Markup
Fractions & DecimalsMarkup is the amount added to the cost price of a product to determine its selling price, usually expressed as a percentage of the cost.
Formula
\text{markup amount} = \text{cost} \times \text{markup rate}; \quad \text{selling price} = \text{cost} \times (1 + \text{markup rate})
Definition
Markup is the extra amount a store adds to what they paid for an item (the cost) to set the selling price. The markup covers expenses and profit. Markup is usually expressed as a percent of the cost.
Example
A store buys a shirt for $\$20$ (cost) and sells it for $\$30$ (selling price). Markup $= \$30 - \$20 = \$10$. Markup rate $= \$10/\$20 = 50\%$. The store marked it up by $50\%$.
Key Insight
Markup is calculated on the cost price (what the store paid), while discount is calculated on the selling price (what you pay). This is a key difference: a $50\%$ markup on $\$20$ is $\$10$; a $50\%$ discount on $\$30$ is $\$15$.
Definition
Markup $M = Cm$, where $C$ is cost and $m$ is the markup rate (decimal). Selling price $S = C(1 + m)$. Note: markup rate is based on cost, while margin (gross profit percentage) is based on selling price. Margin $= \text{markup}/\text{selling price} = m/(1 + m)$. A $50\%$ markup yields a margin of $50/150 = 33.3\%$.
Example
Cost $\$40$, markup $75\%$: $S = 40 \times 1.75 = \$70$. Margin $= 30/70 = 42.9\%$. Compare: if a store says "$50\%$ margin," that means markup $= \text{margin}/(1-\text{margin}) = 0.5/0.5 = 100\%$. So cost $\$40$ sells for $\$80$.
Key Insight
Markup and margin are often confused even by business professionals. A $50\%$ markup is NOT the same as a $50\%$ margin. Markup is always a larger percent than the corresponding margin. When comparing retail performance, always clarify which measure is being used.
Definition
Markup and margin are related by: $m = \text{margin}/(1 - \text{margin})$ and $\text{margin} = m/(1 + m)$, where $m$ is markup rate and margin is gross profit rate. In pricing theory, optimal markup follows the Lerner Index: $(P - MC)/P = -1/\epsilon$, where $\epsilon$ is price elasticity of demand and $MC$ is marginal cost. Higher elasticity implies lower optimal markup - a result from microeconomic theory.
Example
A monopoly faces demand elasticity $\epsilon = -2$. Optimal Lerner: $(P - MC)/P = 1/2$, so $P = 2MC$. If $MC = \$5$, optimal price $= \$10$, markup $= 100\%$, margin $= 50\%$. For $\epsilon = -4$: $P = (4/3)MC \approx 1.33MC$ (markup $\approx 33\%$, margin $= 25\%$).
Key Insight
The Lerner pricing rule connects markup to market power. In a perfectly competitive market, $\epsilon$ approaches negative infinity and the markup approaches zero ($P = MC$). Monopolies can sustain large markups. This mathematical relationship between markup and elasticity is the core of industrial organization economics.