,000 x 100 = 20%.
In mathematics and in economics symbols are often used to express terms. Using symbols is a way to generalize and shorten formulas. For example, the symbol "delta" is often used to express the concept of change and the letter X is often used to express a variable. When a variable such as X has different values it will often be denote with a subscripts, like X1 and X2.
Using symbols we can express the formula for change as:
`X_2 - X_1 = \DeltaX`
Using symbols we can express the formula for percentage change as:
`(X_2 - X_1)/X_1 xx 100 = "Percentage Change"`
Or, using "delta" to indicate change:
`(\DeltaX)/X_1 xx 100 = "%"\DeltaX`
Why should I calculate percentage change?
Often economists are interested in relative comparisons because it's much more meaningful than a comparison of absolutes.
- For example, Mandy had a greater relative pay increase compared to Paula.
- Similarly, economists use percentage change to measure economic growth of countries, changes in prices and changes in employment. This allows economists to compare changes that start from a different base level.
Where is percentage change used in macroeconomics?
- Inflation rate - Economists use changes in the consumer price index (CPI) to measure how quickly prices rise over time (note: if the economy is experiencing a period of negative inflation we call that deflation)
Here's a typical problem:
In 2007 US CPI was 205. In 2006 it was 200. What was the inflation/deflation rate in 2007?
The CPI percentage change formula is:
`("CPI"_t - "CPI"_(t-1))/("CPI"_t) xx 100`
The percentage change in the CPI between 2006 and 2007 is:
`(205 - 200)/200 xx 100 = 5/200 = 0.025 xx 100 = 2.5"% inflation in 2007"`
(since the sign is `+`)
- Rate of economic growth - Economists use changes in real gross domestic product (real GDP) to measure economic growth.
Here's a typical problem:
U.S. GDP in 1999 was $10,500 billion. In 1998 it was 10,000 billion (adjusted for inflation). What was the rate of growth from 1998 to 1999?
The GDP percentage change formula is:
`("GDP"_t - "GDP"_(t-1))/("GDP"_t) xx 100`
The percentage change in GDP between 1998 and 1999 is:
`(10","500 - 10","000)/(10,000) xx 100 = 500/(10","000) = 0.05 xx 100 = 5"% increase in GDP growth in 1999"`
➜ Note
Almost any macroeconomic measurement made can be tracked over time. We use the percentage change formula to calculate the rate at which these measures change through time.
Where is percentage change used in microeconomics?
In microeconomics percent change is used to measure change in price, quantity, revenue, profits, wages, income, and costs. All use the same percentage change formula:
`(X_2-X_1)/X_1 xx 100 = "Percentage Change"`
where `X` could be price, quantity, wage, cost, profit, etc.
You may also be asked to calculate an elasticity, which is measured by the percentage change in one thing divided by the percentage change in another thing. The most common elasticity is the elasticity of demand. It measures the percentage change in the quantity demanded in response to a percentage change in price. Here's a typical problem:
The quantity of packs of cigarettes demanded falls from 10,000 to 9,500 packs as a result of an increase in price from $4 to $5. What is the price elasticity of demand?
`"%"\DeltaQ = ((9","500) - (10","000))/(10","000) xx 100 = (-500)/(10","000) = -0.5 xx 100 = -5"%"`
`"%"\DeltaP = (\$5 - \$4)/(\$4) xx 100 = (\$1)/(\$4) = 0.25 xx 100 = 25"%"`
The price elasticity of demand is:
`("%"\DeltaQ)/("%"\DeltaP) = (-5"%")/(25"%") = -0.2`
➜ Note
Whether we are dealing a simple percent change or a more complicated formula like elasticity, the operation for calculating a percentage change does not change.
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