When a manufacturer allows a 3% commission on the retail price of his product and earns a certain profit, if the commission is reduced by 2% (i.e., from 3% to 1%), his profit percentage will increase because the selling price after deducting commission increases. To illustrate with a similar example from the provided data:
- Suppose the retail price (RP) is 100.
- Original commission = 3% of RP = 3.
- Selling price (SP) after commission = 100 - 3 = 97.
- Let the profit percentage at 3% commission be p%p%p%.
- Cost price (CP) = SP / (1 + profit%) = 97 / (1 + p/100).
If commission is reduced by 2%, new commission = 1% of RP = 1.
- New selling price = 100 - 1 = 99.
- New profit = SP - CP = 99 - CP.
- New profit percentage = 99−CPCP×100\frac{99-CP}{CP}\times 100CP99−CP×100.
Since CP is constant, reducing commission increases SP and thus increases profit percentage. From a detailed example with larger commission rates (36% reduced to 24%), the profit percentage increased from 8.8% to approximately 29.2%
. By analogy, a reduction of commission by 2% from 3% would similarly increase profit percentage, though the exact value depends on the initial profit and cost price. Hence, the manufacturer's profit percentage will increase significantly when the commission is reduced by 2%, as the selling price after commission increases while cost price remains the same, improving profit margin.
