GM Lesson 013 Inflation and Wage Changes

Learning Intentions

By the end of this lesson, students will be able to:

• Use percentage increase to model inflation of costs.
• Use percentage increase to model wage growth.
• Compare changes in costs and wages over time.

Prerequisites

Students should already be able to:

• Calculate a percentage of a quantity.
• Increase a value by a given percentage.
• Calculate a new value after a percentage increase.
• Interpret financial quantities using dollars and cents.
• Compare two financial quantities in context.

Key Idea Summary

Inflation means that the cost of goods and services increases over time. If an item increases by , then its new cost can be calculated using:

Wage growth means that a person’s income increases over time. If a wage increases by , then the new wage can be calculated using:

A person is better off financially when their wage growth is greater than the increase in their costs. A person may be worse off if their costs increase faster than their wages.

For example:

• If prices increase by , then the multiplier is:

• If wages increase by , then the multiplier is:

Since , costs are increasing faster than wages.

Direct Instruction and Worked Examples

Time Allocation

Time Allocation

Time Allocation

• Introduction, warmup and vocabulary: 5 minutes
• Direct instruction: 15 minutes
• Understanding checks: 5 minutes
• Exercises: 20 minutes
• Homework: 20 to 30 minutes outside the lesson it was taught in.

Link to original

Worked Example 1: Modelling Inflation of Costs

A weekly grocery bill was $ . Due to inflation, grocery prices increase by .

Find the new weekly grocery bill.

The percentage increase multiplier is:

So:

Therefore, the new weekly grocery bill is $ .

Worked Example 2: Modelling Wage Growth

A casual worker earns $ per hour. Their hourly wage increases by .

Find their new hourly wage.

The percentage increase multiplier is:

So:

Therefore, the new hourly wage is $ per hour.

Worked Example 3: Comparing Inflation and Wage Growth

A student has a weekly income of $ . Their weekly expenses are $ .

Over one year:

• Their income increases by .
• Their expenses increase by .

Determine whether the student is better or worse off after these changes.

First calculate the new weekly income:

The new weekly income is $ .

Now calculate the new weekly expenses:

The new weekly expenses are $ .

Original surplus:

Original weekly surplus was $ .

New surplus:

New weekly surplus is $ .

Compare the surplus amounts:

Therefore, the student is worse off because their weekly surplus decreased from $ to $ .

Worked Example 4: Two-Year Inflation

A yearly transport cost is $ . It increases by each year for two years.

Find the cost after two years.

After the first year:

After the second year:

Therefore, the transport cost after two years is $ .

This can also be written as:

Understanding Checks

Check 1

A phone plan costs $ per month and increases by .

What multiplier should be used?

Answer:

The multiplier is .

Check 2

A worker earns $ per week. Their wage increases by .

Write the calculation needed to find the new wage.

Answer:

Check 3

A rent payment increases from $ to $ per week.

Find the percentage increase.

The increase is:

The percentage increase is:

So the rent increased by .

Check 4

A worker’s wage increases by , but their living costs increase by .

Are they likely to be better or worse off? Explain.

Answer:

They are likely to be worse off because their costs are increasing faster than their wages.

Exercises

Simple Familiar Exercises

Exercise 1

A loaf of bread costs $ . Its price increases by .

Find the new price.

Exercise 2

A weekly bus fare costs $ . It increases by .

Find the new weekly bus fare.

Exercise 3

An employee earns $ per hour. Their hourly rate increases by .

Find their new hourly rate.

Exercise 4

A monthly electricity bill is $ . It increases by .

Find the new monthly electricity bill.

Exercise 5

A worker earns $ per week. Their weekly wage increases by .

Find their new weekly wage.

Complex Familiar Exercises

Exercise 6

A household spends $ per week on living costs. Inflation causes these costs to increase by .

a) Calculate the new weekly living cost.

b) Calculate the increase in dollars.

Exercise 7

A worker earns $ per year. Their wage increases by .

a) Calculate their new annual wage.

b) Calculate the increase in their annual wage.

Exercise 8

A student earns $ per week from part-time work. Their wage increases by .

Their weekly expenses increase from $ by .

a) Find the new weekly income.

b) Find the new weekly expenses.

c) Find the original weekly surplus.

d) Find the new weekly surplus.

e) State whether the student is better or worse off.

Exercise 9

A family’s weekly grocery cost is $ . It increases by each year for two years.

a) Find the grocery cost after one year.

b) Find the grocery cost after two years.

Exercise 10

A worker’s annual salary is $ . It increases by each year for two years.

a) Find the salary after one year.

b) Find the salary after two years.

c) Find the total increase over the two years.

Homework Problems

Problem 1

A weekly rent payment of $ increases by .

Find the new weekly rent.

Problem 2

A worker earns $ per hour. Their hourly wage increases by .

Find their new hourly wage.

Problem 3

A yearly insurance cost is $ . It increases by each year for two years.

Find the cost after two years.

Problem 4

A person earns $ per week and spends $ per week.

Over one year:

• Their income increases by .
• Their expenses increase by .

a) Find the original weekly surplus.

b) Find the new weekly income.

c) Find the new weekly expenses.

d) Find the new weekly surplus.

e) State whether they are better or worse off.

Problem 5

A student’s monthly phone bill increases from $ to $ .

a) Find the increase in dollars.

b) Find the percentage increase.

Problem 6

A household’s weekly grocery bill was $ . After one year, it became $ .

a) Find the increase in dollars.

b) Find the percentage increase.

c) Explain what this percentage increase means in the context of inflation.

Next: GM Lesson 014 Mark-ups and Discounts