Commission
Fractions & DecimalsA commission is a fee or payment calculated as a percentage of a sale or transaction, earned by a salesperson or agent.
Formula
\text{commission} = \text{sales amount} \times \text{commission rate}
Definition
A commission is money earned as a percent of the total sales you make. Salespeople often earn a commission instead of (or in addition to) a flat salary. The more you sell, the more you earn.
Example
A car salesperson earns a $5\%$ commission. If they sell a car for $\$20{,}000$, their commission $= \$20{,}000 \times 0.05 = \$1{,}000$.
Key Insight
Commission ties pay directly to performance - the bigger the sale, the bigger the paycheck. It is a real-world application of percent that motivates understanding exactly how percentage calculations work.
Definition
Commission $C = Sr$, where $S$ is the sales amount and $r$ is the commission rate (decimal). Total earnings may combine a base salary plus commission: Earnings $= \text{base} + Sr$. To find sales needed for a target earning: $S = (\text{target} - \text{base})/r$. Tiered commissions apply different rates at different sales levels.
Example
A realtor earns $3\%$ on first $\$200{,}000$ of sale price and $2.5\%$ on the amount above $\$200{,}000$. House sells for $\$350{,}000$. Commission $= 0.03 \times 200{,}000 + 0.025 \times 150{,}000 = 6{,}000 + 3{,}750 = \$9{,}750$.
Key Insight
Tiered commission structures create different incentives at different sales levels - similar to progressive tax brackets. Understanding the "breakpoints" helps salespeople plan their effort and helps employers design incentive structures.
Definition
Commission is a linear function of sales: $C(S) = rS$, or piecewise-linear for tiered rates: $C(S) = \sum r_i \max(0, \min(S, b_{i+1}) - b_i)$ over brackets $[b_i, b_{i+1}]$. In principal-agent theory, commission structures are designed to align the agent's incentives with the principal's goals (the "moral hazard" problem). Optimal commission rates balance risk-sharing and incentive provision.
Example
If a salesperson is risk-neutral and effort cost is $C(e) = e^2/2$, and sales $S = e + \text{noise}$, the optimal commission rate in a simple model is $r^* = 1$ (the agent bears all risk). With risk aversion, optimal $r^* < 1$ balances incentive and risk: $r^* = 1/(1 + k\sigma^2)$ where $k$ is risk aversion and $\sigma^2$ is sales variance.
Key Insight
Commission contract design is a classic problem in information economics: the principal cannot observe effort, only output. The optimal contract must be "incentive-compatible" - making honest effort the salesperson's best strategy. This is related to mechanism design and the revelation principle in game theory.