10.02 Wages

A wage is an amount paid to an employee at a certain rate. It may be calculated at an hourly rate, or based on the quantity of work done (e.g. piecework), or calculated at a certain percentage of commission based on sales.

Often people who earn wages are paid a set rate per hour to work a certain number of hours per week. If they work more than this set number of hours, they are entitled to receive overtime, which means that their rate of pay increases. This is done as an incentive to get people to work outside "normal" hours, such as on weekends or public holidays, or for working longer hours in one day than normal.

Common overtime rates

Time-and-a-half: payment to a worker at $1.5$1.5 times their usual hourly rate.

Double time: payment to a worker at $2$2 times their usual hourly rate.

Double time-and-a-half: payment to a worker $2.5$2.5 times their usual hourly rate.

Triple time: payment to a worker $3$3 times their usual hourly rate.

In contrast, a salary is a fixed income that is based on a fixed number of working hours. People normally sign a contract with an agreed salary amount before they start working with a company. An employee may receive a weekly, bi-weekly or monthly salary. The employee will receive the same amount of income each time period, regardless of whether they work more or less hours, as it is thought this will be averaged out.

A salary is normally written as an annual amount. However, it can be helpful to calculate how much money will be receive each week, to help set a budget for spending. Similarly, it may be useful to work out how much money will be earned in a year based on the amount paid bi-weekly. So let's look at some examples of how to solve questions involving salaries and wages.

Practice questions

Question 1

Question 2

So far, we have looked at the two most common income types: wages and salaries, both of which are based on time, that is, work done per hour or per year. We have also looked at additional payments, often associated with wages and salaries.

Other payment methods are based on an employee's performance at work, rather than time spent on the job. Three types of payments associated with performance are commission, piecework, and royalties.

Commission

A commission is paid to an employee based on how much they sell. It is a typical payment method for salespeople selling items like furniture, cars or real estate. Commission is usually paid as a percentage of an employee's total sales. The percentage may be a fixed rate or based on a sliding scale, depending on the amount sold.

Commission payments can make up an employee's entire income, or they can be paid on top of a regular income, called a retainer.  Retainers are typically paid to less experienced salespeople, or in situations where the volume of sales is low, or inconsistent over each pay cycle.

Worked examples

Example 1

Stewart is a car salesman and receives a retainer of $\$450$$450 per week and a commission of $3%$3% of the price of every car he sells.

Calculate Stewart's income in a week he sells one car priced at $\$35000$$35000.

Solution:

Stewart's weekly income is the sum of his retainer and his commission. 

Example 2

Ellie works as a real-estate agent. Her commission is based on a sliding scale of $2.5%$2.5% on the first $\$500000$$500000 of her sales, $1.5%$1.5% on the next $\$1000000$$1000000, and $1%$1% thereafter.

Calculate Ellie's commission on a sale of:

1. $\$400000$$400000
2. $\$1250000$$1250000
3. $\$2150000$$2150000

Solution:

1. The sale is less than $\$500000$$500000, so we only need to find $2.5%$2.5% of the sale.

   Commission	$=$=	$2.5%$2.5% $\text{of }$of  $400000$400000
   	$=$=	$0.025\times400000$0.025×400000
   	$=$=	$\$10000$$10000

2. This sale amount is between $\$500000$$500000 and $\$1500000$$1500000, so we find $2.5%$2.5% of the first $\$500000$$500000 and $1.5%$1.5% of the remaining value.

   Commission	$=$=	$2.5%$2.5% $\text{of }$of $500000$500000 $+$+ $1.5%$1.5% $\text{of }$of  $\left(1250000-500000\right)$(1250000−500000)
   	$=$=	$\left(0.025\times500000\right)+\left(0.015\times750000\right)$(0.025×500000)+(0.015×750000)
   	$=$=	$12500+11250$12500+11250
   	$=$=	$\$23750$$23750

3. This sales is more than $\$1500000$$1500000, so we need to find $2.5%$2.5% of the first $\$500000$$500000, $1.5%$1.5% of the next $\$1000000$$1000000 and $1%$1% of the remaining value.

   Commission	$=$=	$2.5%$2.5% $\text{of }$of $500000$500000 $+$+ $1.5%$1.5% $\text{of }$of  $1000000$1000000$+$+$1%$1%$\text{of }$of $\left(2150000-1500000\right)$(2150000−1500000)
   	$=$=	$\left(0.025\times500000\right)+\left(0.015\times1000000\right)+\left(0.01\times650000\right)$(0.025×500000)+(0.015×1000000)+(0.01×650000)
   	$=$=	$12500+15000+6500$12500+15000+6500
   	$=$=	$\$34000$$34000

Practice questions

Question 3

Question 4

Question 5

Piecework

Piecework, as the name implies, is a fixed rate of pay, per item (or piece) produced. This payment method is used as an alternative to a wage or salary for workers who pick, pack, prune or make things.

Workers who earn their income through piecework might include clothing makers or fruit and vegetable pickers. 

Worked example

Example 3

Charlotte delivers leaflets in her neighbourhood. She is paid $\$0.13$$0.13 for every leaflet she delivers. How much does Charlotte earn if she delivers $640$640 leaflets?

Solution:

Multiply the piecework rate by the number of leaflets.

Practice question

Question 6

Royalties

A royalty is a payment made to the owner of a piece of intellectual property for the ongoing use of their work or product.

For example, a musician may receives royalties for sales of their music or whenever their music is used in a film or performance.

Royalties are paid either as a percentage of total sales or as a fixed price per item. 

Worked example

Example 4

Ainslie is an author. She receives $7.5%$7.5% of the sales of her books. If her book is developed into a film, she receives a further $2.5%$2.5% of the film's gross takings.

If $50000$50000 copies of her book are sold at a price of $\$24.95$$24.95 each, and her book is created into a film which generates $\$650000$$650000 at the movie box-office, calculate her total earnings from royalties.

Solution:

Add together the royalties she receives from book sales and movie takings.

Practice question

Question 7