Quantity Discount: Formula & Example

Instructor: Orin Davis
Quantity discounts are used to sell items in bulk. The discount incites people to buy the number of products that corresponds to amount of product that costs the least to make.

Introduction

Ever heard of a baker's dozen? It is when you buy 12 items and get a 13th free! There are any number of reasons for giving a quantity discount to incentivize large purchases. Whenever an item is produced, there is a cost for making it. But the cost for making multiple items at once may be less than the cost of making a single item, and thus, it may be more economical to work with large quantities. Consider the examples below.

Illustration of Quantity Discount: Making Muffins

For example, making just one muffin takes a certain amount of work and resources. But, note that while it does take three times as many resources to make three muffins, it takes a minimal amount of additional effort. For instance, it does not take three times as much effort to mix the ingredients, and the oven remains the same size whether one puts in one muffin or two dozen muffins. Heating the oven to the right temperature for three muffins certainly takes more energy than heating the oven for one muffin, but it is not three times the energy. And since a muffin tin holds multiple muffins, it makes sense to make as many muffins as the tin will hold. Take a look at this with some hypothetical numbers:

Cost of ingredients per muffin: $0.50

Cost to heat the oven to the correct temperature for one muffin: $1.00

Cost to heat the oven to the correct temperature for each additional muffin: $0.05

Cost of energy for a mixer to combine ingredients for one muffin: $0.30

Cost of energy for a mixer to combine ingredients for each additional muffin: $0.01

Cost of muffin tin: $1.00

In short, to make one muffin costs: $0.50+$1.00+$0.30+$1.00 = $2.80 (cost per muffin, $2.80)

2 muffins: $2.80+$0.50+$0.05+$0.01 = $3.36 (cost per muffin: $3.36/2 = $1.68)

3 muffins: $3.36+$0.50+$0.05+$0.01 = $3.92 (cost per muffin: $3.92/3 ~= $1.31)

4 muffins (requires new muffin tin!): $3.92+$0.50+$0.05+$0.01+$1.00 = $5.48 (cost per muffin: $5.48/4 ~= $1.37)

Notice how the price per muffin goes down until one needs to add a new muffin tin (and likewise until one needs a new mixer). Thus, it makes the most economical sense to make three muffins at a time because that is where the muffins are cheapest to make. Consider the profits from the following selling strategies:

Strategy 1: $2.50 per muffin. Most people find this too high of a price for a muffin, so no one will buy it.

Strategy 2: $2.00 per muffin. This is profitable as long as people are not buying only one (in which case the rest go to waste and the amount charged for the muffin does not even cover the cost).

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